%%% -*-BibTeX-*-
%%% ====================================================================
%%%  BibTeX-file{
%%%     author          = "Nelson H. F. Beebe",
%%%     version         = "1.53",
%%%     date            = "04 March 2013",
%%%     time            = "07:09:01 MST",
%%%     filename        = "benfords-law.bib",
%%%     address         = "University of Utah
%%%                        Department of Mathematics, 110 LCB
%%%                        155 S 1400 E RM 233
%%%                        Salt Lake City, UT 84112-0090
%%%                        USA",
%%%     telephone       = "+1 801 581 5254",
%%%     FAX             = "+1 801 581 4148",
%%%     url             = "http://www.math.utah.edu/~beebe",
%%%     checksum        = "58227 25782 108656 1088759",
%%%     email           = "beebe at math.utah.edu, beebe at acm.org,
%%%                        beebe at computer.org (Internet)",
%%%     codetable       = "ISO/ASCII",
%%%     keywords        = "bibliography; BibTeX; Benford's Law;
%%%                        Bradford's Law; First Digit Phenomenon;
%%%                        Gibrat's Law; Gibrat's Rule of Proportionate
%%%                        Growth; Heaps' Law; Herdan's Law; Law of
%%%                        Anomalous Numbers; Lotka's Law; Pareto
%%%                        Distribution; Pareto Law; Pareto Principle;
%%%                        power law; Significant Digit Law; Simon--Yule
%%%                        model of text generation; Stigler's Law; Yule
%%%                        process; Zipf's Law",
%%%     license         = "public domain",
%%%     supported       = "yes",
%%%     docstring       = "This is a bibliography about a numerical
%%%                        curiousity variously known as Benford's Law
%%%                        (see particularly entries Newcomb:1881:NFU,
%%%                        Benford:1938:LAN, Pinkham:1961:DFS,
%%%                        Logan:1978:FDP, Hill:1998:FDP, and
%%%                        Block:2010:GEB), the Law of Anomalous
%%%                        Numbers, and the Significant Digit Law: in a
%%%                        table of physical constants (and in many
%%%                        other collections of measured numbers), the
%%%                        leading digits do not have equal probability
%%%                        of occurrence: the digit 1 is more common
%%%                        than 2, which is more common than 3, and so
%%%                        on.
%%%
%%%                        Publications recorded here appear in almost
%%%                        380 different journals from accounting,
%%%                        aerobiology, animal behavior, auditing,
%%%                        astronomy, bible studies, biology, botany,
%%%                        business, chaos theory, chemistry, colloid
%%%                        science, complexity, computer science,
%%%                        conflict resolution, cognitive science,
%%%                        criminology, critical phenomena,
%%%                        demographics, drug design, dynamics,
%%%                        earthquake detection, economics, electoral
%%%                        studies, engineering, entropy, expert
%%%                        systems, extinction, finance, forensics,
%%%                        gambling, geography, geophysics, human
%%%                        resources, imaging science, informetrics,
%%%                        language science, library science,
%%%                        linguistics, marine systems, marketing,
%%%                        mathematics, medicine, networking,
%%%                        neuroscience, nuclear engineering, nuclear
%%%                        science, operations research, physics,
%%%                        political analysis, probability, psychology,
%%%                        signal processing, simulation, sociology,
%%%                        statistical mechanics, statistics,
%%%                        stock-market trading, urban development, and
%%%                        urban growth, reflecting the broad interest
%%%                        in the unexpected phenomenon discovered and
%%%                        reported first by the Canadian/American
%%%                        astronomer and mathematician, Simon Newcomb,
%%%                        in a two-page note in 1881, and then
%%%                        independently, and with numerical evidence
%%%                        from much more measured data, by American
%%%                        physicist Frank Benford in 1938.
%%%
%%%                        In Benford's Law, the frequency of leading
%%%                        decimal digit p is roughly log10(1 + (1 /
%%%                        p)): that is, approximately 0.301, 0.176,
%%%                        0.125, 0.097, 0.079, 0.067, 0.058, 0.051, and
%%%                        0.046 for digits 1 through 9, instead of the
%%%                        expected 1/9 ~= 0.111 for values taken from a
%%%                        uniform distribution of random numbers.
%%%
%%%                        Another common statement of Benford's Law is
%%%                        that the probability that a decimal number
%%%                        representing a measured value begins with a
%%%                        nonzero digit not greater than p is log10(1 +
%%%                        p), that is, approximately 0.301, 0.477,
%%%                        0.602, 0.699, 0.778, 0.845, 0.903, 0.954, and
%%%                        1.000 for digits 1 through 9.
%%%
%%%                        For the second digits, the probabilities are
%%%                        determined by the formula (see
%%%                        Todter:2009:BLI)
%%%
%%%                            sum(q = 1:9) log10(1 + 1 / (10*q + p)),
%%%
%%%                        that is, approximately 0.120, 0.114, 0.109,
%%%                        0.104, 0.100, 0.097, 0.093, 0.090, 0.088, and
%%%                        0.085, for second decimal digits p = 0
%%%                        through 9.
%%%
%%%                        Probabilities for later digits are even
%%%                        closer: see entries Newcomb:1881:NFU,
%%%                        Feldstein:1976:CED, and Todter:2009:BLI.
%%%
%%%                        Benford's Law is not restricted to decimal
%%%                        numbers: for base b (as long as b is not
%%%                        huge, according to entry Schatte:1998:BLV),
%%%                        just change the 10 values to b in the
%%%                        previous formulas.  Here are some results for
%%%                        selected bases commonly used in computers,
%%%                        showing the probability of the first (D1) or
%%%                        second (D2) digit (first index) for base b
%%%                        (second index):
%%%
%%%                        P[D1,  2]:        1.000
%%%                        P[D2,  2]: 0.585, 0.415
%%%
%%%                        P[D1,  4]:        0.500, 0.292, 0.208
%%%                        P[D2,  4]: 0.304, 0.261, 0.230, 0.206
%%%
%%%                        P[D1,  8]:        0.333, 0.195, 0.138, 0.107,
%%%                                   0.088, 0.074, 0.064
%%%                        P[D2,  8]: 0.151, 0.141, 0.133, 0.126, 0.120,
%%%                                   0.115, 0.110, 0.105
%%%
%%%                        P[D1, 10]:        0.301, 0.176, 0.125, 0.097,
%%%                                   0.079, 0.067, 0.058, 0.051, 0.046
%%%                        P[D2, 10]: 0.120, 0.114, 0.109, 0.104, 0.100,
%%%                                   0.097, 0.093, 0.090, 0.088, 0.085
%%%
%%%                        P[D1, 16]:        0.250, 0.146, 0.104, 0.080,
%%%                                   0.066, 0.056, 0.048, 0.042, 0.038,
%%%                                   0.034, 0.031, 0.029, 0.027, 0.025,
%%%                                   0.023
%%%                        P[D2, 16]: 0.074, 0.072, 0.070, 0.068, 0.066,
%%%                                   0.065, 0.064, 0.062, 0.061, 0.060,
%%%                                   0.059, 0.058, 0.057, 0.056, 0.055,
%%%                                   0.054
%%%
%%%                        A small filter applied to the 1990 US Census
%%%                        data in the Project Gutenberg file
%%%                        uscen902.txt reports these frequencies of
%%%                        first and second digits for the 5148 integer
%%%                        values with at least 3 digits:
%%%
%%%                        F[D1]:        0.298, 0.215, 0.113, 0.082,
%%%                               0.098, 0.056, 0.055, 0.034, 0.049
%%%                        F[D2]: 0.166, 0.090, 0.096, 0.081, 0.100,
%%%                               0.122, 0.076, 0.073, 0.066, 0.130
%%%
%%%                        For the 110 numbers in the atomic weights
%%%                        section of the GNU units utility data file,
%%%                        units.dat, we have
%%%
%%%                        F[D1]:        0.391, 0.309, 0.045, 0.036,
%%%                               0.055, 0.036, 0.036, 0.036, 0.055
%%%                        F[D2]: 0.173, 0.045, 0.109, 0.100, 0.145,
%%%                               0.145, 0.055, 0.055, 0.091, 0.082
%%%
%%%                        From a snapshot of the country-area section
%%%                        of the US CIA World Factbook
%%%
%%%                            https://www.cia.gov/library/publications/the-world-factbook/rankorder/2147rank.html
%%%
%%%                        taken at 18 November 2011, we find 1505
%%%                        numbers with these frequencies:
%%%
%%%                        F[D1]:        0.312, 0.275, 0.100, 0.067,
%%%                               0.058, 0.062, 0.046, 0.029, 0.050
%%%                        F[D2]: 0.167, 0.221, 0.092, 0.092, 0.062,
%%%                               0.067, 0.075, 0.067, 0.083, 0.075
%%%
%%%                        From the country-population section
%%%
%%%                            https://www.cia.gov/library/publications/the-world-factbook/rankorder/2119rank.html
%%%
%%%                        of that book, including only the 163 values
%%%                        of 1,000,000 or larger, we find
%%%
%%%                        F[D1]:        0.301, 0.202, 0.092, 0.135,
%%%                               0.055, 0.067, 0.055, 0.037, 0.055
%%%                        F[D2]: 0.147, 0.153, 0.110, 0.098, 0.098,
%%%                               0.123, 0.086, 0.043, 0.049, 0.092
%%%
%%%                        From the section with the infant mortality
%%%                        rates per 1000 births,
%%%
%%%                            https://www.cia.gov/library/publications/the-world-factbook/rankorder/2091rank.html
%%%
%%%                        there are 208 values with at least 4 digits,
%%%                        with these frequencies:
%%%
%%%                        F[D1]:        0.361, 0.293, 0.043, 0.072,
%%%                               0.062, 0.087, 0.038, 0.014, 0.029
%%%                        F[D2]: 0.303, 0.139, 0.077, 0.058, 0.077,
%%%                               0.077, 0.106, 0.067, 0.043, 0.053
%%%
%%%                        In the 2010 annual financial report for IBM
%%%                        Corporation (its hundredth year of business)
%%%
%%%                            ftp://public.dhe.ibm.com/annualreport/2010/2010_ibm_annual.pdf
%%%
%%%                        there are 6126 numbers of two or more digits
%%%                        that do not look like year dates (19xx and
%%%                        20xx), and they have these digit frequencies:
%%%
%%%                        F[D1]:        0.333, 0.160, 0.163, 0.086,
%%%                               0.068, 0.053, 0.047, 0.045, 0.046
%%%                        F[D2]: 0.172, 0.169, 0.096, 0.084, 0.085,
%%%                               0.095, 0.079, 0.074, 0.079, 0.068
%%%
%%%                        For the first 100,000 primes, we have
%%%
%%%                        F[D1]:        0.311, 0.091, 0.090, 0.087,
%%%                               0.086, 0.085, 0.084, 0.083, 0.082
%%%                        F[D2]: 0.152, 0.151, 0.150, 0.078, 0.078,
%%%                               0.078, 0.078, 0.079, 0.078, 0.078
%%%
%%%                        For the Fibonacci numbers, f(n), which
%%%                        satisfy the recurrence f(n) = f(n-1) + f(n-2)
%%%                        with f(1) = f(2) = 1, using the first 10000
%%%                        such numbers (the last of which has 2091
%%%                        digits), we find for the 9994 f(n) values
%%%                        with at least two digits these frequencies:
%%%
%%%                        F[D1]:        0.301, 0.176, 0.125, 0.097,
%%%                               0.079, 0.067, 0.058, 0.051, 0.046
%%%                        F[D2]: 0.120, 0.114, 0.109, 0.105, 0.100,
%%%                               0.097, 0.094, 0.090, 0.088, 0.085
%%%
%%%                        If we take the same set of Fibonacci numbers,
%%%                        we find these frequencies for values output
%%%                        in base 4:
%%%
%%%                        F[D1]:        0.500, 0.292, 0.208
%%%                        F[D2]: 0.303, 0.262, 0.230, 0.205
%%%
%%%                        The Fibonacci numbers, and the members of
%%%                        many other such sequences, can be proved
%%%                        mathematically to obey Benford's Law exactly
%%%                        (see entries Raimi:1976:FDP, Berger:2011:BLS,
%%%                        and Berger:2011:BTB).
%%%
%%%                        Although many papers purport to explain
%%%                        Benford's Law, a recent paper (entry
%%%                        Berger:2011:BLS) argues that several of the
%%%                        prior published explanations are flawed.  An
%%%                        earlier paper (entry Raimi:1976:FDP) examines
%%%                        the literature on Benford's Law up to 1976,
%%%                        and points out flaws in several previous
%%%                        explanations of the law.  That paper also
%%%                        gives a bibliography of previous important
%%%                        works on the problem.  A recent survey (entry
%%%                        Berger:2011:BTB) may provide stronger
%%%                        mathematical grounds for Benford's Law.
%%%
%%%                        Benford's Law has been applied to the problem
%%%                        of detection of fraud in data, elections, and
%%%                        finance (see, among other entries,
%%%                        Hill:1998:FDP, Nigrini:1992:DIE,
%%%                        Swanson:2003:DPF, Durtschi:2004:EUB,
%%%                        Geyer:2004:DFD, Bhattacharya:2005:CPA,
%%%                        Cleary:2005:ADA, Lu:2005:DFH, Lu:2006:AFD,
%%%                        Schneider:2006:RAS, Cho:2007:BBL,
%%%                        Diekmann:2007:FDU, Hand:2007:DDD,
%%%                        Todter:2009:BLI, and Corazza:2010:CFM, and
%%%                        the cautionary view in Diekmann:2010:BLF).
%%%
%%%                        Benford's Law also applies to floating-point
%%%                        numbers in computer arithmetic (see entries
%%%                        Konheim:1965:MDT, Hamming:1970:DN,
%%%                        Tsao:1974:DSD, Feldstein:1976:CED,
%%%                        Feldstein:1986:OUS, Schatte:1988:ASC), where
%%%                        it has implications for the frequency of
%%%                        significance loss in subtraction of
%%%                        like-signed numbers.
%%%
%%%                        This bibliography also includes publications
%%%                        about two related empirical laws: Heaps' Law
%%%                        and Zipf's Law, because they often occur in
%%%                        discussions of Benford's Law.
%%%
%%%                        Heaps' Law (see entry Heaps:1978:IRC) is an
%%%                        empirical observation from linguistics that
%%%                        the proportion of words from a vocabulary
%%%                        grows exponentially (but with a small
%%%                        exponent, often between 0.4 and 0.6) with the
%%%                        number of words in the text of documents.
%%%
%%%                        Zipf's Law says that if S is some stochastic
%%%                        (random) variable, the probability that S
%%%                        exceeds s is proportional to 1 / s.  The
%%%                        variable S might be, for example, the
%%%                        population of a city (small cities are more
%%%                        numerous than large ones).  Zipf's Law is
%%%                        a special case of the Pareto distribution
%%%                        (see remark in entry Pareto:1896:CEP).
%%%
%%%                        Zipf's law finds application in the design of
%%%                        information retrieval systems (e.g., hash
%%%                        tables, databases, filesystems, and Web
%%%                        searches), as well as in astronomy, biology,
%%%                        computer science, demography, earth science,
%%%                        economics, and physics.  See entry
%%%                        Newman:2005:PLP for an outstanding survey
%%%                        that deserves to be widely read by
%%%                        scientists, and entry Baldi:2003:MIW for a
%%%                        book-length treatment.
%%%
%%%                        There is an actively-maintained bibliography
%%%                        of Benford's Law at
%%%
%%%                            http://www.benfordonline.net/
%%%
%%%                        (see entry Berger:2009:BOB).  It includes
%%%                        material from entries Hurlimann:2006:BLB and
%%%                        Nigrini:1992:DIE.  Although BibTeX output is
%%%                        mentioned, it may not yet be implemented.
%%%
%%%                        There is an online bibliography of Zipf's Law
%%%                        at
%%%
%%%                            http://www.nslij-genetics.org/wli/zipf/
%%%
%%%                        (see entry Li:2011:ZLB).
%%%
%%%                        There is a collection of several papers on
%%%                        election-fraud detection, some of them using
%%%                        Benford's Law analyses, at
%%%
%%%                            http://www-personal.umich.edu/~wmebane/
%%%
%%%                        At version 1.53, the year coverage looked like
%%%                        this:
%%%
%%%                             1881 (   1)    1926 (   1)    1971 (   2)
%%%                             1882 (   0)    1927 (   1)    1972 (   6)
%%%                             1883 (   0)    1928 (   2)    1973 (   8)
%%%                             1884 (   0)    1929 (   1)    1974 (  11)
%%%                             1885 (   0)    1930 (   0)    1975 (  11)
%%%                             1886 (   0)    1931 (   1)    1976 (  10)
%%%                             1887 (   0)    1932 (   2)    1977 (   5)
%%%                             1888 (   0)    1933 (   0)    1978 (   8)
%%%                             1889 (   0)    1934 (   1)    1979 (   4)
%%%                             1890 (   0)    1935 (   1)    1980 (   8)
%%%                             1891 (   0)    1936 (   1)    1981 (   9)
%%%                             1892 (   0)    1937 (   0)    1982 (   8)
%%%                             1893 (   0)    1938 (   2)    1983 (   6)
%%%                             1894 (   0)    1939 (   0)    1984 (  15)
%%%                             1895 (   0)    1940 (   0)    1985 (   9)
%%%                             1896 (   1)    1941 (   0)    1986 (  10)
%%%                             1897 (   0)    1942 (   0)    1987 (  14)
%%%                             1898 (   0)    1943 (   1)    1988 (  12)
%%%                             1899 (   0)    1944 (   1)    1989 (  11)
%%%                             1900 (   0)    1945 (   2)    1990 (   6)
%%%                             1901 (   0)    1946 (   1)    1991 (   9)
%%%                             1902 (   0)    1947 (   0)    1992 (  10)
%%%                             1903 (   0)    1948 (   2)    1993 (   8)
%%%                             1904 (   0)    1949 (   2)    1994 (   7)
%%%                             1905 (   0)    1950 (   3)    1995 (  15)
%%%                             1906 (   0)    1951 (   0)    1996 (  19)
%%%                             1907 (   0)    1952 (   1)    1997 (  12)
%%%                             1908 (   0)    1953 (   1)    1998 (  16)
%%%                             1909 (   0)    1954 (   1)    1999 (  26)
%%%                             1910 (   0)    1955 (   1)    2000 (  15)
%%%                             1911 (   0)    1956 (   0)    2001 (  25)
%%%                             1912 (   1)    1957 (   5)    2002 (  25)
%%%                             1913 (   1)    1958 (   1)    2003 (  36)
%%%                             1914 (   0)    1959 (   1)    2004 (  40)
%%%                             1915 (   1)    1960 (   1)    2005 (  59)
%%%                             1916 (   1)    1961 (   2)    2006 (  55)
%%%                             1917 (   1)    1962 (   2)    2007 (  42)
%%%                             1918 (   0)    1963 (   1)    2008 (  40)
%%%                             1919 (   0)    1964 (   1)    2009 (  56)
%%%                             1920 (   1)    1965 (   4)    2010 (  75)
%%%                             1921 (   0)    1966 (   3)    2011 (  76)
%%%                             1922 (   1)    1967 (   2)    2012 (  39)
%%%                             1923 (   0)    1968 (   3)    2013 (  10)
%%%                             1924 (   0)    1969 (  11)
%%%                             1925 (   1)    1970 (   8)
%%%
%%%                             Article:        761
%%%                             Book:            65
%%%                             InCollection:    26
%%%                             InProceedings:   39
%%%                             Manual:           1
%%%                             MastersThesis:    4
%%%                             Misc:            15
%%%                             PhdThesis:        8
%%%                             Proceedings:      7
%%%                             TechReport:      43
%%%                             Unpublished:      3
%%%
%%%                             Total entries:  972
%%%
%%%                        Data for this bibliography have been
%%%                        collected from
%%%
%%%                            * the University of Utah Mathematics
%%%                              Department bibliography archives
%%%
%%%                            * the TeX User Group bibliography
%%%                              archives
%%%
%%%                            * the Karlsruhe Computer Science
%%%                              bibliography archives
%%%
%%%                            * the Karlsruhe virtual catalog at
%%%                              http://www.ubka.uni-karlsruhe.de/kvk_en.html
%%%
%%%                            * the US Library of Congress catalog at
%%%                              http://catalog.loc.gov/
%%%
%%%                            * the author's cattobib utility, which
%%%                              provides Z39.50 interfaces to many
%%%                              large libraries around the world, at
%%%                              http://www.math.utah.edu/pub/cattobib/
%%%
%%%                            * the American Institute of Physics
%%%                              Scitation database at
%%%                              http://scitation.aip.org/search_scitation
%%%
%%%                            * the American Physical Society PROLA
%%%                              database at
%%%                              http://publish.aps.org/search
%%%
%%%                            * the American Mathematical Society
%%%                              MathSciNet database at
%%%                              http://ams.rice.edu/mathscinet/search.html
%%%
%%%                            * the Bulletin of the Atomic Scientists
%%%                              (archives available, albeit inconveniently,
%%%                              via http://books.google.com/ and
%%%                              http://bos.sagepub.com/search)
%%%
%%%                            * the Canadian Journal of Physics
%%%                              database at
%%%                              http://www.nrcresearchpress.com/search/advanced
%%%
%%%                            * the European Mathematical Society
%%%                              Zentralblatt fuer Mathematik database
%%%                              at http://zb.msri.org/ZMATH/zmath/en/
%%%
%%%                            * the Europhysics journal archive at
%%%                              http://www.europhysicsnews.org/
%%%
%%%                            * the JSTOR database at
%%%                              http://www.jstor.org/
%%%
%%%                            * the Nature journal archive at
%%%                              http://www.nature.com/search/
%%%
%%%                            * the journal archives of the National
%%%                              Academy of Science at
%%%                              http://www.pnas.org/
%%%
%%%                            * the Project Euclid archives at
%%%                              http://projecteuclid.org/
%%%
%%%                            * the SAO/NASA Astrophysics Data System at
%%%                              http://adsabs.harvard.edu/
%%%
%%%                            * the Science journal archive at
%%%                              http://www.sciencemag.org/search
%%%
%%%                            * the SPIRES high-energy physics
%%%                              literature database at the Stanford
%%%                              Linear Accelerator at Stanford
%%%                              University at
%%%                              http://www.slac.stanford.edu/spires/hep/search/
%%%
%%%                            * the Springer journal database at
%%%                              http://www.springer.com/?SGWID=0-102-13-0-0
%%%
%%%                            * the Wiley journal database at
%%%                              http://onlinelibrary.wiley.com/
%%%
%%%                            * many online library catalogs, including
%%%                              those of the British Library, the
%%%                              Karlsruhe Virtual Library catalog, the
%%%                              Oxford University Library, the University of
%%%                              California library system, and the US
%%%                              Library of Congress.
%%%
%%%                        The checksum field above contains a CRC-16
%%%                        checksum as the first value, followed by the
%%%                        equivalent of the standard UNIX wc (word
%%%                        count) utility output of lines, words, and
%%%                        characters.  This is produced by Robert
%%%                        Solovay's checksum utility.",
%%%  }
%%% ====================================================================

@Preamble{
   "\let \k = \c" #
   "\ifx \undefined \booktitle \def \booktitle#1{{{\em #1}}} \fi" #
   "\ifx \undefined \circled    \def \circled #1{(#1)}\fi" #
   "\ifx \undefined \cprime     \def \cprime{$'$} \fi" #
   "\ifx \undefined \mathcal    \def \mathcal #1{{\cal #1}}\fi" #
   "\ifx \undefined \polhk      \def \polhk #1{\setbox0=\hbox{#1}{\ooalign{\hidewidth \lower1.5ex\hbox{`}\hidewidth\crcr\unhbox0}}} \fi" #
   "\ifx \undefined \reg        \def \reg {\circled{R}}\fi" #
   "\ifx \undefined \url        \input{path.sty} \fi"
}

%%% ====================================================================
%%% Acknowledgement abbreviations:

@String{ack-nhfb = "Nelson H. F. Beebe,
                    University of Utah,
                    Department of Mathematics, 110 LCB,
                    155 S 1400 E RM 233,
                    Salt Lake City, UT 84112-0090, USA,
                    Tel: +1 801 581 5254,
                    FAX: +1 801 581 4148,
                    e-mail: \path|beebe@math.utah.edu|,
                            \path|beebe@acm.org|,
                            \path|beebe@computer.org| (Internet),
                    url: \path|http://www.math.utah.edu/~beebe/|"}

%%% ====================================================================
%%% Journal abbreviations:

@String{j-ACCOUNTANCY           = "Accountancy: The journal of the {Institute of
                                  Chartered Accountants in England and Wales}"}

@String{j-ACCOUNT-HIST-J        = "Accounting Historians Journal"}

@String{j-ACCOUNT-RES           = "Accountability in Research"}

@String{j-ACCOUNT-REV           = "The Accounting Review"}

@String{j-ACTA-ARITHMETICA      = "Acta Arithmetica"}

@String{j-ACTA-ASTRONAUT        = "Acta Astronautica"}

@String{j-ADV-APPL-STAT         = "Advances and Applications in Statistics"}

@String{j-ADV-COMPLEX-SYST      = "Advances in Complex Systems"}

@String{j-AEQUATIONES-MATHEMATICAE = "Aequationes Mathematicae"}

@String{j-AEROBIOLOGIA          = "Aerobiologia"}

@String{j-AM-J-ECON-SOCIOL      = "The American Journal of Economics and
                                  Sociology"}

@String{j-AM-J-MATH             = "American Journal of Mathematics"}

@String{j-AM-J-MATH-MANAGE-SCI  = "American Journal of Mathematical and
                                  Management Sciences"}

@String{j-AM-SCI                = "American Scientist"}

@String{j-AMER-J-PHYSICS        = "American Journal of Physics"}

@String{j-AMER-J-PSYCHOLOGY     = "The American Journal of Psychology"}

@String{j-AMER-MATH-MONTHLY     = "American Mathematical Monthly"}

@String{j-AMER-STAT             = "The American Statistician"}

@String{j-ANALYST               = "The Analyst"}

@String{j-ANIM-BEHAV            = "Animal Behaviour"}

@String{j-ANN-APPL-PROBAB       = "Annals of Applied Probability"}

@String{j-ANN-INST-STAT-MATH-TOKYO = "Annals of the Institute of Statistical
                                  Mathematics (Tokyo)"}

@String{j-ANN-MATH-STAT         = "Annals of Mathematical Statistics"}

@String{j-ANN-PROBAB            = "Annals of Probability"}

@String{j-ANN-STAT              = "Annals of Statistics"}

@String{j-APPL-ECON-LETT        = "Applied Economics Letters"}

@String{j-APPL-FINANC-ECON      = "Applied Financial Economics"}

@String{j-APPL-MATH-COMP        = "Applied Mathematics and Computation"}

@String{j-APPL-STAT             = "Applied Statistics"}

@String{j-AQUAT-BOT             = "Aquatic Botany"}

@String{j-ASLIB-PROC            = "ASLIB Proceedings"}

@String{j-ASTROPART-PHYS        = "Astroparticle Physics"}

@String{j-AUDITING              = "Auditing: A Journal of Practice \& Theory"}

@String{j-AUSTRALIAN-COMP-J     = "Australian Computer Journal"}

@String{j-AUSTRALIAN-MATH-SOC-GAZ = "Australian Mathematical Society Gazette"}

@String{j-BELL-SYST-TECH-J      = "The Bell System Technical Journal"}

@String{j-BIOINFORMATICS        = "Bioinformatics"}

@String{j-BIOMETRIKA            = "Biometrika"}

@String{j-BIOSYSTEMS            = "Biosystems (A6E)"}

@String{j-BRAIN-COGN            = "Brain and Cognition"}

@String{j-BULL-INST-MATH-STAT   = "Bulletin --- Institute of Mathematical
                                  Statistics"}

@String{j-C-R-ACAD-SCI-PARIS-SER-AB = "Comptes Rendus Hebdomadaires des
                                  S{\'e}ances de l'Acad{\'e}mie des Sciences.
                                  S{\'e}ries A et B"}

@String{j-C-R-ACAD-SCI-I        = "Comptes rendus de l'Acad{\'e}mie des
                                  sciences. S{\'e}rie I, Math{\'e}matique"}

@String{j-C-R-BIOL              = "Comptes Rendus Biologies"}

@String{j-CACM                  = "Communications of the ACM"}

@String{j-CAN-J-MATH            = "Canadian Journal of Mathematics = Journal
                                  canadien de math{\'e}matiques"}

@String{j-CHANCE                = "Chance: a magazine for people interested in
                                  the analysis of data"}

@String{j-CHAOS                 = "Chaos (Woodbury, NY)"}

@String{j-CHAOS-SOLITONS-FRACTALS = "Chaos, Solitons \& Fractals"}

@String{j-CHIN-PHYS-LETT        = "Chinese Physics Letters"}

@String{j-COGN-SCI              = "Cognitive Science"}

@String{j-COGNITION             = "Cognition"}

@String{j-COLLEGE-MATH-J        = "College Mathematics Journal"}

@String{j-COLLOQ-MATH           = "Colloquium Mathematicum"}

@String{j-COMM-PURE-APPL-MATH   = "Communications on Pure and Applied
                                  Mathematics (New York)"}

@String{j-COMM-STAT             = "Communications in Statistics"}

@String{j-COMM-THEOR-PHYS       = "Communications in Theoretical Physics"}

@String{j-COMMUN-STAT-SIMUL-COMPUT = "Communications in Statistics: Simulation
                                  and Computation"}

@String{j-COMP-J                = "The Computer Journal"}

@String{j-COMP-MATH-APPL        = "Computers and Mathematics with Applications"}

@String{j-COMP-MUSIC-J          = "Computer Music Journal"}

@String{j-COMP-NET              = "Computer Networks"}

@String{j-COMP-NET-AMSTERDAM    = "Computer Networks (Amsterdam, Netherlands:
                                  1999)"}

@String{j-COMP-SURV             = "ACM Computing Surveys"}

@String{j-COMPLEXITY            = "Complexity"}

@String{j-COMPOS-MATH           = "Compositio Mathematica"}

@String{j-COMPUT-STAT-DATA-ANAL = "Computational Statistics \& Data Analysis"}

@String{j-COMPUTING             = "Computing: Archiv f{\"u}r Informatik und
                                  Numerik"}

@String{j-CONTEMP-PHYS          = "Contemporary Physics"}

@String{j-DEC-SUPP-SYS          = "Decision Support Systems"}

@String{j-DEMOGRAPHY            = "Demography"}

@String{j-DEUTSCH-MATH-V        = "Jber. Deutsch. Math.--Verein"}

@String{j-DISCRETE-CONTIN-DYN-SYST = "Discrete and Continuous Dynamical Systems.
                                  Series A"}

@String{j-DISCRETE-DYN-NAT-SOC  = "Discrete Dynamics in Nature and Society"}

@String{j-DISCRETE-MATH         = "Discrete Mathematics"}

@String{j-DOKL-AKAD-NAUK        = "Doklady Akademii Nauk SSSR"}

@String{j-DOKL-MATH             = "Doklady Mathematics"}

@String{j-DRUG-DISCOVERY-TODAY  = "Drug Discovery Today"}

@String{j-ECONOM-LETT           = "Economics Letters"}

@String{j-ECONOMIST             = "The Economist"}

@String{j-EDPACS                = "EDPACS"}

@String{j-ELECT-J-COMB          = "Electronic Journal of Combinatorics"}

@String{j-ELECT-STUDIES         = "Electoral Studies"}

@String{j-ELECTRON-COMMUN-PROBAB = "Electronic Communications in Probability"}

@String{j-ELEK-INFO-KYBER       = "Elektronische Informationsverarbeitung und
                                  Kybernetik (EIK)"}

@String{j-ELEM-MATH             = "Elemente der Mathematik"}

@String{j-EMPIRICA              = "Empirica"}

@String{j-ENTROPY               = "Entropy"}

@String{j-EUR-J-OPER-RES        = "European Journal of Operational Research"}

@String{j-EUR-J-PHYS            = "European Journal of Physics"}

@String{j-EUR-PHYS-J-A          = "European Physical Journal A: Hadrons and
                                  Nuclei"}

@String{j-EUR-PHYS-J-B          = "European Physical Journal B: Condensed Matter
                                  and Complex Systems"}

@String{j-EUROPHYS-LETT         = "Europhysics Letters"}

@String{j-EXP-MATH              = "Experimental Mathematics"}

@String{j-EXPERT-SYST-APPL      = "Expert Systems with Applications"}

@String{j-EXPO-MATH             = "Expositiones Mathematicae"}

@String{j-FIB-QUART             = "Fibonacci Quarterly"}

@String{j-FORUM-MATH            = "Forum Mathematicum"}

@String{j-FRACTALS              = "Fractals"}

@String{j-FUNDAM-MATH           = "Fundamenta mathematicae"}

@String{j-GER-ECON-REV          = "German Economic Review"}

@String{j-GLOB-FINANCE-J        = "Global Finance Journal"}

@String{j-IEEE-ANN-HIST-COMPUT  = "IEEE Annals of the History of Computing"}

@String{j-IEEE-POT              = "IEEE Potentials"}

@String{j-IEEE-SIGNAL-PROCESS-MAG = "IEEE Signal Processing Magazine"}

@String{j-IEEE-TRANS-ELEC-COMPUT = "IEEE Transactions on Electronic Computers"}

@String{j-IEEE-TRANS-ELECTROMAGN-COMPAT = "IEEE Transactions on Electromagnetic
                                  Compatibility"}

@String{j-IEEE-TRANS-FUZZY-SYSTEMS = "IEEE Transactions on Fuzzy Systems"}

@String{j-IEEE-TRANS-INF-THEORY = "IEEE Transactions on Information Theory"}

@String{j-IEEE-TRANS-NETWORKING = "IEEE\slash ACM Transactions on Networking"}

@String{j-IEEE-TRANS-NUCL-SCI   = "IEEE Transactions on Nuclear Science"}

@String{j-IEEE-TRANS-PAR-DIST-SYS = "IEEE Transactions on Parallel and
                                  Distributed Systems"}

@String{j-IEEE-TRANS-RELIAB     = "IEEE Transactions on Reliability"}

@String{j-IMA-J-NUMER-ANAL      = "IMA Journal of Numerical Analysis"}

@String{j-INF-CONTROL           = "Information and Control"}

@String{j-INFO-PROC-LETT        = "Information Processing Letters"}

@String{j-INFO-PROC-MAN         = "Information Processing and Management"}

@String{j-INFO-SCI              = "Information Sciences"}

@String{j-INT-ECON-REV          = "International Economic Review"}

@String{j-INT-J-ACCOUNT-INFO-SYS = "International Journal of Accounting
                                  Information Systems"}

@String{j-INT-J-FOUND-COMP-SCI  = "International Journal of Foundations of
                                  Computer Science (IJFCS)"}

@String{j-INT-J-MATH-EDU-SCI-TECH = "International Journal of Mathematical
                                  Education in Science and Technology"}

@String{j-INT-J-MATH-MATH-SCI   = "International Journal of Mathematics and
                                  Mathematical Sciences"}

@String{j-INT-J-MOD-PHYS-C      = "International Journal of Modern Physics C
                                  [Physics and Computers]"}

@String{j-INT-J-PROD-ECON       = "International Journal of Production
                                  Economics"}

@String{j-INT-J-PURE-APPL-MATH  = "International Journal of Pure and Applied
                                  Mathematics"}

@String{j-INT-J-RES-MARK        = "International Journal of Research in
                                  Marketing"}

@String{j-INT-J-SYST-SCI        = "International Journal of Systems Science"}

@String{j-INT-J-THEOR-PHYS      = "International Journal of Theoretical
                                  Physics"}

@String{j-INTERNET-MATH         = "Internet Mathematics"}

@String{j-IZV-AKAD-NAUK-SSSR-MAT = "Izvestiia Akademii Nauk. USSR Seriia
                                  Matematicheskaia (Moscow)"}

@String{j-J-ACCOUNT-EDUC        = "Journal of Accounting Education"}

@String{j-J-ACCOUNTANCY         = "Journal of Accountancy"}

@String{j-J-ACM                 = "Journal of the ACM"}

@String{j-J-AM-SOC-INF-SCI      = "Journal of the American Society for
                                  Information Science"}

@String{j-J-AM-SOC-INF-SCI-TECHNOL = "Journal of the American Society for
                                  Information Science and Technology"}

@String{j-J-AM-STAT-ASSOC       = "Journal of the American Statistical
                                  Association"}

@String{j-J-APPL-PROBAB         = "Journal of Applied Probability"}

@String{j-J-APPL-STAT           = "Journal of Applied Statistics"}

@String{j-J-ASSET-MANAGE        = "Journal of Asset Management"}

@String{j-J-CLIN-PSYCHOL        = "Journal of Clinical Psychology"}

@String{j-J-COLLOID-INTERFACE-SCI = "Journal of Colloid and Interface Science"}

@String{j-J-COMB-THEORY-A       = "Journal of Combinatorial Theory (Series A)"}

@String{j-J-CONFL-RESOLUT       = "Journal of Conflict Resolution"}

@String{j-J-DIFFERENCE-EQU-APPL = "Journal of Difference Equations and
                                 Applications"}

@String{j-J-DOC                 = "Journal of Documentation"}

@String{j-J-ECON-DYN-CONTROL    = "Journal of Economic Dynamics and Control"}

@String{j-J-EMPIR-FINANCE       = "Journal of Empirical Finance"}

@String{j-J-EXP-PSYCH-GEN       = "Journal of Experimental Psychology: General"}

@String{j-J-FORENSIC-ACCOUNT    = "Journal of Forensic Accounting"}

@String{j-J-GAMBL-STUD          = "Journal of Gambling Studies"}

@String{j-J-GEN-PSYCH           = "The Journal of General Psychology"}

@String{j-J-HUM-RESOUR          = "Journal of Human Resources"}

@String{j-J-INFO-ORG-SCI        = "Journal of Informational and Organizational
                                  Sciences"}

@String{j-J-INFO-PROC-CYBERNETICS-EIK = "Journal of Information Processing and
                                  Cybernetics: EIK"}

@String{j-J-INFO-SCI-PRINCIPLES-PRACTICE = "Journal of Information Science,
                                  Principles and Practice"}

@String{j-J-INFORMETRICS        = "Journal of Informetrics"}

@String{j-J-INT-ECON            = "Journal of International Economics"}

@String{j-J-INT-FINANC-MANAG-ACCOUNT = "Journal of International Financial
                                  Management and Accounting"}

@String{j-J-JPN-INT-ECON        = "Journal of the {Japanese} and International
                                  Economies"}

@String{j-J-MAR-SYST            = "Journal of Marine Systems"}

@String{j-J-MATH-ANAL-APPL      = "Journal of Mathematical Analysis and
                                  Applications"}

@String{j-J-MATH-ARTS           = "Journal of Mathematics and the Arts"}

@String{j-J-MATH-IMAG-VIS       = "Journal of Mathematical Imaging and Vision:
                                  JMIV"}

@String{j-J-MATH-SOC-JPN        = "Journal of the {Mathematical Society of
                                  Japan}"}

@String{j-J-NUMBER-THEORY       = "Journal of Number Theory"}

@String{j-J-PHYS-A              = "Journal of Physics A (Mathematical and
                                  General)"}

@String{j-J-PHYS-SOC-JAP        = "Journal of the Physical Society of Japan"}

@String{j-J-PROD-BRAND-MANAG    = "Journal of Product \& Brand Management"}

@String{j-J-QUANT-CRIMINOL      = "Journal of Quantitative Criminology"}

@String{j-J-QUANT-LINGUISTICS   = "Journal of Quantitative Linguistics"}

@String{j-J-R-STAT-SOC          = "Journal of the Royal Statistical Society"}

@String{j-J-R-STAT-SOC-SER-D-STATISTICIAN = "Journal of the Royal Statistical
                                  Society. Series D (The Statistician)"}

@String{j-J-REG-SCI             = "Journal of Regional Science"}

@String{j-J-STAT-MECH-THEORY-EXP = "Journal of Statistical Mechanics: Theory and
                                  Experiment"}

@String{j-J-STAT-PHYS           = "Journal of Statistical Physics"}

@String{j-J-THEOR-BIOL          = "Journal of Theoretical Biology"}

@String{j-J-URBAN-ECON          = "Journal of Urban Economics"}

@String{j-J-WASH-ACAD-SCI       = "Journal of the Washington Academy of
                                  Sciences"}

@String{j-KNOWL-INFO-SYS        = "Knowledge and Information Systems"}

@String{j-LANG-SCI              = "Language Sciences"}

@String{j-LECT-NOTES-COMP-SCI   = "Lecture Notes in Computer Science"}

@String{j-LIBR-TRENDS           = "Library Trends"}

@String{j-MAT-ZAMETKI           = "Matematicheskie Zametki"}

@String{j-MATH-ANN              = "Mathematische Annalen"}

@String{j-MATH-COMP-MODELLING   = "Mathematical and Computer Modelling"}

@String{j-MATH-COMPUT           = "Mathematics of Computation"}

@String{j-MATH-GAZ              = "The Mathematical Gazette"}

@String{j-MATH-GEOL             = "Mathematical Geology"}

@String{j-MATH-GEOSCI           = "Mathematical Geosciences"}

@String{j-MATH-INTEL            = "The Mathematical Intelligencer"}

@String{j-MATH-MAG              = "Mathematics Magazine"}

@String{j-MATH-NACHR            = "Mathematische Nachrichten"}

@String{j-MATH-NOTES-ACAD-SCI-USSR = "Mathematical Notes of the {Academy of
                                  Sciences of the USSR = Matematicheskie
                                  Zametki}"}

@String{j-MICROELECT-RELIABILITY = "Microelectronics and Reliability"}

@String{j-MOD-PHYS-LETT-A       = "Modern Physics Letters A (MPLA)"}

@String{j-MONAT-MATH            = "Monatshefte f{\"u}r Mathematik"}

@String{j-NATURE                = "Nature"}

@String{j-NEW-J-PHYS            = "New Journal of Physics"}

@String{j-NEW-SCIENTIST         = "New Scientist"}

@String{j-NY-TIMES              = "New York Times"}

@String{j-OPER-SYS-REV          = "Operating Systems Review"}

@String{j-PAP-REG-SCI           = "Papers in Regional Science"}

@String{j-PHILOS-TRANS-R-SOC-LOND-SER-B-BIO-SCI = "Philosophical
                                  transactions of the Royal Society of
                                  London Series B, Biological sciences"}

@String{j-PHYS-LET-A            = "Physics Letters A"}

@String{j-PHYS-REV              = "Physical Review"}

@String{j-PHYS-REV-A            = "Physical Review A (Atomic, Molecular, and
                                  Optical Physics)"}

@String{j-PHYS-REV-C            = "Physical Review C (Nuclear Physics)"}

@String{j-PHYS-REV-E            = "Physical Review E (Statistical physics,
                                  plasmas, fluids, and related
                                  interdisciplinary topics)"}

@String{j-PHYS-REV-LET          = "Physical Review Letters"}

@String{j-PHYSICA-A             = "Physica A: Statistical Mechanics and its
                                  Applications"}

@String{j-PHYSICA-D             = "Physica. D, Nonlinear phenomena"}

@String{j-PLOS-MED              = "PLoS Medicine"}

@String{j-PLOS-ONE              = "PLoS One"}

@String{j-POLIT-ANAL            = "Political Analysis"}

@String{j-PROBAB-SURV           = "Probabability Surveys"}

@String{j-PROBAB-THEORY-RELAT-FIELDS = "Probability Theory and Related Fields"}

@String{j-PROC-AM-MATH-SOC      = "Proceedings of the American Mathematical
                                  Society"}

@String{j-PROC-AMER-PHIL-SOC    = "Proceedings of the American Philosophical
                                  Society"}

@String{j-PROC-INST-STATIST-MATH = "Proceedings of the Institute of Statistical
                                  Mathematics"}

@String{j-PROC-NATL-ACAD-SCI-USA = "Proceedings of the National Academy of
                                  Sciences of the United States of America"}

@String{j-PROC-R-SOC-LOND-SER-A-MATH-PHYS-ENG-SCI = "Proceedings of the Royal
                                  Society A: Mathematical, Physical, \&
                                  Engineering Sciences"}

@String{j-PROC-R-SOC-LOND-SER-B-BIO-SCI = "Proceedings of the Royal Society of
                                  London. Series B. Biological sciences"}

@String{j-PROG-THEOR-PHYS       = "Progress of Theoretical Physics"}

@String{j-PSYCHOL-REP           = "Psychological Reports"}

@String{j-Q-J-ECON              = "The Quarterly Journal of Economics"}

@String{j-RAND-STRUCT           = "Random Structures and Algorithms"}

@String{j-REG-SCI-URBAN-ECON    = "Regional Science and Urban Economics"}

@String{j-RELIABLE-COMPUTING    = "Reliable Computing = Nadezhnye vychisleniia"}

@String{j-REV-INT-ECON          = "Review of International Economics"}

@String{j-REV-MOD-PHYS = "Reviews of Modern Physics"}

@String{j-ROCKY-MOUNTAIN-J-MATH = "Rocky Mountain Journal of Mathematics"}

@String{j-RUSS-J-MATH-PHYS      = "Russian Journal of Mathematical Physics"}

@String{j-SANKHYA-B             = "Sankhy{\=a} (Indian Journal of Statistics),
                                  Series B. Methodological"}

@String{j-SCI-AMER              = "Scientific American"}

@String{j-SCI-REP               = "Scientific Reports"}

@String{j-SCIENCE               = "Science"}

@String{j-SCIENTOMETRICS        = "Scientometrics"}

@String{j-SIAM-J-APPL-MATH      = "SIAM Journal on Applied Mathematics"}

@String{j-SIAM-J-MAT-ANA-APPL   = "SIAM Journal on Matrix Analysis and
                                  Applications"}

@String{j-SIAM-REVIEW           = "SIAM Review"}

@String{j-SIGMETRICS            = "ACM SIGMETRICS Performance Evaluation
                                  Review"}

@String{j-SIGMOD                = "SIGMOD Record (ACM Special Interest Group
                                  on Management of Data)"}

@String{j-SIGNAL-PROCESS-IMAGE-COMMUN = "Signal Processing: Image
                                  Communication"}

@String{j-SIGNIF                = "Significance ({Oxford, England})"}

@String{j-SIGPLAN               = "ACM SIG{\-}PLAN Notices"}

@String{j-SOC-METH-RES          = "Sociological Methods and Research"}

@String{j-SPE                   = "Soft\-ware --- Prac\-tice and Experience"}

@String{j-STAT-PROB-LETT        = "Statistics \& Probability Letters"}

@String{j-STAT-SCI              = "Statistical Science"}

@String{j-STATISTICA-BOLOGNA    = "Statistica (Bologna)"}

@String{j-STUD-HIST-PHILOS-SCI  = "Studies in History and Philosophy of Science
                                  Part {A}"}

@String{j-STUD-LINGUISTICA      = "Studia Linguistica"}

@String{j-STOCH-DYNAM           = "Stochastics and Dynamics"}

@String{j-STOCH-PROC-APPL       = "Stochastic Processes and Their Applications"}

@String{j-SYSTEM                = "System"}

@String{j-THEOR-COMP-SCI        = "Theoretical Computer Science"}

@String{j-THEORY-PROBAB-MATH-STAT = "Theory of Probability and Mathematical
                                  Statistics"}

@String{j-TECHNOMETRICS         = "Technometrics"}

@String{j-TEORET-MATH-FIZ       = "Teoreticheskaya i Matematicheskaya Fizika"}

@String{j-THEORY-PROBAB-APPL    = "Theory of Probability and its Applications"}

@String{j-TKDD                  = "ACM Transactions on Knowledge Discovery
                                  from Data (TKDD)"}

@String{j-TODS                  = "ACM Transactions on Database Systems"}

@String{j-TOIS                  = "ACM Transactions on Information Systems"}

@String{j-TOS                   = "ACM Transactions on Storage"}

@String{j-TRANS-AM-MATH-SOC     = "Transactions of the American Mathematical
                                  Society"}

@String{j-TRAV-HUM              = "Le Travail Humain"}

@String{j-WALL-ST-J             = "Wall Street Journal"}

@String{j-Z-ANGE-MATH-MECH      = "{Zeitschrift f{\"u}r Angewandte Mathematik
                                  und Mechanik}"}

@String{j-Z-ANAL-ANWEND         = "{Zeitschrift f{\"u}r Analysis und ihre
                                  Anwendungen}"}

@String{j-Z-NATURFORSCH         = "{Zeitschrift f{\"u}r Naturforschung}"}

@String{j-ZASTOS-MAT            = "Zastosowania Matematyki"}

%%% ====================================================================
%%% Publisher abbreviations:

@String{pub-ACADEMIC            = "Academic Press"}
@String{pub-ACADEMIC:adr        = "New York, USA"}

@String{pub-ACM                 = "ACM Press"}
@String{pub-ACM:adr             = "New York, NY 10036, USA"}

@String{pub-ADAM-HILGER         = "Adam Hilger Ltd."}
@String{pub-ADAM-HILGER:adr     = "Bristol, UK"}

@String{pub-AW                  = "Ad{\-d}i{\-s}on-Wes{\-l}ey"}
@String{pub-AW:adr              = "Reading, MA, USA"}

@String{pub-BASIC-BOOKS         = "Basic Books"}
@String{pub-BASIC-BOOKS:adr     = "New York, NY, USA"}

@String{pub-BUTTERWORTHS        = "Butterworths"}
@String{pub-BUTTERWORTHS:adr    = "London, UK"}

@String{pub-CAMBRIDGE           = "Cambridge University Press"}
@String{pub-CAMBRIDGE:adr       = "Cambridge, UK"}

@String{pub-CLARENDON           = "Clarendon Press"}
@String{pub-CLARENDON:adr       = "Oxford, UK"}

@String{pub-DOVER               = "Dover Publications, Inc."}
@String{pub-DOVER:adr           = "New York, NY, USA"}

@String{pub-ELSEVIER            = "Elsevier"}
@String{pub-ELSEVIER:adr        = "Amsterdam, The Netherlands"}

@String{pub-HARVARD             = "Harvard University Press"}
@String{pub-HARVARD:adr         = "Cambridge, MA, USA"}

@String{pub-HOUGHTON-MIFFLIN   = "Houghton-Mifflin"}
@String{pub-HOUGHTON-MIFFLIN:adr = "Boston, MA, USA"}

@String{pub-IEEE                = "IEEE Computer Society Press"}
@String{pub-IEEE:adr            = "1109 Spring Street, Suite 300,
                                  Silver Spring, MD 20910, USA"}

@String{pub-MATH-ASSOC-AMER     = "Mathematical Association of America"}
@String{pub-MATH-ASSOC-AMER:adr = "Washington, DC, USA"}

@String{pub-MCGRAW-HILL         = "Mc{\-}Graw-Hill"}
@String{pub-MCGRAW-HILL:adr     = "New York, NY, USA"}

@String{pub-MIT                 = "MIT Press"}
@String{pub-MIT:adr             = "Cambridge, MA, USA"}

@String{pub-MORGAN-KAUFMANN     = "Morgan Kaufmann Publishers"}
@String{pub-MORGAN-KAUFMANN:adr = "Los Altos, CA 94022, USA"}

@String{pub-NORTH-HOLLAND       = "North-Holland Publishing Co."}
@String{pub-NORTH-HOLLAND:adr   = "Amsterdam, The Netherlands"}

@String{pub-OXFORD              = "Oxford University Press"}
@String{pub-OXFORD:adr          = "Walton Street, Oxford OX2 6DP, UK"}

@String{pub-PH                  = "Pren{\-}tice-Hall"}
@String{pub-PH:adr              = "Upper Saddle River, NJ, USA"}

@String{pub-PRINCETON           = "Princeton University Press"}
@String{pub-PRINCETON:adr       = "Princeton, NJ, USA"}

@String{pub-SPIE                = "SPIE Optical Engineering Press"}
@String{pub-SPIE:adr            = "Bellingham, WA, USA"}

@String{pub-SV                  = "Spring{\-}er-Ver{\-}lag"}
@String{pub-SV:adr              = "Berlin, Germany~/ Heidelberg,
                                  Germany~/ London, UK~/ etc."}

@String{pub-U-MICHIGAN          = "University of Michigan Press"}
@String{pub-U-MICHIGAN:adr      = "Ann Arbor, MI, USA"}

@String{pub-WILEY               = "Wiley"}
@String{pub-WILEY:adr           = "New York, NY, USA"}

@String{pub-WORLD-SCI           = "World Scientific Publishing
                                  Co. Pte. Ltd."}
@String{pub-WORLD-SCI:adr       = "P. O. Box 128, Farrer Road,
                                  Singapore 9128"}

@String{pub-YALE                = "Yale University Press"}
@String{pub-YALE:adr            = "New Haven, CT, USA"}

%%% ====================================================================
%%% Series abbreviations:

@String{ser-LNAI                = "Lecture Notes in Artificial Intelligence"}

@String{ser-LNCS                = "Lecture Notes in Computer Science"}

@String{ser-LNM                 = "Lecture Notes in Mathematics"}

%%% ====================================================================
%%% Bibliography entries, sorted by year, and then by citation label:

@Article{Newcomb:1881:NFU,
  author =       "Simon Newcomb",
  title =        "Note on the frequency of use of the different digits
                 in natural numbers",
  journal =      j-AM-J-MATH,
  volume =       "4",
  number =       "1--4",
  pages =        "39--40",
  year =         "1881",
  coden =        "AJMAAN",
  issn =         "0002-9327 (print), 1080-6377 (electronic)",
  issn-l =       "0002-9327",
  bibdate =      "Thu Feb 15 16:35:24 2007",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 http://www.math.utah.edu/pub/tex/bib/fparith.bib",
  url =          "http://www.jstor.org/stable/2369148",
  abstract =     "That the ten digits do not occur with equal frequency
                 must be evident to any one making much use of
                 logarithmic tables, and noticing how much faster the
                 first pages wear out than the last ones. The first
                 significant figure is oftener 1 than any other digit,
                 and the frequency diminishes up to 9.",
  acknowledgement = ack-nhfb,
  author-dates = "March 12, 1835--July 11, 1909",
  fjournal =     "American Journal of Mathematics",
  keywords =     "Benford's Law; Law of Anomalous Numbers; Zipf's Law",
  remark =       "From p. 40: ``The law of probability of the occurrence
                 of numbers is such that all mantissas of their
                 logarithms are equally probable.''. The article
                 contains no references to earlier work.",
  remark-2 =     "The papers \cite{Boring:1920:LNL,Raimi:1976:FDP} are
                 the earliest citations of Newcomb's work that I have
                 yet found in connection with Benford's Law.",
  xxurl =        "http://en.wikipedia.org/wiki/Simon_Newcomb",
}

@Book{Pareto:1896:CEP,
  author =       "Vilfredo Pareto",
  title =        "Cours d'{\'e}conomie politique profess{\'e} a
                 l'universit{\'e} de {Lausanne}. (French) [{Course} on
                 political economy given at the {University of
                 Lausanne}]",
  publisher =    "F. Rouge",
  address =      "Lausanne, Switzerland",
  pages =        "????",
  year =         "1896--1897",
  lccn =         "HB173 .P22",
  bibdate =      "Wed Nov 16 08:41:03 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  language =     "French",
  remark =       "Two volumes issued in successive years. The Italian
                 economist and mathematician, Vilfredo Federico (born in
                 Paris, France, and initially named Wilfried Fritz)
                 Pareto (15 July 1848--19 August 1923), introduced the
                 80--20 rule in economics (80\% of the wealth is owned
                 by 20\% of the people, which was true at the time in
                 Italy, and found to be similar in other countries). He
                 developed the Pareto distribution, in which a random
                 variable $X$ has the property that the probability that
                 it is greater than some number $x$ is given by ${\rm
                 Pr}(X > x) = (x_m / x)^\alpha$ for $x > x_m$, and ${\rm
                 Pr}(X > x) = 1$ otherwise. The positive value $x_m$ is
                 a cutoff, and as $\alpha \to \infty$, the Pareto
                 distribution approaches a Dirac delta function,
                 $\delta(x - x_m)$. When this models the distribution of
                 wealth, the exponent $\alpha$ is called the {\em Pareto
                 index}.",
}

@Book{Poincare:1912:CPL,
  author =       "H. Poincar{\'e}",
  title =        "Calcul des Probabilit{\'e}s: Le{\c{c}}ons
                 profess{\'e}es pendant le deuxi{\`e} me semestre
                 1893--1894. ({French}) [{Calculation} of Probabilities:
                 Lectures from the second semester 1893--1894]",
  publisher =    "Gauthier-Villars",
  address =      "Paris, France",
  pages =        "ii + 274",
  year =         "1912",
  lccn =         "QA273 .P75",
  bibdate =      "Mon Nov 14 10:08:18 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  author-dates = "1854--1912",
  language =     "French",
  remark =       "See pp. 313--320.",
}

@Article{Auerbach:1913:GBG,
  author =       "Felix Auerbach",
  title =        "{Das Gesetz der Bev{\"o}lkerungskonzentration}.
                 ({German}) [{The} law of population concentration]",
  journal =      "{Petermann's Geographische Mitteilungen}",
  volume =       "59",
  number =       "1",
  pages =        "74--76",
  month =        "????",
  year =         "1913",
  coden =        "PGGMA3",
  issn =         "0031-6229",
  issn-l =       "0031-6229",
  bibdate =      "Thu Nov 24 10:49:06 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  note =         "This paper is reported in \cite{Newman:2005:PLP} to be
                 the first discovery of {\em Zipf's Law\/} in connection
                 with city populations (see \cite{Zipf:1932:SSP}). See
                 also \cite{Estoup:1916:GSM}.",
  url =          "http://hdl.handle.net/2027/mdp.39015035583528?urlappend=%3Bseq=122",
  acknowledgement = ack-nhfb,
  ajournal =     "Petermanns Geogr. Mitteilung",
  ajournal-2 =   "Petermanns Geogr. Mitt.",
  language =     "German",
}

@Article{Weyl:1915:GZM,
  author =       "Hermann Weyl",
  title =        "{{\"U}ber die Gleichverteilung von Zahlen mod. Eins}.
                 ({German}) [{On} the uniform distribution of numbers
                 mod. one]",
  journal =      j-MATH-ANN,
  volume =       "77",
  number =       "3",
  pages =        "313--352",
  month =        "????",
  year =         "1915",
  coden =        "MAANA3",
  doi =          "http://dx.doi.org/10.1007/BF01475864",
  issn =         "0025-5831 (print), 1432-1807 (electronic)",
  issn-l =       "0025-5831",
  bibdate =      "Sun Nov 13 10:54:49 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  ajournal =     "Math. Ann.",
  fjournal =     "Mathematische Annalen",
  language =     "German",
  xxyear =       "1916",
}

@Book{Estoup:1916:GSM,
  author =       "J. B. Estoup",
  title =        "Gammes St{\'e}nographiques: m{\'e}thode \& exercices
                 pour l'acquisition de la vitesse ({French})
                 [Stenographic ranges: method and exercises for
                 achieving speed]",
  publisher =    "Institut St{\'e}nographique de France",
  address =      "Paris, France",
  edition =      "Fourth",
  pages =        "151",
  year =         "1916",
  lccn =         "????",
  bibdate =      "Thu Nov 24 14:24:28 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  note =         "This on shorthand writing is the earliest known
                 publication of the power-law distribution of word
                 frequencies, generally credited to
                 \cite{Zipf:1932:SSP}.",
  acknowledgement = ack-nhfb,
  keywords =     "Zipf's Law",
  language =     "French",
}

@Article{Franel:1917:PTL,
  author =       "J. Franel",
  title =        "{\`A} propos des tables de logarithmes. ({French})
                 [{On} tables of logarithms]",
  journal =      "Festschrift Naturforschenden der Gesellschaft in
                 Z{\"u}rich Vierteljahrsschrift",
  volume =       "62",
  number =       "??",
  pages =        "286--295",
  month =        "????",
  year =         "1917",
  coden =        "????",
  issn =         "????",
  bibdate =      "Mon Nov 14 10:09:40 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  language =     "French",
}

@Article{Boring:1920:LNL,
  author =       "Edwin G. Boring",
  title =        "The Logic of the Normal Law of Error in Mental
                 Measurement",
  journal =      j-AMER-J-PSYCHOLOGY,
  volume =       "31",
  number =       "1",
  pages =        "1--33",
  month =        jan,
  year =         "1920",
  coden =        "AJPCAA",
  issn =         "0002-9556 (print), 1939-8298 (electronic)",
  issn-l =       "0002-9556",
  bibdate =      "Thu Dec 01 21:35:43 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  url =          "http://www.jstor.org/stable/1413989",
  acknowledgement = ack-nhfb,
  fjournal =     "The American journal of psychology",
  remark =       "A citation search in Google Scholar on 1-Dec-2011
                 found this article as the only one citing Newcomb's
                 work \cite{Newcomb:1881:NFU} before it was brought to
                 wider view by Raimi's frequently-cited paper
                 \cite{Raimi:1976:FDP}. Boring's article has only brief
                 mention of Newcomb's work, and then solely in
                 connection with the believed randomness of digits of
                 transcendental numbers.",
}

@InCollection{Macaulay:1922:PLG,
  author =       "F. R. Macaulay",
  editor =       "W. C. Mitchell",
  booktitle =    "Income in the {United States}: Its Amount and
                 Distribution: 1909--1919",
  title =        "{Pareto}'s law and the general problem of mathematical
                 describing the frequency of distribution of income",
  publisher =    "National Bureau of Economic Research",
  address =      "New York, NY, USA",
  pages =        "??--??",
  year =         "1922",
  lccn =         "????",
  bibdate =      "Fri Nov 25 09:06:43 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
}

@Article{Yule:1925:MTE,
  author =       "G. Udny Yule",
  title =        "A Mathematical Theory of Evolution, Based on the
                 Conclusions of {Dr. J. C. Willis, F.R.S.}",
  journal =      j-PHILOS-TRANS-R-SOC-LOND-SER-B-BIO-SCI,
  volume =       "213",
  number =       "??",
  pages =        "21--87",
  day =          "14",
  month =        may,
  year =         "1925",
  coden =        "PTRBAE",
  doi =          "http://dx.doi.org/10.1098/rstb.1925.0002",
  issn =         "0962-8436",
  issn-l =       "0962-8436",
  bibdate =      "Tue Nov 15 10:45:15 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  url =          "http://rstb.royalsocietypublishing.org/content/213/402-410/21",
  acknowledgement = ack-nhfb,
  fjournal =     "Philosophical transactions of the Royal Society of
                 London Series B, Biological sciences",
}

@Article{Lotka:1926:FDS,
  author =       "Alfred J. Lotka",
  title =        "The Frequency Distribution of Scientific
                 Productivity",
  journal =      j-J-WASH-ACAD-SCI,
  volume =       "16",
  number =       "12",
  pages =        "317--323",
  month =        dec,
  year =         "1926",
  coden =        "JWASA3",
  issn =         "0043-0439",
  issn-l =       "0043-0439",
  bibdate =      "Thu Nov 24 14:36:11 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  note =         "This is the earliest known publication on the
                 phenomenon known as Zipf's Law, here applied to
                 publication counts of chemists and physicists. Lotka's
                 Law (a term possibly first used in
                 \cite{Zipf:1949:HBP}) says that the number of authors
                 producing $n$ publications is about $1 / n^2$ of the
                 number producing only one. This `law' seems to have
                 been misunderstood and misapplied in other fields; see
                 \cite{Potter:1981:LLR}.",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of the Washington Academy of Sciences",
  keywords =     "Lotka's Law",
}

@Article{Yule:1927:RS,
  author =       "G. Udny Yule",
  title =        "On Reading a Scale",
  journal =      j-J-R-STAT-SOC,
  volume =       "90",
  number =       "3",
  pages =        "570--587",
  month =        "????",
  year =         "1927",
  issn =         "0952-8385",
  issn-l =       "0952-8385",
  bibdate =      "Wed Nov 23 12:29:25 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  note =         "See related later work \cite{Preece:1981:DFD}.",
  url =          "http://www.jstor.org/stable/2341205",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of the Royal Statistical Society",
  remark =       "This paper reports on human bias in the recording of
                 last digits in measurements, or from roundings, or from
                 later scale conversions.",
}

@Article{Condon:1928:SV,
  author =       "E. U. Condon",
  title =        "Statistics of vocabulary",
  journal =      j-SCIENCE,
  volume =       "67",
  number =       "1733",
  pages =        "300--??",
  day =          "16",
  month =        mar,
  year =         "1928",
  coden =        "SCIEAS",
  doi =          "http://dx.doi.org/10.1126/science.67.1733.300",
  issn =         "0036-8075 (print), 1095-9203 (electronic)",
  issn-l =       "0036-8075",
  bibdate =      "Fri Nov 25 09:04:50 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Science",
}

@Article{Sun:1928:EFD,
  author =       "C. P. Sun",
  title =        "On the Examination of Final Digits by Experiments in
                 Artificial Sampling",
  journal =      j-BIOMETRIKA,
  volume =       "20A",
  number =       "1--2",
  pages =        "64--68",
  month =        jul,
  year =         "1928",
  coden =        "BIOKAX",
  issn =         "0006-3444 (print), 1464-3510 (electronic)",
  issn-l =       "0006-3444",
  bibdate =      "Wed Nov 23 12:16:40 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  url =          "http://www.jstor.org/stable/2331941",
  acknowledgement = ack-nhfb,
  fjournal =     "Biometrika",
}

@Article{Zipf:1929:RFD,
  author =       "George Kingsley Zipf",
  title =        "Relative frequency as a determinant of phonetic
                 change",
  journal =      "Harvard Studies in Classical Philology",
  volume =       "40",
  number =       "??",
  pages =        "1--95",
  month =        "????",
  year =         "1929",
  coden =        "????",
  issn =         "0073-0688",
  issn-l =       "0073-0688",
  bibdate =      "Fri Nov 25 09:02:14 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  url =          "http://www.jstor.org/journals/00730688.html;
                 http://www.jstor.org/stable/310585",
  acknowledgement = ack-nhfb,
}

@Book{Gibrat:1931:IE,
  author =       "Robert Gibrat",
  title =        "Les In{\'e}galit{\'e}s {\'e}conomiques",
  publisher =    "Librairie du Recueil Sirey",
  address =      "Paris, France",
  pages =        "286",
  year =         "1931",
  lccn =         "HB251.GIB",
  bibdate =      "Mon Feb 18 14:43:11 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 library.ox.ac.uk:210/ADVANCE",
  note =         "Applications: aux in{\'e}galit{\'e}s des richesses,
                 {\`a} la concentration des entreprises, aux populations
                 des villes, aux statistiques des familles, etc. d'une
                 loi nouvelle. La loi de l'effet proportionnel.",
  url =          "http://en.wikipedia.org/wiki/Gibrat%27s_law",
  acknowledgement = ack-nhfb,
  author-dates = "1904--1980",
  remark-1 =     "According to at least one library catalog (SWB), this
                 book may be the author's doctoral dissertation from
                 l'Universit{\'e} de Paris in 1931.",
  remark-2 =     "This book is cited as the origin of Gibrat's Law, or
                 Gibrat's rule of proportionate growth, that ``the size
                 of a firm and its growth rate are independent''.",
}

@Misc{Anonymous:1932:FL,
  author =       "Anonymous",
  title =        "Fishpole Lamp",
  howpublished = "Web site",
  day =          "30",
  month =        apr,
  year =         "1932",
  bibdate =      "Sat Feb 23 14:52:20 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  note =         "This Web site reports that General Electric researcher
                 Frank Benford invented the electric light pointer, the
                 forerunner of the modern laser pointer.",
  url =          "http://scienceservice.si.edu/pages/012020.htm",
  acknowledgement = ack-nhfb,
  remark =       "CD 2478048, E\&MP12.020, Electric Appliances \
                 Apparatus.",
}

@Book{Zipf:1932:SSP,
  author =       "George Kingsley Zipf",
  title =        "Selected studies of the principle of relative
                 frequency in language",
  publisher =    pub-HARVARD,
  address =      pub-HARVARD:adr,
  pages =        "51",
  year =         "1932",
  lccn =         "P123 .Z5",
  bibdate =      "Wed Nov 16 09:03:46 MST 2011",
  bibsource =    "fsz3950.oclc.org:210/WorldCat;
                 http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  note =         "This book is the origin of {\em Zipf's Law}, but the
                 phenomenon was apparently first reported two decades
                 earlier in \cite{Auerbach:1913:GBG} for city
                 populations, in \cite{Estoup:1916:GSM} for word
                 frequencies, and in \cite{Lotka:1926:FDS} for
                 researcher publication counts.",
  acknowledgement = ack-nhfb,
  author-dates = "1902--1950",
  subject =      "Plautus, Titus Maccius; language and languages;
                 semantics; comparative linguistics; Chinese language;
                 phonology; Latin language; glossaries, vocabularies,
                 etc; dialects; China; Beijing",
}

@Article{Bradford:1934:SIS,
  author =       "Samuel C. Bradford",
  title =        "Sources of Information on Specific Subjects",
  journal =      "Engineering: An Illustrated Weekly Journal (London)",
  volume =       "137",
  number =       "??",
  pages =        "85--86",
  day =          "26",
  month =        jan,
  year =         "1934",
  coden =        "????",
  issn =         "????",
  bibdate =      "Fri Nov 25 11:47:10 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  note =         "This paper (reprinted in \cite{Bradford:1985:SIS})
                 introduces an observation later known as Bradford's
                 Law: there are exponentially-diminishing returns of
                 extending a search for references in journals.",
  url =          "http://en.wikipedia.org/wiki/Bradford%27s_law",
  acknowledgement = ack-nhfb,
}

@Book{Zipf:1935:PBL,
  author =       "George Kingsley Zipf",
  title =        "The psycho-biology of language: an introduction to
                 dynamic philology",
  publisher =    pub-HOUGHTON-MIFFLIN,
  address =      pub-HOUGHTON-MIFFLIN:adr,
  pages =        "ix + 336",
  year =         "1935",
  lccn =         "P105 .Z5",
  bibdate =      "Wed Nov 16 09:07:09 MST 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 prodorbis.library.yale.edu:7090/voyager",
  acknowledgement = ack-nhfb,
  author-dates = "1902--1950",
  subject =      "language and languages; semantics; comparative
                 linguistics",
}

@Book{Moon:1936:SBI,
  author =       "Parry Moon",
  title =        "The Scientific Basis of Illuminating Engineering",
  publisher =    pub-MCGRAW-HILL,
  address =      pub-MCGRAW-HILL:adr,
  pages =        "xi + 608",
  year =         "1936",
  lccn =         "TH7703 .M65",
  bibdate =      "Mon Nov 14 10:11:54 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Benford's Law",
  remark =       "See pages 420ff.",
}

@Article{Benford:1938:LAN,
  author =       "Frank Benford",
  title =        "The Law of Anomalous Numbers",
  journal =      j-PROC-AMER-PHIL-SOC,
  volume =       "78",
  number =       "4",
  pages =        "551--572",
  month =        mar,
  year =         "1938",
  coden =        "PAPCAA",
  issn =         "0003-049X",
  issn-l =       "0003-049X",
  bibdate =      "Thu Feb 15 16:28:28 2007",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib;
                 http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib;
                 http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  note =         "See comments about Benford's biased rounding practices
                 \cite{Diaconis:1979:RP}.",
  url =          "http://links.jstor.org/sici?sici=0003-049X%2819380331%2978%3A4%3C551%3ATLOAN%3E2.0.CO%3B2-G",
  zmnumber =     "JFM 64.0555.03; Zbl 0018.26502",
  abstract =     "It has been observed that the first pages of a table
                 of common logarithms show more wear than do the last
                 pages, indicating that more used numbers begin with the
                 digit 1 than with the digit 9. A compilation of some
                 20,000 first digits taken from widely divergent sources
                 shows that there is a logarithmic distribution of first
                 digits when the numbers are composed of four or more
                 digits. An analysis of the numbers from different
                 sources shows that the numbers taken from unrelated
                 subjects, such as a group of newspaper items, show a
                 much better agreement with a logarithmic distribution
                 than do numbers from mathematical tabulations or other
                 formal data. There is here the peculiar fact that
                 numbers that individually are without relationship are,
                 when considered in large groups, in good agreement with
                 a distribution law---hence the name ``Anomalous
                 Numbers.''\par

                 A further analysis of the data shows a strong tendency
                 for bodies of numerical data to fall into geometric
                 series. If the series is made up of numbers containing
                 three or more digits the first digits form a
                 logarithmic series. If the numbers contain only single
                 digits the geometric relation still holds but the
                 simple logarithmic relation no longer applies.\par

                 An equation is given showing the frequencies of first
                 digits in the different orders of numbers 1 to 10, 10
                 to 100, etc.\par

                 The equation also gives the frequency of digits in the
                 second, third + place of a multi-digit number, and it
                 is shown that the same law applies to
                 reciprocals.\par

                 There are many instances showing that the geometric
                 series, or the logarithmic law, has long been
                 recognized as a common phenomenon in factual literature
                 and in the ordinary affairs of life. The wire gauge and
                 drill gauge of the mechanic, the magnitude scale of the
                 astronomer and the sensory response curves of the
                 psychologist are all particular examples of a
                 relationship that seems to extend to all human affairs.
                 The Law of Anomalous Numbers is thus a general
                 probability law of widespread application.",
  acknowledgement = ack-nhfb,
  author-dates = "1883--December 4, 1948",
  fjournal =     "Proceedings of the {American Philosophical Society}
                 held at {Philadelphia} for promoting useful knowledge",
  keywords =     "Benford's Law; Law of Anomalous Numbers; Zipf's Law",
  remark =       "From \cite{Logan:1978:FDP}: ``Benford's paper was
                 published in 1938 in a journal of rather limited
                 circulation and not usually read by mathematicians. It
                 so happened that it was immediately followed in the
                 same issue by a physics paper which became of some
                 importance for secret nuclear work during World War II
                 [H. A. Bethe, M. E. Rose, and L. P. Smith, `The
                 Multiple Scattering of Electrons', Proc. Amer. Phil.
                 Soc. 78(4), 573--585 (1938)]. That is why Benford's
                 paper caught the attention of physicists in the early
                 1940's and was much discussed. This led to the notes in
                 Nature by Goudsmit and Furry [3] and Furry and Hurwitz
                 [4] containing an effort to explain Benford's law. We
                 considered it at that time merely a welcome diversion
                 and did not expect that over thirty papers would be
                 devoted to this subject in subsequent years.'' The 2006
                 bibliography \cite{Hurlimann:2006:BLB} cites 325
                 publications about Benford's Law.",
  xxurl =        "http://en.wikipedia.org/wiki/Frank_Benford",
}

@Article{Bethe:1938:MSE,
  author =       "H. A. Bethe and M. E. Rose and L. P. Smith",
  title =        "The Multiple Scattering of Electrons",
  journal =      j-PROC-AMER-PHIL-SOC,
  volume =       "78",
  number =       "4",
  pages =        "573--585",
  month =        mar,
  year =         "1938",
  coden =        "PAPCAA",
  issn =         "0003-049X",
  issn-l =       "0003-049X",
  bibdate =      "Wed Nov 23 14:27:52 2011",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/b/bethe-hans.bib;
                 http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  note =         "This paper, which immediately follows Benford's
                 \cite{Benford:1938:LAN} in this journal issue, is
                 reported in \cite[p. 197]{Logan:1978:FDP} to have been
                 of considerable interest to scientists involved in
                 secret nuclear physics work in World War II. That is
                 how Benford's paper ``in a journal of rather limited
                 circulation and not usually read by mathematicians''
                 came to be noticed by physicists.",
  url =          "http://www.jstor.org/stable/984803",
  acknowledgement = ack-nhfb,
  author-dates = "Hans Albrecht Bethe (1906--2005)",
  fjournal =     "Proceedings of the {American Philosophical Society}
                 held at {Philadelphia} for promoting useful knowledge",
  remark =       "Biography supplement in \cite{Lee:2007:HAB} has this
                 as Proc. Am. Philos. Soc., 89, 373--383 (1938), but
                 that seems to be wrong: check??",
}

@Article{Benford:1943:PAG,
  author =       "Frank Benford",
  title =        "The Probable Accuracy of the General Physical
                 Constants",
  journal =      j-PHYS-REV,
  volume =       "63",
  number =       "5--6",
  pages =        "212--212",
  month =        mar,
  year =         "1943",
  coden =        "PHRVAO",
  doi =          "http://dx.doi.org/10.1103/PhysRev.63.212",
  issn =         "0031-899X (print), 1536-6065 (electronic)",
  issn-l =       "0031-899X",
  bibdate =      "Mon Nov 21 21:52:58 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  url =          "http://link.aps.org/doi/10.1103/PhysRev.63.212",
  acknowledgement = ack-nhfb,
  fjournal =     "Physical Review",
}

@Article{Goudsmit:1944:SFN,
  author =       "S. A. Goudsmit and W. H. Furry",
  title =        "Significant Figures of Numbers in Statistical Tables",
  journal =      j-NATURE,
  volume =       "154",
  number =       "3921",
  pages =        "800--801",
  day =          "23",
  month =        dec,
  year =         "1944",
  coden =        "NATUAS",
  doi =          "http://dx.doi.org/10.1038/154800a0",
  issn =         "0028-0836 (print), 1476-4687 (electronic)",
  issn-l =       "0028-0836",
  bibdate =      "Sun Sep 18 11:57:19 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  note =         "See later work \cite{Logan:1978:FDP}, and severe
                 criticism \cite{Raimi:1976:FDP,Raimi:1985:FDP}.",
  url =          "http://www.nature.com/nature/journal/v154/n3921/pdf/154800a0.pdf",
  abstract =     "A rough qualitative explanation of this fact can
                 easily be given. If we consider tables in which the
                 entries become rarer the larger they are, we can draw
                 the obvious conclusion that in any interval, say,
                 between 10 and 99, or 10,000 and 99,999, there are more
                 entries on the small side than on the large side.",
  acknowledgement = ack-nhfb,
  author-dates = "Samuel A. Goudsmit (July 11, 1902--December 4, 1978)",
  fjournal =     "Nature",
  keywords =     "Benford's Law; Law of Anomalous Numbers; Zipf's Law",
  remark =       "In 1925, Samuel Goudsmit and George Uhlenbeck proposed
                 the concept of electron spin, a critical step forward
                 in the quantum mechanics of many-electron systems.
                 Surprisingly, that work did not get them the Nobel
                 Prize, but it did spur Wolfgang Pauli to present his
                 Exclusion Principle in 1925, for which he received the
                 1945 Nobel Prize in Physics. After World War II,
                 Goudsmit was the scientific head of the Alsos mission
                 to capture German nuclear scientists. In the 1950s, he
                 founded the journal Physical Review Letters. During the
                 1960s and 1970s, he was Editor-in-Chief of the main
                 American physics journal, the Physical Review.",
}

@Article{Furry:1945:DND,
  author =       "W. H. Furry and Henry Hurwitz",
  title =        "Distribution of Numbers and Distribution of
                 Significant Figures",
  journal =      j-NATURE,
  volume =       "155",
  number =       "3924",
  pages =        "52--53",
  day =          "13",
  month =        jan,
  year =         "1945",
  coden =        "NATUAS",
  doi =          "http://dx.doi.org/10.1038/155052a0",
  issn =         "0028-0836 (print), 1476-4687 (electronic)",
  issn-l =       "0028-0836",
  bibdate =      "Sun Sep 18 11:51:37 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  url =          "http://www.nature.com/nature/journal/v155/n3924/pdf/155052a0.pdf",
  acknowledgement = ack-nhfb,
  fjournal =     "Nature",
  keywords =     "Benford's Law; Law of Anomalous Numbers; Zipf's Law",
}

@Unpublished{Stigler:1945:DLD,
  author =       "George J. Stigler",
  title =        "The distribution of leading digits in statistical
                 tables",
  year =         "1945",
  bibdate =      "Sat Nov 12 16:07:40 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  note =         "Unpublished, but written about 1945--1946, and
                 presented in an 1975 address at Haskell Hall,
                 University of Chicago. Stigler's distribution is more
                 complex than that of Newcomb and Benford. Stigler has
                 $F_d = (d \ln(d) - (d + 1) \ln(d + 1) + (1 + (10 /
                 9)\ln(10))) / 9$, which gives leading-digit frequencies
                 of 0.2413, 0.1832, 0.1455, 0.1174, 0.0950, 0.0764,
                 0.0605, 0.0465, and 0.0342. See \cite{Lee:2010:SAR} for
                 a comparison of the Benford and Stigler distributions,
                 and their relations to Zipf and Pareto distributions.
                 For derivations of Stigler's distribution, see
                 \cite{Logan:1978:FDP,Raimi:1985:FDP}.",
  url =          "http://www.nobelprize.org/nobel_prizes/economics/laureates/1982/",
  acknowledgement = ack-nhfb,
  remark =       "Stigler won the 1982 Sveriges Riksbank Prize in
                 Economic Sciences in Memory of Alfred Nobel (often
                 called the Nobel Prize in Economics, although that
                 field was not among the original ones funded by Nobel's
                 will).",
}

@Book{Furlan:1946:HSU,
  author =       "Luigi Vladimir Furlan",
  title =        "{Das Harmoniegesetz der Statistik: Eine Untersuchung
                 {\"u}ber die metrische Interdependenz der sozialen
                 Erscheinungen}. ({German}) [{The} {Law of Harmony} in
                 statistics: an investigation of the metrical
                 interdependence of social phenomena]",
  volume =       "2",
  publisher =    "Verlag f{\"u}r Recht und Gesellschaft A.-G.",
  address =      "Basel, Switzerland",
  pages =        "xii + 504",
  year =         "1946",
  lccn =         "HA29 .F85",
  bibdate =      "Mon Nov 14 09:40:24 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  series =       "{Beihefte zum Assekuranzjahrbuch}",
  acknowledgement = ack-nhfb,
  author-dates = "1886--",
  keywords =     "Benford--Furlan Law",
  language =     "German",
}

@Article{Geiringer:1948:RVF,
  author =       "Hilda Geiringer",
  title =        "Review of {L. V. Furlan}'s book: {Das Harmoniegesetz
                 der Statistik: Eine Untersuchung {\"u}ber die metrische
                 Interdependenz der sozialen Erscheinungen}. ({German})
                 [{The} {Law of Harmony} in statistics: an investigation
                 of the metrical interdependence of social phenomena]",
  journal =      j-J-AM-STAT-ASSOC,
  volume =       "43",
  number =       "242",
  pages =        "325--328",
  month =        jun,
  year =         "1948",
  coden =        "JSTNAL",
  issn =         "0162-1459 (print), 1537-274X (electronic)",
  issn-l =       "0162-1459",
  bibdate =      "Mon Nov 14 09:42:45 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 http://www.math.utah.edu/pub/tex/bib/jamstatassoc.bib",
  note =         "See \cite{Furlan:1946:HSU}.",
  url =          "http://www.jstor.org/stable/2280379",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of the American Statistical Association",
}

@Article{Hsu:1948:ESM,
  author =       "E. H. Hs{\"u}",
  title =        "An Experimental Study on ``Mental Numbers'' and a New
                 Application",
  journal =      j-J-GEN-PSYCH,
  volume =       "38",
  number =       "1",
  pages =        "57--67",
  month =        "????",
  year =         "1948",
  coden =        "JGPSAY",
  doi =          "http://dx.doi.org/10.1080/00221309.1948.9711768",
  issn =         "0022-1309 (print), 1940-0888 (electronic)",
  issn-l =       "0022-1309",
  bibdate =      "Sat Jan 07 09:29:53 2012",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  url =          "http://www.tandfonline.com/doi/abs/10.1080/00221309.1948.9711768",
  acknowledgement = ack-nhfb,
  fjournal =     "The Journal of General Psychology",
  keywords =     "Benford's Law",
  onlinedate =   "06 Jul 2010",
}

@Book{Hardy:1949:DS,
  author =       "G. H. (Godfrey Harold) Hardy",
  title =        "Divergent series",
  publisher =    pub-CLARENDON,
  address =      pub-CLARENDON:adr,
  pages =        "xvi + 396",
  year =         "1949",
  lccn =         "QA295 .H29",
  bibdate =      "Wed Nov 16 08:14:50 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 z3950.loc.gov:7090/Voyager",
  acknowledgement = ack-nhfb,
  author-dates = "1877--1947",
}

@Book{Zipf:1949:HBP,
  author =       "George Kingsley Zipf",
  title =        "Human behaviour and the principle of least effort",
  publisher =    "Hafner Pub. Co.",
  address =      "New York, NY, USA",
  pages =        "xi + 573",
  year =         "1949",
  lccn =         "H91 .Z5 1949a",
  bibdate =      "Tue Nov 15 09:35:14 MST 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 z3950.loc.gov:7090/Voyager",
  acknowledgement = ack-nhfb,
  author-dates = "1902--1950",
  remark =       "Reprinted 1965.",
  subject =      "Human ecology",
}

@Article{Anonymous:1950:BRZ,
  author =       "Anonymous",
  title =        "Book review: {Zipf, George K., \booktitle{Human
                 behavior and the principle of least effort}. Cambridge,
                 (Mass.): Addison-Wesley, 1949, pp. 573}",
  journal =      j-J-CLIN-PSYCHOL,
  volume =       "6",
  number =       "3",
  pages =        "306--306",
  year =         "1950",
  coden =        "JCPYAO",
  doi =          "http://dx.doi.org/10.1002/1097-4679(195007)6:3<306::AID-JCLP2270060331>3.0.CO;2-7",
  issn =         "0021-9762 (print), 1097-4679 (electronic)",
  issn-l =       "0021-9762",
  bibdate =      "Mon Feb 25 06:13:56 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Clinical Psychology",
}

@Book{Feller:1950:IPT,
  author =       "William Feller",
  title =        "Introduction to Probability Theory",
  volume =       "2",
  publisher =    pub-WILEY,
  address =      pub-WILEY:adr,
  pages =        "????",
  year =         "1950",
  lccn =         "QA273 .F37",
  bibdate =      "Mon Nov 14 09:57:35 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  series =       "Wiley series in probability and mathematical
                 statistics. Probability and mathematical statistics",
  acknowledgement = ack-nhfb,
  author-dates = "William Feller (1906--1970)",
}

@Article{Macon:1950:DFD,
  author =       "N. Macon and L. Moser",
  title =        "On the distribution of first digits of powers",
  journal =      "Scripta Mathematica",
  volume =       "16",
  number =       "??",
  pages =        "290--291",
  month =        "????",
  year =         "1950",
  coden =        "????",
  issn =         "0036-9713",
  issn-l =       "0036-9713",
  bibdate =      "Sat Nov 12 16:28:13 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  ajournal =     "Scripta Math.",
  fjournal =     "Scripta Mathematica",
}

@Article{Tsuji:1952:UDN,
  author =       "M. Tsuji",
  title =        "On the uniform distribution of numbers $ \bmod 1 $",
  journal =      j-J-MATH-SOC-JPN,
  volume =       "4",
  number =       "3--4",
  pages =        "313--322",
  month =        "????",
  year =         "1952",
  coden =        "NISUBC",
  doi =          "http://dx.doi.org/10.2969/jmsj/00430313",
  issn =         "0025-5645",
  issn-l =       "0025-5645",
  bibdate =      "Sun Feb 17 06:33:32 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  url =          "http://projecteuclid.org/euclid.jmsj/1261415780",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of the {Mathematical Society of Japan}",
}

@InProceedings{Mandelbrot:1953:ITS,
  author =       "Beno{\^\i}t B. Mandelbrot",
  editor =       "Willis Jackson",
  booktitle =    "{Communication theory: papers read at a Symposium on
                 ``Applications of Communication Theory'' held at the
                 Institution of Electrical Engineers, London, September
                 22nd--26th 1952}",
  title =        "An Informational Theory of the Statistical Structure
                 of Languages",
  publisher =    pub-BUTTERWORTHS,
  address =      pub-BUTTERWORTHS:adr,
  pages =        "486--502",
  year =         "1953",
  lccn =         "Q350 .S92 1952",
  bibdate =      "Wed Nov 16 09:37:30 2011",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/m/mandelbrot-benoit.bib;
                 http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  url =          "http://lccn.loc.gov/53004215;
                 http://www.nytimes.com/2010/10/17/us/17mandelbrot.html",
  acknowledgement = ack-nhfb,
  bookpages =    "xii + 532",
  remark =       "The paper is incorrectly referenced as a book in
                 \cite{Baek:2011:ZLU}. Mandelbrot got his Master of
                 Science in Aeronautics at CalTech in 1948, and his
                 Docteur d'{\'E}tat {\`e}s Sciences Math{\'e}matiques in
                 1952 in Paris, so perhaps this is a translation of his
                 thesis work.",
}

@Book{Blackwell:1954:TGS,
  author =       "David Blackwell and Meyer A. Girshick",
  title =        "Theory of Games and Statistical Decisions",
  publisher =    pub-WILEY,
  address =      pub-WILEY:adr,
  pages =        "xi + 355",
  year =         "1954",
  lccn =         "QA269 .B5",
  bibdate =      "Mon Nov 14 10:04:24 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  url =          "http://catalog.hathitrust.org/Record/000577721",
  acknowledgement = ack-nhfb,
  author-dates = "David Blackwell (1919--2010)",
  keywords =     "Benford's Law",
  remark =       "Brief mention of Benford's Law on page 74, problem
                 2.7.2 (??).",
}

@Article{Simon:1955:CSD,
  author =       "Herbert A. Simon",
  title =        "On a Class of Skew Distribution Functions",
  journal =      j-BIOMETRIKA,
  volume =       "42",
  number =       "3--4",
  pages =        "425--440",
  month =        dec,
  year =         "1955",
  coden =        "BIOKAX",
  issn =         "0006-3444 (print), 1464-3510 (electronic)",
  issn-l =       "0006-3444",
  bibdate =      "Tue Nov 15 10:08:58 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  url =          "http://www.jstor.org/stable/2333389",
  acknowledgement = ack-nhfb,
  fjournal =     "Biometrika",
  keywords =     "distribution of income; distribution of species among
                 genera; distributions of city populations;
                 distributions of document word frequencies;
                 distributions of scientific publication counts; Zipf's
                 Law",
  remark =       "This work is an extension of Yule's work
                 \cite{Yule:1925:MTE}. See discussion
                 \cite{Mandelbrot:1959:NCS} and comments
                 \cite{Mitzenmacher:2003:BHG}.",
}

@Article{Devooght:1957:LZM,
  author =       "J. Devooght",
  title =        "Sur la loi de {Zipf--Mandelbrot}. ({French}) [On the
                 {Zipf--Mandelbrot} law]",
  journal =      "Acad. Roy. Belg. Bull. Cl. Sci. (5)",
  volume =       "43",
  pages =        "244--251",
  year =         "1957",
  coden =        "????",
  issn =         "0001-4141",
  issn-l =       "0001-4141",
  mrclass =      "94.0X",
  mrnumber =     "0088412 (19,516a)",
  bibdate =      "Sat Nov 12 09:13:23 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Acad{\'e}mie Royale de Belgique. Bulletin de la Classe
                 des Sciences. Koninklijke Belgische Academie.
                 Mededelingen van de Klasse der Wetenschappen. 5e
                 S{\'e}rie",
}

@Book{Feller:1957:IPT,
  author =       "William Feller",
  title =        "Introduction to Probability Theory",
  volume =       "2",
  publisher =    pub-WILEY,
  address =      pub-WILEY:adr,
  pages =        "461 (vol. 1), 626 (vol. 2)",
  year =         "1957",
  lccn =         "QA273 .F3712",
  bibdate =      "Mon Nov 14 09:57:35 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  url =          "http://catdir.loc.gov/catdir/toc/onix01/57010805.html",
  acknowledgement = ack-nhfb,
  author-dates = "William Feller (1906--1970)",
}

@Article{Gini:1957:SFD,
  author =       "Corrado Gini",
  title =        "Sulla frequenza delle cifre iniziali dei numeri
                 osservati. ({Italian}) [{On} the frequency of initial
                 digits of observed numbers]",
  journal =      "{Bulletin de l'Institut International de
                 Statistique}",
  volume =       "35",
  number =       "2",
  pages =        "57--76",
  year =         "1957",
  coden =        "BISQA3",
  issn =         "????",
  mrclass =      "62.00",
  mrnumber =     "0117807 (22 \#8581)",
  bibdate =      "Sun Sep 18 11:54:25 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  note =         "29th session, 2nd delivery, Rio de Janerio.",
  acknowledgement = ack-nhfb,
  ajournal =     "Bull. Inst. Internat. Stat.",
  keywords =     "Benford's Law; Law of Anomalous Numbers; Zipf's Law",
  language =     "Italian",
  xxvolume =     "34 (wrong!)",
}

@Article{Herzel:1957:SDD,
  author =       "Amato Herzel",
  title =        "Sulla distribuzione della cifre iniziali dei numeri
                 statistici. ({Italian}) [{On} the frequency of initial
                 digits of statistical numbers]",
  journal =      "{Atti dell XV e XVII Riunione, Societa Italiana di
                 Statistica}",
  volume =       "??",
  number =       "??",
  pages =        "205--228",
  year =         "1957",
  coden =        "????",
  issn =         "????",
  bibdate =      "Sun Sep 18 12:00:07 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Benford's Law; Law of Anomalous Numbers; Zipf's Law",
  language =     "Italian",
}

@Article{Miller:1957:SEI,
  author =       "George A. Miller",
  title =        "Some Effects of Intermittent Silence",
  journal =      j-AMER-J-PSYCHOLOGY,
  volume =       "70",
  number =       "2",
  pages =        "311--314",
  month =        jun,
  year =         "1957",
  coden =        "AJPCAA",
  issn =         "0002-9556 (print), 1939-8298 (electronic)",
  issn-l =       "0002-9556",
  bibdate =      "Tue Nov 15 09:40:05 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  url =          "http://www.jstor.org/stable/1419346",
  acknowledgement = ack-nhfb,
  fjournal =     "The American Journal of Psychology",
  keywords =     "Zipf's Law",
}

@Book{Zeller:1958:TLG,
  author =       "Karl Zeller",
  title =        "{Theorie der Limitierungsverfahren}. (German)
                 [{Theory} of limiting processes]",
  volume =       "15",
  publisher =    pub-SV,
  address =      pub-SV:adr,
  pages =        "242",
  year =         "1958",
  lccn =         "QA295 .Z4",
  bibdate =      "Wed Nov 16 06:43:43 MST 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 z3950.loc.gov:7090/Voyager",
  series =       "{Ergebnisse der Mathematik und ihrer Grenzgebiete}",
  acknowledgement = ack-nhfb,
  language =     "German",
  subject =      "series; convergence",
}

@Article{Mandelbrot:1959:NCS,
  author =       "Beno{\^\i}t Mandelbrot",
  title =        "A note on a class of skew distribution functions:
                 analysis and critique of a paper by {H. A. Simon}",
  journal =      j-INF-CONTROL,
  volume =       "2",
  number =       "??",
  pages =        "90--99",
  month =        apr,
  year =         "1959",
  coden =        "IFCNA4",
  doi =          "http://dx.doi.org/10.1016/S0019-9958(59)90098-1",
  issn =         "0019-9958 (print), 1878-2981 (electronic)",
  issn-l =       "0019-9958",
  bibdate =      "Wed Nov 16 09:45:49 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  note =         "See \cite{Simon:1955:CSD}.",
  abstract =     "This note is a discussion of H. A. Simon's model
                 (1955) concerning the class of frequency distributions
                 generally associated with the name of G. K. Zipf. The
                 main purpose is to show that Simon's model is
                 analytically circular in the case of the linguistic
                 laws of Estoup--Zipf and Willis--Yule. Insofar as the
                 economic law of Pareto is concerned, Simon has himself
                 noted that his model is a particular case of that of
                 Champernowne; this is correct, with some reservation. A
                 simplified version of Simon's model is included.",
  acknowledgement = ack-nhfb,
  fjournal =     "Information and Control",
}

@Article{Mandelbrot:1960:PLL,
  author =       "Beno{\^\i}t Mandelbrot",
  title =        "The {Pareto--Levy} law and the distribution of
                 income",
  journal =      j-INT-ECON-REV,
  volume =       "1",
  number =       "??",
  pages =        "79--106",
  month =        "????",
  year =         "1960",
  coden =        "INERAE",
  issn =         "0020-6598 (print), 1468-2354 (electronic)",
  issn-l =       "0020-6598",
  bibdate =      "Wed Nov 23 11:07:01 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  url =          "http://www.ingenta.com/journals/browse/bpl/iere",
  acknowledgement = ack-nhfb,
  fjournal =     "International Economic Review",
}

@Article{Cigler:1961:NET,
  author =       "J. Cigler and G. Helmberg",
  title =        "{Neuere Entwicklungen der Theorie der
                 Gleichverteilung}. ({German}) [{Recent} developments in
                 the theory of uniform distribution]",
  journal =      j-DEUTSCH-MATH-V,
  volume =       "64",
  number =       "??",
  pages =        "1--50",
  month =        "????",
  year =         "1961",
  coden =        "????",
  issn =         "????",
  bibdate =      "Sat Nov 12 16:33:37 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Jber. Deutsch. Math.--Verein",
  language =     "German",
}

@Article{Pinkham:1961:DFS,
  author =       "Roger S. Pinkham",
  title =        "On the Distribution of First Significant Digits",
  journal =      j-ANN-MATH-STAT,
  volume =       "32",
  number =       "4",
  pages =        "1223--1230",
  month =        dec,
  year =         "1961",
  coden =        "AASTAD",
  issn =         "0003-4851",
  issn-l =       "0003-4851",
  bibdate =      "Sat Sep 17 10:19:00 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  url =          "http://www.jstor.org/stable/2237922",
  abstract =     "It has been noticed by astute observers that well used
                 tables of logarithms are invariably dirtier at the
                 front than at the back. Upon reflection one is led to
                 inquire whether there are more physical constants with
                 low order first significant digits than high. Actual
                 counts by Benford [2] show that not only is this the
                 case but that it seems to be an empirical truth that
                 whenever one has a large body of physical data,
                 Farmer's Almanac, Census Reports, Chemical Rubber
                 Handbook, etc., the proportion of these data with first
                 significant digit $n$ or less is approximately
                 $\log_{10}(n + 1)$. Any reader formerly unaware of this
                 ``peculiarity'' will find an actual sampling experiment
                 wondrously tantalizing. Thus, for example,
                 approximately $0.7$ of the physical constants in the
                 Chemical Rubber Handbook begin with $4$ or less
                 ($\log_{10}(4 + 1) = 0.699$). This is to be contrasted
                 with the widespread intuitive evaluation $4/9$ths.",
  acknowledgement = ack-nhfb,
  fjournal =     "Annals of Mathematical Statistics",
  keywords =     "Benford's Law; Law of Anomalous Numbers; Zipf's Law",
  remark =       "From p. 1223: ``\ldots{} the proportion of these data
                 with first significant digit $n$ or less is
                 approximately $\log_{10}(n + 1)$.''\par

                 \ldots{} ``The only distribution for first significant
                 digits which is invariant under scale change of the
                 underlying distribution is $\log_{10}(n + 1)$. Contrary
                 to suspicion this is a non-trivial mathematical result,
                 for the variable $n$ is discrete.''.\par

                 From p. 1230: ``The foregoing results bear on questions
                 of round-off in computing machines. Since $d(uv) = u dv
                 + v du$, the error resulting from multiplying two
                 rounded numbers will be governed primarily by the first
                 significant digits of the two numbers being multiplied.
                 Now the distribution of first significant digits,
                 favoring as it does low order digits, tends to produce
                 less error than would be the case if first significant
                 digits were uniform as has sometimes been
                 assumed.''\par

                 Cited in \cite{Sterbenz:1974:FPC}.",
}

@Book{Hamming:1962:NMS,
  author =       "R. W. (Richard Wesley) Hamming",
  title =        "Numerical methods for scientists and engineers",
  publisher =    pub-MCGRAW-HILL,
  address =      pub-MCGRAW-HILL:adr,
  pages =        "411",
  year =         "1962",
  lccn =         "QA297 .H28",
  bibdate =      "Fri Aug 20 09:12:08 MDT 2010",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 z3950.loc.gov:7090/Voyager",
  series =       "International series in pure and applied mathematics",
  acknowledgement = ack-nhfb,
  remark =       "Cited in \cite{Sterbenz:1974:FPC}.",
  subject =      "Numerical analysis; Electronic digital computers",
}

@TechReport{Mandelbrot:1962:SNR,
  author =       "Beno{\^\i}t Mandelbrot",
  title =        "Statistics of natural resources and the law of
                 {Pareto}",
  type =         "Research Note",
  number =       "NC-146",
  institution =  "IBM",
  address =      "Yorktown Heights, NY, USA",
  day =          "29",
  month =        jun,
  year =         "1962",
  bibdate =      "Mon Sep 10 17:35:59 2012",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/m/mandelbrot-benoit.bib;
                 http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
}

@Book{Weaver:1963:LLT,
  author =       "Warren Weaver",
  title =        "{Lady Luck}: The Theory of Probability",
  publisher =    "Doubleday Anchor Series",
  address =      "New York, NY, USA",
  pages =        "392",
  year =         "1963",
  lccn =         "QA273 .W4",
  bibdate =      "Mon Nov 14 09:54:47 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  note =         "Benford's Law is discussed on pp. 270--277.",
  acknowledgement = ack-nhfb,
  author-dates = "Warren, Weaver (1894--1978)",
  remark =       "Reprinted in \cite{Weaver:1982:LLT}.",
}

@Article{Cigler:1964:MSU,
  author =       "J. Cigler",
  title =        "Methods of summability and uniform distribution $\bmod
                 1$",
  journal =      j-COMPOS-MATH,
  volume =       "16",
  number =       "??",
  pages =        "44--51",
  year =         "1964",
  coden =        "CMPMAF",
  issn =         "0010-437X (print), 1570-5846 (electronic)",
  issn-l =       "0010-437X",
  bibdate =      "Mon Nov 14 10:15:31 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Compositio Mathematica",
}

@Article{Good:1965:LE,
  author =       "I. J. Good",
  title =        "Letter to the Editor",
  journal =      j-AMER-STAT,
  volume =       "19",
  number =       "3",
  pages =        "43--43",
  month =        jun,
  year =         "1965",
  coden =        "ASTAAJ",
  issn =         "0003-1305 (print), 1537-2731 (electronic)",
  issn-l =       "0003-1305",
  bibdate =      "Mon Nov 14 09:56:33 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  url =          "http://www.jstor.org/stable/2681423",
  acknowledgement = ack-nhfb,
  fjournal =     "The American Statistician",
  keywords =     "Benford's Law",
  remark =       "Refers to \cite{Pinkham:1961:DFS}, and cites a review
                 of that article published by Good in Mathematical
                 Reviews (1962), page 214, which I have not yet been
                 able to locate.",
}

@Article{Hamming:1965:NLB,
  author =       "R. W. Hamming and W. L. Mammel",
  title =        "A Note on the Location of the Binary Point in a
                 Computing Machine",
  journal =      j-IEEE-TRANS-ELEC-COMPUT,
  volume =       "EC-14",
  number =       "2",
  pages =        "260--261",
  month =        apr,
  year =         "1965",
  coden =        "IEECA8",
  doi =          "http://dx.doi.org/10.1109/PGEC.1965.264258",
  issn =         "0367-7508",
  issn-l =       "0367-7508",
  bibdate =      "Thu Jul 14 06:26:22 MDT 2011",
  bibsource =    "http://www.computer.org/tc/;
                 http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 http://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 http://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
  url =          "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=4038414",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Electronic Computers",
  remark =       "The authors consider the low-level multiplication
                 circuit efficiency of placing the binary point before
                 or after the first bit. If the leading bit is equally
                 likely to be a 0 or a 1, then their analysis shows that
                 it is better to place the point before the leading bit.
                 However, they report that a more likely distribution is
                 logarithmic (as predicted by Benford's Law, although
                 the Newcomb / Benford work is neither mentioned nor
                 cited), in which case there is no advantage for either
                 choice of placement of the binary point. They conclude
                 that it would be humane to place it after the leading
                 digit, by analogy with how people learn decimal
                 arithmetic.",
}

@Article{Konheim:1965:MDT,
  author =       "Alan G. Konheim",
  title =        "Mantissa Distributions (in {Technical Notes and Short
                 Papers})",
  journal =      j-MATH-COMPUT,
  volume =       "19",
  number =       "89",
  pages =        "143--144",
  month =        apr,
  year =         "1965",
  coden =        "MCMPAF",
  doi =          "http://dx.doi.org/10.2307/2004111",
  issn =         "0025-5718 (print), 1088-6842 (electronic)",
  issn-l =       "0025-5718",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 http://www.math.utah.edu/pub/tex/bib/mathcomp1960.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  fjournal =     "Mathematics of Computation",
}

@Book{Zipf:1965:PBL,
  author =       "George Kingsley Zipf",
  title =        "The psycho-biology of language: an introduction to
                 dynamic philology",
  publisher =    pub-MIT,
  address =      pub-MIT:adr,
  pages =        "xv + 336",
  year =         "1965",
  lccn =         "P105 .Z5 1965",
  bibdate =      "Wed Nov 16 09:07:09 MST 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 prodorbis.library.yale.edu:7090/voyager",
  acknowledgement = ack-nhfb,
  author-dates = "1902--1950",
  remark =       "Reprint of \cite{Zipf:1935:PBL}.",
  subject =      "language; philology; semantics; psycholinguistics;
                 comparative linguistics",
}

@Book{Feller:1966:IPT,
  author =       "William Feller",
  title =        "Introduction to Probability Theory",
  volume =       "2",
  publisher =    pub-WILEY,
  address =      pub-WILEY:adr,
  edition =      "Second",
  pages =        "xviii + 626",
  year =         "1966",
  issn =         "0271-6232",
  lccn =         "QA273 .F3727 1966",
  bibdate =      "Mon Nov 14 09:57:35 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  series =       "Wiley series in probability and mathematical
                 statistics. Probability and mathematical statistics",
  acknowledgement = ack-nhfb,
  author-dates = "William Feller (1906--1970)",
  remark =       "Benford's Law is discussed on p. 62.",
}

@Article{Flehinger:1966:PRI,
  author =       "B. J. (Betty J.) Flehinger",
  title =        "On the probability that a random integer has initial
                 digit {$A$}",
  journal =      j-AMER-MATH-MONTHLY,
  volume =       "73",
  number =       "10",
  pages =        "1056--1061",
  month =        dec,
  year =         "1966",
  coden =        "AMMYAE",
  doi =          "http://dx.doi.org/10.2307/2314636",
  issn =         "0002-9890 (print), 1930-0972 (electronic)",
  issn-l =       "0002-9890",
  bibdate =      "Sat Nov 12 15:33:14 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  url =          "http://www.jstor.org/stable/2314636",
  acknowledgement = ack-nhfb,
  fjournal =     "American Mathematical Monthly",
}

@Book{Petersen:1966:RMT,
  author =       "Gordon Marshall Petersen",
  title =        "Regular Matrix Transformations",
  publisher =    pub-MCGRAW-HILL,
  address =      pub-MCGRAW-HILL:adr,
  pages =        "viii + 142",
  year =         "1966",
  lccn =         "QA263 .P415 1966",
  bibdate =      "Mon Nov 14 10:18:15 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
}

@Article{Duncan:1967:AUD,
  author =       "R. L. Duncan",
  title =        "An Application of Uniform Distributions to the
                 {Fibonacci} Numbers",
  journal =      j-FIB-QUART,
  volume =       "5",
  number =       "2",
  pages =        "137--140",
  month =        apr,
  year =         "1967",
  coden =        "FIBQAU",
  issn =         "0015-0517",
  issn-l =       "0015-0517",
  bibdate =      "Thu Oct 20 18:04:52 MDT 2011",
  bibsource =    "http://www.fq.math.ca/5-2.html;
                 http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 http://www.math.utah.edu/pub/tex/bib/fibquart.bib",
  url =          "http://www.fq.math.ca/Scanned/5-2/duncan.pdf",
  acknowledgement = ack-nhfb,
  ajournal =     "Fib. Quart",
  fjournal =     "The Fibonacci Quarterly. Official Organ of the
                 Fibonacci Association",
}

@Article{Mosteller:1967:DSR,
  author =       "Frederick Mosteller and Cleo Youtz and Douglas Zahn",
  title =        "The Distribution of Sums of Rounded Percentages",
  journal =      j-DEMOGRAPHY,
  volume =       "4",
  number =       "2",
  pages =        "850--858",
  month =        jun,
  year =         "1967",
  coden =        "????",
  issn =         "0070-3370 (print), 1533-7790 (electronic)",
  issn-l =       "0070-3370",
  bibdate =      "Thu Nov 24 08:03:16 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  note =         "See \cite{Diaconis:1979:RP} for further work.",
  url =          "http://muse.jhu.edu/journals/dem/;
                 http://www.biomedsearch.com/nih/Distribution-Sums-Rounded-Percentages/21318695.html;
                 http://www.jstor.org/stable/2060324",
  abstract =     "When percentages are computed for counts in several
                 categories or for several positive measurements0 each
                 taken as a fraction of their sum, the rounded
                 percentages often fail to add to 100 percent. We
                 investigate how frequently this failure occurs and what
                 the distributions of sums of rounded percentages are
                 for (1) an empirical set of data, (2) the multinomial
                 distribution in small samples, (3) spacings between
                 points dropped on an interval --- the broken-stick
                 model; and (4) for simulation for several categories.
                 The several methods produce similar distributions.We
                 find that the probability that the sum of rounded
                 percentages adds to exactly 100 percent is certain for
                 two categories, about three-fourths for three
                 categories, about two-thirds for four categories, and
                 about [Formula: see text] for larger numbers of
                 categories, c, on the average when categories are not
                 improbable.",
  acknowledgement = ack-nhfb,
  fjournal =     "Demography",
  pubmedid =     "21318695",
}

@Article{Adhikari:1968:DMS,
  author =       "A. K. Adhikari and B. P. Sarkar",
  title =        "Distribution of most significant digit in certain
                 functions whose arguments are random variables",
  journal =      j-SANKHYA-B,
  volume =       "30",
  number =       "??",
  pages =        "47--58",
  month =        "????",
  year =         "1968",
  coden =        "SANBBV",
  issn =         "0581-5738",
  issn-l =       "0581-5738",
  bibdate =      "Sat Nov 12 16:09:30 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  ajournal =     "Sankhya Ser. B (Indian J. of Statist.)",
  fjournal =     "Sankhy{\=a} (Indian Journal of Statistics), Series B.
                 Methodological",
}

@Book{Feller:1968:IPT,
  author =       "William Feller",
  title =        "Introduction to Probability Theory and its
                 Applications",
  volume =       "2",
  publisher =    pub-WILEY,
  address =      pub-WILEY:adr,
  edition =      "Third",
  pages =        "xviii + 509",
  year =         "1968",
  isbn =         "0-471-25708-7",
  isbn-13 =      "978-0-471-25708-0",
  lccn =         "QA273 .F3713",
  bibdate =      "Mon Nov 14 09:57:35 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  note =         "See \cite{Berger:2010:FFFa,Berger:2010:FFFb} for a
                 discussion of flaws in the derivation of Benford's Law
                 in this book.",
  acknowledgement = ack-nhfb,
  author-dates = "William Feller (1906--1970)",
  remark =       "Pages 63--64 (of xxiv + 669) in 1971 printing have
                 only brief mention of two papers
                 \cite{Benford:1938:LAN,Pinkham:1961:DFS}.",
}

@Article{Shenton:1968:PDM,
  author =       "L. R. Shenton",
  title =        "Periodicity and Density of Modified {Fibonacci}
                 Sequences",
  journal =      j-FIB-QUART,
  volume =       "6",
  number =       "2",
  pages =        "109--116",
  month =        apr,
  year =         "1968",
  coden =        "FIBQAU",
  issn =         "0015-0517",
  issn-l =       "0015-0517",
  bibdate =      "Thu Oct 20 18:05:02 MDT 2011",
  bibsource =    "http://www.fq.math.ca/6-2.html;
                 http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 http://www.math.utah.edu/pub/tex/bib/fibquart.bib",
  url =          "http://www.fq.math.ca/Scanned/6-2/shenton.pdf",
  acknowledgement = ack-nhfb,
  ajournal =     "Fib. Quart",
  fjournal =     "The Fibonacci Quarterly. Official Organ of the
                 Fibonacci Association",
  keywords =     "Benford's Law",
}

@Article{Adhikari:1969:SRD,
  author =       "A. K. Adhikari",
  title =        "Some results on the distribution of the most
                 significant digit",
  journal =      j-SANKHYA-B,
  volume =       "31",
  number =       "??",
  pages =        "413--420",
  month =        "????",
  year =         "1969",
  coden =        "SANBBV",
  issn =         "0581-5738",
  issn-l =       "0581-5738",
  bibdate =      "Sat Nov 12 16:12:50 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  ajournal =     "Sankhya Ser. B (Indian J. of Statist.)",
  fjournal =     "Sankhy{\=a} (Indian Journal of Statistics), Series B.
                 Methodological",
}

@Article{Bumby:1969:FAM,
  author =       "R. Bumby and E. Ellentuck",
  title =        "Finitely additive measures and the first digit
                 problem",
  journal =      j-FUNDAM-MATH,
  volume =       "65",
  number =       "??",
  pages =        "33--42",
  month =        "????",
  year =         "1969",
  coden =        "????",
  issn =         "0016-2736",
  issn-l =       "0016-2736",
  bibdate =      "Sat Nov 12 16:19:19 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Fundamenta mathematicae",
}

@Article{Duncan:1969:NID,
  author =       "R. L. Duncan",
  title =        "Note on the Initial Digit Problem",
  journal =      j-FIB-QUART,
  volume =       "7",
  number =       "5",
  pages =        "474--475",
  month =        dec,
  year =         "1969",
  coden =        "FIBQAU",
  issn =         "0015-0517",
  issn-l =       "0015-0517",
  bibdate =      "Thu Oct 20 18:05:21 MDT 2011",
  bibsource =    "http://www.fq.math.ca/7-5.html;
                 http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 http://www.math.utah.edu/pub/tex/bib/fibquart.bib",
  url =          "http://www.fq.math.ca/Scanned/7-5/duncan.pdf",
  acknowledgement = ack-nhfb,
  ajournal =     "Fib. Quart",
  fjournal =     "The Fibonacci Quarterly",
}

@Article{Fairthorne:1969:PDE,
  author =       "Robert A. Fairthorne",
  title =        "Progress in Documentation: Empirical Hyperbolic
                 Distributions ({Bradford--Zipf--Mandelbrot}) for
                 Bibliometric Description and Prediction",
  journal =      j-J-DOC,
  volume =       "25",
  number =       "4",
  pages =        "313--343",
  month =        dec,
  year =         "1969",
  coden =        "JDOCAS",
  doi =          "http://dx.doi.org/10.1108/eb026481",
  issn =         "0022-0418 (print), 1758-7379 (electronic)",
  issn-l =       "0022-0418",
  bibdate =      "Fri Nov 25 06:27:27 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  note =         "Reprinted in \cite{Fairthorne:2005:PDE}.",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Documentation",
  remark =       "According to \cite{Potter:1981:LLR}, this paper is the
                 first to link the distributions of Bradford, Zipf,
                 Mandelbrot, and Lotka.",
}

@Unpublished{Hafner:1969:CSR,
  author =       "Everett M. Hafner",
  title =        "Circular slide roulette",
  year =         "1969",
  bibdate =      "Mon Nov 14 10:00:25 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  note =         "Unpublished but dated 1969. Presented in 1975 in an
                 address at Hampshire College, Amherst, MA, USA",
  acknowledgement = ack-nhfb,
}

@Article{Haight:1969:TPD,
  author =       "F. A. Haight",
  title =        "Two probability distributions connected with {Zipf}'s
                 rank-size conjecture",
  journal =      j-ZASTOS-MAT,
  volume =       "10",
  pages =        "225--228",
  year =         "1969",
  coden =        "ZAMTAK",
  issn =         "0044-1899",
  issn-l =       "0044-1899",
  mrclass =      "62.31",
  mrnumber =     "0246425 (39 \#7729)",
  bibdate =      "Sat Nov 12 09:13:23 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Polska Akademia Nauk. Instytut Matematyczny.
                 Zastosowania Matematyki",
}

@Book{Knuth:1969:SNM,
  author =       "Donald E. Knuth",
  title =        "Semi\-nu\-mer\-i\-cal Algorithms",
  volume =       "2",
  publisher =    pub-AW,
  address =      pub-AW:adr,
  pages =        "xi + 624",
  year =         "1969",
  isbn =         "0-201-03802-1",
  isbn-13 =      "978-0-201-03802-6",
  lccn =         "QA76.5 .K57",
  bibdate =      "Wed Dec 15 15:47:38 1993",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 http://www.math.utah.edu/pub/tex/bib/master.bib",
  note =         "Benford's Law is discussed on pp. 219--229.",
  price =        "US\$19.75",
  series =       "The Art of Computer Programming",
}

@Article{Kuipers:1969:RPR,
  author =       "L. Kuipers",
  title =        "Remark on a Paper by {R. L. Duncan} Concerning the
                 Uniform Distribution Mod $1$ of the Sequence of the
                 Logarithms of the {Fibonacci} Numbers",
  journal =      j-FIB-QUART,
  volume =       "7",
  number =       "5",
  pages =        "465--466",
  month =        dec,
  year =         "1969",
  coden =        "FIBQAU",
  issn =         "0015-0517",
  issn-l =       "0015-0517",
  bibdate =      "Thu Oct 20 18:05:21 MDT 2011",
  bibsource =    "http://www.fq.math.ca/7-5.html;
                 http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 http://www.math.utah.edu/pub/tex/bib/fibquart.bib",
  url =          "http://www.fq.math.ca/Scanned/7-5/kuipers-a.pdf",
  acknowledgement = ack-nhfb,
  ajournal =     "Fib. Quart",
  fjournal =     "The Fibonacci Quarterly. Official Organ of the
                 Fibonacci Association",
}

@Article{Raimi:1969:DFS,
  author =       "R. A. Raimi",
  title =        "On the Distribution of First Significant Figures",
  journal =      j-AMER-MATH-MONTHLY,
  volume =       "76",
  number =       "4",
  pages =        "342--348",
  month =        apr,
  year =         "1969",
  coden =        "AMMYAE",
  doi =          "http://dx.doi.org/10.2307/2316424",
  issn =         "0002-9890 (print), 1930-0972 (electronic)",
  issn-l =       "0002-9890",
  bibdate =      "Mon Jun 28 12:39:22 MDT 1999",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  fjournal =     "American Mathematical Monthly",
}

@Article{Raimi:1969:PDF,
  author =       "R. Raimi",
  title =        "The peculiar distribution of first significant
                 digits",
  journal =      j-SCI-AMER,
  volume =       "221",
  number =       "6",
  pages =        "109--120",
  month =        dec,
  year =         "1969",
  coden =        "SCAMAC",
  doi =          "http://dx.doi.org/10.1038/scientificamerican1269-109",
  issn =         "0036-8733 (print), 1946-7087 (electronic)",
  issn-l =       "0036-8733",
  bibdate =      "Sat Nov 12 16:39:08 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Scientific American",
}

@PhdThesis{Wong:1969:GDS,
  author =       "James Teng Wong",
  title =        "On the Generalization of the Distribution of the
                 Significant Digits Under Computation",
  type =         "{Ph.D.} thesis",
  school =       "Department of Mathematics, Oregon State University",
  address =      "Corvallis, OR, USA",
  pages =        "52",
  year =         "1969",
  bibdate =      "Fri Nov 25 15:41:42 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  url =          "http://search.proquest.com/docview/302476508?accountid=14677",
  acknowledgement = ack-nhfb,
}

@Article{Aigner:1970:EPL,
  author =       "Dennis J. Aigner and Arthur S. Goldberger",
  title =        "Estimation of {Pareto's Law} from Grouped
                 Observations",
  journal =      j-J-AM-STAT-ASSOC,
  volume =       "65",
  number =       "330",
  pages =        "712--723",
  month =        jun,
  year =         "1970",
  coden =        "JSTNAL",
  issn =         "0162-1459 (print), 1537-274X (electronic)",
  issn-l =       "0162-1459",
  bibdate =      "Wed Jan 25 08:05:44 MST 2012",
  bibsource =    "http://www.jstor.org/journals/01621459.html;
                 http://www.jstor.org/stable/i314212;
                 http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 http://www.math.utah.edu/pub/tex/bib/jamstatassoc1970.bib",
  url =          "http://www.jstor.org/stable/2284582",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of the American Statistical Association",
}

@Article{Blum:1970:SID,
  author =       "M. Blum",
  title =        "On the Sums of Independently Distributed {Pareto}
                 Variates",
  journal =      j-SIAM-J-APPL-MATH,
  volume =       "19",
  number =       "1",
  pages =        "191--198",
  month =        jul,
  year =         "1970",
  coden =        "SMJMAP",
  issn =         "0036-1399 (print), 1095-712X (electronic)",
  issn-l =       "0036-1399",
  bibdate =      "Thu Oct 15 18:16:06 MDT 1998",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 http://www.math.utah.edu/pub/tex/bib/siamjapplmath.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  fjournal =     "SIAM Journal on Applied Mathematics",
}

@Article{Brown:1970:MOU,
  author =       "J. L. {Brown, Jr.} and R. L. Duncan",
  title =        "Modulo One Uniform Distribution of the Sequence of
                 Logarithms of Certain Recursive Sequences",
  journal =      j-FIB-QUART,
  volume =       "8",
  number =       "5",
  pages =        "482--486",
  month =        dec,
  year =         "1970",
  coden =        "FIBQAU",
  issn =         "0015-0517",
  issn-l =       "0015-0517",
  bibdate =      "Thu Oct 20 18:05:31 MDT 2011",
  bibsource =    "http://www.fq.math.ca/8-5.html;
                 http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 http://www.math.utah.edu/pub/tex/bib/fibquart.bib",
  note =         "See remark \cite{Kuipers:1973:RPD}.",
  url =          "http://www.fq.math.ca/Scanned/8-5/brown.pdf",
  acknowledgement = ack-nhfb,
  ajournal =     "Fib. Quart",
  fjournal =     "The Fibonacci Quarterly. Official Organ of the
                 Fibonacci Association",
}

@Article{Hamming:1970:DN,
  author =       "R. W. Hamming",
  title =        "On the Distribution of Numbers",
  journal =      j-BELL-SYST-TECH-J,
  volume =       "49",
  number =       "8",
  pages =        "1609--1625",
  month =        oct,
  year =         "1970",
  coden =        "BSTJAN",
  issn =         "0005-8580",
  issn-l =       "0005-8580",
  bibdate =      "Tue Nov 9 11:15:55 MST 2010",
  bibsource =    "http://bstj.bell-labs.com/oldfiles/year.1970/BSTJ.1970.4908.html;
                 http://www.alcatel-lucent.com/bstj/vol49-1970/bstj-vol49-issue08.html;
                 http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  url =          "http://bstj.bell-labs.com/BSTJ/images/Vol49/bstj49-8-1609.pdf;
                 http://www.alcatel-lucent.com/bstj/vol49-1970/articles/bstj49-8-1609.pdf",
  abstract =     "This paper examines the distribution of the mantissas
                 of floating-point numbers and shows how the arithmetic
                 operations of a computer transform various
                 distributions toward the limiting distribution $$r(x) =
                 1/(x \ln b) \qquad (1/b \leq x \leq 1)$$ (where $b$ is
                 the base of the number system). The paper also gives a
                 number of applications to hardware, software, and
                 general computing which show that this distribution is
                 not merely an amusing curiosity. A brief examination of
                 the distribution of exponents is include.",
  acknowledgement = ack-nhfb,
  fjournal =     "The Bell System Technical Journal",
}

@Article{Hill:1970:ZLP,
  author =       "Bruce M. Hill",
  title =        "{Zipf}'s law and prior distributions for the
                 composition of a population",
  journal =      j-J-AM-STAT-ASSOC,
  volume =       "65",
  number =       "331",
  pages =        "1220--1232",
  month =        sep,
  year =         "1970",
  coden =        "JSTNAL",
  issn =         "0162-1459 (print), 1537-274X (electronic)",
  issn-l =       "0162-1459",
  mrclass =      "62.35",
  mrnumber =     "0279936 (43 \#5657)",
  mrreviewer =   "I. J. Good",
  bibdate =      "Sat Nov 12 09:13:23 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 http://www.math.utah.edu/pub/tex/bib/jamstatassoc.bib",
  url =          "http://www.jstor.org/stable/2284288",
  zmnumber =     "Zbl 0224.92011",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of the American Statistical Association",
}

@Article{Orlov:1970:GZM,
  author =       "Ju. K. Orlov",
  title =        "A generalization of the {Zipf--Mandelbrot} law",
  journal =      "Sakharthvelos SSR Mecnierebatha Akademiis Moambe",
  volume =       "57",
  pages =        "37--40",
  year =         "1970",
  coden =        "????",
  issn =         "????",
  mrclass =      "94.50",
  mrnumber =     "0274234 (42 \#9109)",
  mrreviewer =   "T. Nemetz",
  bibdate =      "Sat Nov 12 09:13:23 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  ajournal =     "Sakharth. SSR Mech. Akad. Moambe",
}

@Article{Taguchi:1970:ZLC,
  author =       "Tokio Taguchi",
  title =        "On {Zipf}'s law. {A} characterization of distributions
                 in linguistics and demography",
  journal =      j-PROC-INST-STATIST-MATH,
  volume =       "17",
  pages =        "83--90",
  year =         "1970",
  coden =        "????",
  issn =         "0912-6112",
  issn-l =       "0912-6112",
  bibdate =      "Sat Nov 12 10:39:57 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  zmnumber =     "0238.68026",
  acknowledgement = ack-nhfb,
  ajournal =     "Proc. Inst. Statist. Math.",
  classmath =    "68Q45 (Formal languages)",
  fjournal =     "Proceedings of the Institute of Statistical
                 Mathematics",
  language =     "Japanese",
}

@Book{Zeller:1970:TLG,
  author =       "Karl Zeller and Wolfgang Beekmann",
  title =        "{Theorie der Limitierungsverfahren}. (German)
                 [{Theory} of limiting processes]",
  volume =       "15",
  publisher =    pub-SV,
  address =      pub-SV:adr,
  edition =      "Second",
  pages =        "xii + 314",
  year =         "1970",
  lccn =         "QA295 .Z4 1970",
  bibdate =      "Wed Nov 16 06:43:43 MST 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 z3950.loc.gov:7090/Voyager",
  series =       "Ergebnisse der Mathematik und ihrer Grenzgebiete",
  acknowledgement = ack-nhfb,
  language =     "German",
  subject =      "series; convergence",
}

@Article{Thorp:1971:PCD,
  author =       "E. Thorp and R. Whitley",
  title =        "{Poincar{\'e}}'s conjecture and the distribution of
                 digits in logarithm tables",
  journal =      j-COMPOS-MATH,
  volume =       "21",
  number =       "??",
  pages =        "233--250",
  month =        "????",
  year =         "1971",
  coden =        "CMPMAF",
  issn =         "0010-437X (print), 1570-5846 (electronic)",
  issn-l =       "0010-437X",
  bibdate =      "Sat Nov 12 16:36:41 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  ajournal =     "Comp. Math.",
  fjournal =     "Compositio Mathematica",
}

@Article{Wlodarski:1971:FLN,
  author =       "J. Wlodarski",
  title =        "{Fibonacci} and {Lucas} Numbers Tend to Obey
                 {Benford's Law}",
  journal =      j-FIB-QUART,
  volume =       "9",
  number =       "1",
  pages =        "87--88",
  month =        feb,
  year =         "1971",
  coden =        "FIBQAU",
  issn =         "0015-0517",
  issn-l =       "0015-0517",
  bibdate =      "Thu Oct 20 18:05:33 MDT 2011",
  bibsource =    "http://www.fq.math.ca/9-1.html;
                 http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 http://www.math.utah.edu/pub/tex/bib/fibquart.bib",
  url =          "http://www.fq.math.ca/Scanned/9-1/wlodarski2.pdf",
  acknowledgement = ack-nhfb,
  ajournal =     "Fib. Quart",
  fjournal =     "The Fibonacci Quarterly",
}

@Article{Aigner:1972:CEP,
  author =       "Dennis J. Aigner and Arthur S. Goldberger",
  title =        "Corrigenda: Estimation of {Pareto's Law} from Grouped
                 Observations",
  journal =      j-J-AM-STAT-ASSOC,
  volume =       "67",
  number =       "337",
  pages =        "252--252",
  month =        mar,
  year =         "1972",
  coden =        "JSTNAL",
  issn =         "0162-1459 (print), 1537-274X (electronic)",
  issn-l =       "0162-1459",
  bibdate =      "Wed Jan 25 08:05:45 MST 2012",
  bibsource =    "http://www.jstor.org/journals/01621459.html;
                 http://www.jstor.org/stable/i314217;
                 http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 http://www.math.utah.edu/pub/tex/bib/jamstatassoc1970.bib",
  url =          "http://www.jstor.org/stable/2284755",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of the American Statistical Association",
}

@Article{Krevitt:1972:CSZ,
  author =       "Beth Krevitt and Belver C. Griffith",
  title =        "A comparison of several {Zipf}-type distributions in
                 their goodness of fit to language data",
  journal =      j-J-AM-SOC-INF-SCI,
  volume =       "23",
  number =       "3",
  pages =        "220--221",
  year =         "1972",
  coden =        "AISJB6",
  doi =          "http://dx.doi.org/10.1002/asi.4630230310",
  issn =         "0002-8231 (print), 1097-4571 (electronic)",
  issn-l =       "0002-8231",
  bibdate =      "Mon Feb 25 06:13:56 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of the American Society for Information
                 Science",
}

@Article{Varian:1972:LEB,
  author =       "Hal R. Varian",
  title =        "Letter to the {Editor}: {Benford's Law}",
  journal =      j-AMER-STAT,
  volume =       "26",
  number =       "3",
  pages =        "65--66",
  month =        jun,
  year =         "1972",
  coden =        "ASTAAJ",
  issn =         "0003-1305 (print), 1537-2731 (electronic)",
  issn-l =       "0003-1305",
  bibdate =      "Fri Mar 30 11:34:37 2007",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/amstat.bib;
                 http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  url =          "http://links.jstor.org/sici?sici=0003-1305%28197206%2926%3A3%3C62%3ALTTE%3E2.0.CO%3B2-Q",
  abstract =     "Around 1938 the physicist Frank Benford observed a
                 rather strange fact: tables of logarithms in libraries
                 tend to be dirtier at the beginning than at the end.
                 This indicated to Benford that people had more occasion
                 to calculate with numbers beginning with 1 or 2 than
                 with 8 or 9.\par

                 Benford also found that the frequency of the digit $p$
                 being the first digit of a decimal number was very
                 closely approximated by $\log(p + 1) - \log p$ [i.e.,
                 $\log(1 + 1/p)$]. This has become known as Benford's
                 law.",
  acknowledgement = ack-nhfb,
  fjournal =     "The American Statistician",
  keywords =     "Benford's Law; Law of Anomalous Numbers; Zipf's Law",
}

@Article{Vlachy:1972:VFS,
  author =       "Jan Vlach{\'y}",
  title =        "Variable Factors in Scientific Communities
                 (Observations on {Lotka's Law})",
  journal =      "Teorie a Metoda",
  volume =       "4",
  number =       "??",
  pages =        "91--120",
  month =        "????",
  year =         "1972",
  coden =        "????",
  issn =         "????",
  bibdate =      "Fri Nov 25 07:53:43 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  xxvolume =     "6",
}

@Article{Whitney:1972:MNI,
  author =       "R. E. Whitney",
  title =        "Mathematical Notes: Initial Digits for the Sequence of
                 Primes",
  journal =      j-AMER-MATH-MONTHLY,
  volume =       "79",
  number =       "2",
  pages =        "150--152",
  month =        feb,
  year =         "1972",
  coden =        "AMMYAE",
  doi =          "http://dx.doi.org/10.2307/2316536",
  issn =         "0002-9890 (print), 1930-0972 (electronic)",
  issn-l =       "0002-9890",
  bibdate =      "Mon Jun 28 12:36:38 MDT 1999",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  fjournal =     "American Mathematical Monthly",
}

@Article{Wilkinson:1972:ABL,
  author =       "Elizabeth A. Wilkinson",
  title =        "The Ambiguity of {Bradford's Law}",
  journal =      j-J-DOC,
  volume =       "28",
  number =       "2",
  pages =        "122--130",
  month =        "????",
  year =         "1972",
  coden =        "JDOCAS",
  doi =          "http://dx.doi.org/10.1108/eb026534",
  issn =         "0022-0418 (print), 1758-7379 (electronic)",
  issn-l =       "0022-0418",
  bibdate =      "Fri Nov 25 07:20:34 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Documentation",
}

@TechReport{Diaconis:1973:LMI,
  author =       "Persi Diaconis",
  title =        "Limits of measures of the integers with applications
                 to random number generators and the distribution of
                 leading digits",
  type =         "Memorandum",
  number =       "NS-211",
  institution =  "Department of Statistics, Harvard University",
  address =      "Cambridge, MA, USA",
  day =          "22",
  month =        mar,
  year =         "1973",
  bibdate =      "Sat Nov 12 16:23:20 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
}

@Article{Kreifelts:1973:OBG,
  author =       "Thomas Kreifelts",
  title =        "{Optimale Basiswahl f{\"u}r eine
                 Gleitkomma-Arithmetik}. ({German}) [{Optimal} Choice of
                 Basis for a Floating-Point Arithmetic]",
  journal =      j-COMPUTING,
  volume =       "11",
  number =       "4",
  pages =        "353--363",
  month =        dec,
  year =         "1973",
  coden =        "CMPTA2",
  issn =         "0010-485X (print), 1436-5057 (electronic)",
  issn-l =       "0010-485X",
  bibdate =      "Tue Jan 2 17:40:51 MST 2001",
  bibsource =    "Compendex database;
                 garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt;
                 http://www.math.utah.edu/pub/tex/bib/benfords-law.bib
                 http://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 http://www.math.utah.edu/pub/tex/bib/computing.bib;
                 INSPEC Axiom database (1968--date)",
  note =         "See correction \cite{Kreifelts:1975:OBF}.",
  acknowledgement = ack-nj # " and " # ack-nhfb,
  affiliation =  "Inst. Numerische Datenverarbeitung, Bonn, West
                 Germany",
  classification = "723; 921; C5230",
  description =  "digital arithmetic",
  fjournal =     "Computing",
  journalabr =   "Comput (Vienna/NY)",
  keywords =     "base; computer programming; floating point arithmetic;
                 mathematical techniques; optimal choice; rounding
                 errors",
  language =     "German",
}

@Article{Kuipers:1973:RPD,
  author =       "L. Kuipers and Jau-shyong Shiue",
  title =        "Remark on a Paper by {Duncan} and {Brown} on the
                 Sequence of Logarithms of Certain Recursive Sequences",
  journal =      j-FIB-QUART,
  volume =       "11",
  number =       "3",
  pages =        "292--293",
  month =        oct,
  year =         "1973",
  coden =        "FIBQAU",
  issn =         "0015-0517",
  issn-l =       "0015-0517",
  bibdate =      "Thu Oct 20 17:58:42 MDT 2011",
  bibsource =    "http://www.fq.math.ca/11-3.html;
                 http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 http://www.math.utah.edu/pub/tex/bib/fibquart.bib",
  note =         "See \cite{Brown:1970:MOU}.",
  url =          "http://www.fq.math.ca/Scanned/11-3/kuipers.pdf",
  acknowledgement = ack-nhfb,
  ajournal =     "Fib. Quart",
  fjournal =     "The Fibonacci Quarterly. Official Organ of the
                 Fibonacci Association",
}

@Article{Murphy:1973:LLH,
  author =       "Larry J. Murphy",
  title =        "{Lotka's Law} in the Humanities?",
  journal =      j-J-AM-SOC-INF-SCI,
  volume =       "24",
  number =       "6",
  pages =        "461--462",
  month =        nov # "\slash " # dec,
  year =         "1973",
  coden =        "AISJB6",
  doi =          "http://dx.doi.org/10.1002/asi.4630240607",
  issn =         "0002-8231 (print), 1097-4571 (electronic)",
  issn-l =       "0002-8231",
  bibdate =      "Fri Nov 25 08:09:40 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of the American Society for Information
                 Science",
}

@Article{Petruszewycz:1973:LLE,
  author =       "M. Petruszewycz",
  title =        "{L'histoire} de la loi d'{Estoup--Zipf}: documents.
                 ({French}) [{The} history of the {Estoup--Zipf} law]",
  journal =      "Math. Sci. Humaines",
  volume =       "??",
  number =       "44",
  pages =        "41--56",
  year =         "1973",
  coden =        "????",
  issn =         "0025-5815",
  issn-l =       "0025-5815",
  mrclass =      "92A25",
  mrnumber =     "0354071 (50 \#6553)",
  mrreviewer =   "J. S. Joel",
  bibdate =      "Sat Nov 12 09:13:23 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Centre de Math{\'e}matique Sociale. \'Ecole Pratique
                 des Hautes \'Etudes. Math{\'e}matiques et Sciences
                 Humaines",
  language =     "French",
}

@Article{Sarkar:1973:OSD,
  author =       "B. P. Sarkar",
  title =        "An observation on the significant digits of the
                 binomial coefficients and factorials",
  journal =      j-SANKHYA-B,
  volume =       "35",
  number =       "??",
  pages =        "363--364",
  month =        "????",
  year =         "1973",
  coden =        "SANBBV",
  issn =         "0581-5738",
  issn-l =       "0581-5738",
  bibdate =      "Sat Nov 12 16:29:39 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  ajournal =     "Sankhya Ser. B (Indian J. of Statist.)",
  fjournal =     "Sankhy{\=a} (Indian Journal of Statistics), Series B.
                 Methodological",
}

@Article{Schatte:1973:VMG,
  author =       "Peter Schatte",
  title =        "{Zur Verteilung der Mantisse in der
                 Gleitkommadarstellung einer Zufallsgr{\"o}{\ss}e}.
                 ({German}) [Distribution of the mantissa in the
                 floating-point representation of a random variable]",
  journal =      j-Z-ANGE-MATH-MECH,
  volume =       "53",
  number =       "??",
  pages =        "553--565",
  month =        "????",
  year =         "1973",
  coden =        "ZAMMAX",
  issn =         "0044-2267 (print), 1521-4001 (electronic)",
  issn-l =       "0044-2267",
  bibdate =      "Mon Nov 14 16:35:28 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "{Zeitschrift f{\"u}r Angewandte Mathematik und
                 Mechanik}",
  language =     "German",
}

@Article{Sentance:1973:FAB,
  author =       "W. A. Sentance",
  title =        "A Further Analysis of {Benford's Law}",
  journal =      j-FIB-QUART,
  volume =       "11",
  number =       "5",
  pages =        "490--494",
  month =        dec,
  year =         "1973",
  coden =        "FIBQAU",
  issn =         "0015-0517",
  issn-l =       "0015-0517",
  bibdate =      "Thu Oct 20 17:58:46 MDT 2011",
  bibsource =    "http://www.fq.math.ca/11-5.html;
                 http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 http://www.math.utah.edu/pub/tex/bib/fibquart.bib",
  url =          "http://www.fq.math.ca/Scanned/11-5/sentance.pdf",
  acknowledgement = ack-nhfb,
  ajournal =     "Fib. Quart",
  fjournal =     "The Fibonacci Quarterly",
}

@Article{Banks:1974:AMN,
  author =       "William P. Banks and David K. Hill",
  title =        "The apparent magnitude of number scaled by random
                 production",
  journal =      j-J-EXP-PSYCH-GEN,
  volume =       "102",
  number =       "2",
  pages =        "353--376",
  month =        feb,
  year =         "1974",
  coden =        "JPGEDD",
  doi =          "http://psycnet.apa.org/doi/10.1037/h0035850",
  issn =         "0096-3445 (print), 1939-2222 (electronic)",
  issn-l =       "0096-3445",
  bibdate =      "Fri Feb 15 06:32:17 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  url =          "http://psycnet.apa.org/journals/xge/102/2/353/;
                 http://psycnet.apa.org/psycinfo/1974-24305-001",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Experimental Psychology: General",
}

@PhdThesis{Diaconis:1974:WSA,
  author =       "Persi Diaconis",
  title =        "Weak and Strong Averages in probability and the theory
                 numbers",
  type =         "{Ph.D.} thesis",
  school =       "Department of Statistics, Harvard University",
  address =      "Cambridge, MA, USA",
  pages =        "xvii + 117",
  year =         "1974",
  bibdate =      "Mon Nov 14 10:26:03 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
}

@Article{Duran:1974:ACS,
  author =       "J. Peter Duran",
  title =        "Almost convergence, summability and ergodicity",
  journal =      j-CAN-J-MATH,
  volume =       "26",
  number =       "??",
  pages =        "372--387",
  month =        "????",
  year =         "1974",
  coden =        "CJMAAB",
  doi =          "http://dx.doi.org/10.4153/CJM-1974-039-6",
  issn =         "0008-414X (print), 1496-4279 (electronic)",
  issn-l =       "0008-414X",
  bibdate =      "Sat Sep 10 15:38:45 MDT 2011",
  bibsource =    "http://cms.math.ca/cjm/v26/;
                 http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 http://www.math.utah.edu/pub/tex/bib/canjmath1970.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Canadian Journal of Mathematics = Journal canadien de
                 math{\'e}matiques",
  remark =       "In relation to Benford's Law, see theorem 6.2.",
}

@Article{Hill:1974:RFF,
  author =       "Bruce M. Hill",
  title =        "The rank-frequency form of {Zipf}'s law",
  journal =      j-J-AM-STAT-ASSOC,
  volume =       "69",
  number =       "348",
  pages =        "1017--1026",
  month =        dec,
  year =         "1974",
  coden =        "JSTNAL",
  issn =         "0162-1459 (print), 1537-274X (electronic)",
  issn-l =       "0162-1459",
  mrclass =      "62E15",
  mrnumber =     "0426242 (54 \#14188)",
  mrreviewer =   "S. M. Samuels",
  bibdate =      "Sat Nov 12 09:13:23 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 http://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 http://www.math.utah.edu/pub/tex/bib/jamstatassoc.bib",
  zmnumber =     "Zbl 0301.60011",
  acknowledgement = ack-nhfb,
  classification = "B0240 (Probability and statistics); C1140
                 (Probability and statistics)",
  corpsource =   "Dept. of Statistics, Univ. of Michigan, Ann Arbor, MI,
                 USA",
  fjournal =     "Journal of the American Statistical Association",
  keywords =     "Bose--Einstein allocation; distribution; random
                 processes; rank frequency form; statistics; Zipf's
                 law",
  treatment =    "T Theoretical or Mathematical",
}

@Book{Kuipers:1974:UDS,
  author =       "Lauwerens Kuipers and Harald Niederreiter",
  title =        "Uniform distribution of sequences",
  publisher =    pub-WILEY,
  address =      pub-WILEY:adr,
  pages =        "xiv + 390",
  year =         "1974",
  isbn =         "0-471-51045-9",
  isbn-13 =      "978-0-471-51045-1",
  lccn =         "QA292 .K84",
  bibdate =      "Sat Nov 12 15:42:53 MST 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 z3950.loc.gov:7090/Voyager",
  series =       "Pure and applied mathematics",
  acknowledgement = ack-nhfb,
  remark =       "``A Wiley-Interscience publication.''.",
  subject =      "Sequences (Mathematics); Uniform distribution
                 (Probability theory)",
}

@Article{Schorr:1974:LLL,
  author =       "Alan E. Schorr",
  title =        "{Lotka's Law} and Library Science",
  journal =      "RQ",
  volume =       "14",
  number =       "1",
  pages =        "32--33",
  month =        "Fall",
  year =         "1974",
  coden =        "????",
  issn =         "0033-7072",
  issn-l =       "0033-7072",
  bibdate =      "Fri Nov 25 08:12:46 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  ajournal =     "RQ",
  fjournal =     "Reference Quarterly",
}

@Unpublished{Singmaster:1974:RSB,
  author =       "D. Singmaster",
  title =        "Recurrent sequences and {Benford}'s law",
  year =         "1974",
  bibdate =      "Sat Nov 12 16:25:29 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  note =         "Preprint submitted to Fibonacci Quarterly in 1974, but
                 never published there.",
  acknowledgement = ack-nhfb,
}

@Article{Tsao:1974:DSD,
  author =       "Nai Kuan Tsao",
  title =        "On the Distributions of Significant Digits and
                 Roundoff Errors",
  journal =      j-CACM,
  volume =       "17",
  number =       "5",
  pages =        "269--271",
  month =        may,
  year =         "1974",
  coden =        "CACMA2",
  issn =         "0001-0782 (print), 1557-7317 (electronic)",
  issn-l =       "0001-0782",
  mrclass =      "65G05",
  mrnumber =     "49 6595",
  mrreviewer =   "N. N. Abdelmalek",
  bibdate =      "Mon Jan 22 07:26:38 MST 2001",
  bibsource =    "Compendex database;
                 ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 http://dblp.uni-trier.de/db/journals/cacm/cacm17.html#Tsao74;
                 http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  abstract =     "Generalized logarithmic law is derived for the
                 distribution of the first $t$ significant digits of a
                 random digital integer. This result is then used to
                 determine the distribution of the roundoff errors in
                 floating-point operations, which is a mixture of
                 uniform and reciprocal distributions.",
  acknowledgement = ack-nhfb,
  classcodes =   "C5230 (Digital arithmetic methods)",
  classification = "921",
  corpsource =   "Aerospace Res. Labs., Wright-Patterson AFB, OH, USA",
  fjournal =     "Communications of the ACM",
  journalabr =   "Commun ACM",
  keywords =     "Benford's Law; digital arithmetic; digital integer;
                 distributions; error analysis; floating point
                 operations; Law of Anomalous Numbers; logarithmic law;
                 mathematical techniques; mean value; random;
                 reciprocal; roundoff errors; significant digits;
                 uniform distribution; variance; Zipf's Law",
  oldlabel =     "Tsao74",
  treatment =    "T Theoretical or Mathematical",
  XMLdata =      "ftp://ftp.informatik.uni-trier.de/pub/users/Ley/bib/records.tar.gz#journals/cacm/Tsao74",
}

@Article{Voos:1974:LIS,
  author =       "Henry Voos",
  title =        "{Lotka} and Information Science",
  journal =      j-J-AM-SOC-INF-SCI,
  volume =       "25",
  number =       "4",
  pages =        "270--272",
  month =        jul # "\slash " # aug,
  year =         "1974",
  coden =        "AISJB6",
  issn =         "0002-8231 (print), 1097-4571 (electronic)",
  issn-l =       "0002-8231",
  bibdate =      "Fri Nov 25 08:14:01 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of the American Society for Information
                 Science",
  keywords =     "Lotka's Law",
}

@Article{Yavuz:1974:ZLE,
  author =       "Davras Yavuz",
  title =        "{Zipf}'s law and entropy",
  journal =      j-IEEE-TRANS-INF-THEORY,
  volume =       "20",
  number =       "5",
  pages =        "650--650",
  year =         "1974",
  coden =        "IETTAW",
  doi =          "http://dx.doi.org/10.1109/TIT.1974.1055269",
  issn =         "0018-9448 (print), 1557-9654 (electronic)",
  issn-l =       "0018-9448",
  bibdate =      "Sat Nov 12 10:43:30 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  zmnumber =     "0295.94048",
  acknowledgement = ack-nhfb,
  classmath =    "94A15 (General topics of information theory)",
  fjournal =     "IEEE Transactions on Information Theory",
}

@InProceedings{Bennett:1975:SDI,
  author =       "John M. Bennett",
  booktitle =    "Int. Comput. Symp. 1975, Proc., Antibes, (1975)",
  title =        "Storage design for information retrieval: {Scarrott}'s
                 conjecture and {Zipf}'s law",
  publisher =    "????",
  address =      "????",
  pages =        "233--237",
  year =         "1975",
  bibdate =      "Sat Nov 12 10:49:15 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  zmnumber =     "0322.68068",
  acknowledgement = ack-nhfb,
  classmath =    "68P20 (Information storage and retrieval) 68N01
                 (General)",
}

@Book{Hardy:1975:ITN,
  author =       "Godfrey H. Hardy and Edward M. Wright",
  title =        "An Introduction to the Theory of Numbers",
  publisher =    pub-CLARENDON,
  address =      pub-CLARENDON:adr,
  edition =      "Fourth",
  pages =        "421",
  year =         "1975",
  isbn =         "0-19-853310-1",
  isbn-13 =      "978-0-19-853310-8",
  lccn =         "????",
  bibdate =      "Fri Jun 24 12:32:14 2005",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
}

@Article{Hill:1975:SFZ,
  author =       "Bruce M. Hill and Michael Woodroofe",
  title =        "Stronger forms of {Zipf}'s law",
  journal =      j-J-AM-STAT-ASSOC,
  volume =       "70",
  number =       "349",
  pages =        "212--219",
  month =        mar,
  year =         "1975",
  coden =        "JSTNAL",
  issn =         "0162-1459 (print), 1537-274X (electronic)",
  issn-l =       "0162-1459",
  mrclass =      "62E15 (62D05)",
  mrnumber =     "0440763 (55 \#13633)",
  mrreviewer =   "I. J. Good",
  bibdate =      "Sat Nov 12 09:13:23 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 http://www.math.utah.edu/pub/tex/bib/jamstatassoc.bib",
  zmnumber =     "Zbl 0326.92014",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of the American Statistical Association",
}

@Article{Kemperman:1975:BDM,
  author =       "J. H. B. Kemperman",
  title =        "Bounds on the discrepancy modulo $1$ of a real random
                 variable",
  journal =      j-BULL-INST-MATH-STAT,
  volume =       "4",
  number =       "??",
  pages =        "138--??",
  month =        "????",
  year =         "1975",
  coden =        "SMBCVA",
  issn =         "0146-3942",
  issn-l =       "0146-3942",
  bibdate =      "Sat Nov 12 16:26:37 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  note =         "Abstract no. 75t-47.",
  acknowledgement = ack-nhfb,
  fjournal =     "Bulletin --- Institute of Mathematical Statistics",
}

@Article{Kreifelts:1975:OBF,
  author =       "T. Kreifelts",
  title =        "{Optimale Basiswahl f{\"u}r eine Gleitkomma-Arithmetik
                 (Berichtigung)} ({German}) {Optimal Basis Choice for a
                 Floating-Point Arithmetic (Correction)}",
  journal =      j-COMPUTING,
  volume =       "14",
  number =       "3",
  pages =        "313--314",
  month =        sep,
  year =         "1975",
  coden =        "CMPTA2",
  issn =         "0010-485X (print), 1436-5057 (electronic)",
  issn-l =       "0010-485X",
  bibdate =      "Fri Sep 16 16:30:39 1994",
  bibsource =    "garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt;
                 http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 http://www.math.utah.edu/pub/tex/bib/computing.bib;
                 http://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "See \cite{Kreifelts:1973:OBG}.",
  acknowledgement = ack-nj,
  fjournal =     "Computing",
  language =     "German",
}

@Article{Partridge:1975:DDW,
  author =       "D. Partridge",
  title =        "A dynamic database which automatically removes
                 unwanted generalisation for the efficient analysis of
                 language features that exhibit a disparate frequency
                 distribution",
  journal =      j-COMP-J,
  volume =       "18",
  number =       "1",
  pages =        "43--48",
  month =        feb,
  year =         "1975",
  coden =        "CMPJA6",
  issn =         "0010-4620 (print), 1460-2067 (electronic)",
  issn-l =       "0010-4620",
  bibdate =      "Tue Mar 25 13:51:56 MST 1997",
  bibsource =    "Compendex database;
                 http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_18/Issue_01/",
  url =          "http://www3.oup.co.uk/computer_journal/hdb/Volume_18/Issue_01/tiff/43.tif;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_18/Issue_01/tiff/44.tif;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_18/Issue_01/tiff/45.tif;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_18/Issue_01/tiff/46.tif;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_18/Issue_01/tiff/47.tif;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_18/Issue_01/tiff/48.tif",
  abstract =     "A self-organising database was developed as part of a
                 general language analysis system. The periodic,
                 automatic reorganisation of the database was aimed at
                 increasing the efficiency of analysis of a language in
                 which the constituent features exhibit a Zipfian type
                 rank-frequency relationship. Such a distribution means
                 that only a small number of features account for a
                 large proportion of the information, while a large
                 number of possible features are seldom encountered and
                 thus seldom accessed within the database. The mechanism
                 described aims at reconciling two conflicting
                 procedures: condensation by generalisation of language
                 features to minimise the total size of the database,
                 and the particularisation of the few commonly occurring
                 features to minimise the average analysis time. Results
                 are presented for the application of this mechanism to
                 the analysis of batches of FORTRAN programs that
                 constituted part of the `normal' workload for computers
                 within five different environments.",
  acknowledgement = ack-nhfb,
  classcodes =   "C6120 (File organisation); C7820 (Humanities
                 computing)",
  classification = "723",
  corpsource =   "Univ. Nairobi, Kenya",
  fjournal =     "The Computer Journal",
  keywords =     "analysis; data bases; data processing; disparate
                 frequency distribution; dynamic database; file
                 organisation; language; language translation and
                 linguistics; self organising; unwanted generalisation",
  treatment =    "P Practical",
}

@Article{Schorr:1975:LLH,
  author =       "Alan E. Schorr",
  title =        "{Lotka's Law} and the History of Legal Medicine",
  journal =      "Research in Librarianship",
  volume =       "30",
  number =       "??",
  pages =        "205--209",
  month =        sep,
  year =         "1975",
  coden =        "????",
  issn =         "0034-5245",
  issn-l =       "0034-5245",
  bibdate =      "Fri Nov 25 08:17:00 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  ajournal =     "Res. Librarianship",
}

@Article{Schorr:1975:LLM,
  author =       "Alan E. Schorr",
  title =        "{Lotka's Law} and Map Librarianship",
  journal =      j-J-AM-SOC-INF-SCI,
  volume =       "26",
  number =       "3",
  pages =        "189--190",
  month =        may # "\slash " # jun,
  year =         "1975",
  coden =        "AISJB6",
  issn =         "0002-8231 (print), 1097-4571 (electronic)",
  issn-l =       "0002-8231",
  bibdate =      "Fri Nov 25 08:11:19 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of the American Society for Information
                 Science",
}

@Article{Webb:1975:DFD,
  author =       "William Webb",
  title =        "Distribution of the First Digits of {Fibonacci}
                 Numbers",
  journal =      j-FIB-QUART,
  volume =       "13",
  number =       "4",
  pages =        "334--336",
  month =        dec,
  year =         "1975",
  coden =        "FIBQAU",
  issn =         "0015-0517",
  issn-l =       "0015-0517",
  bibdate =      "Thu Oct 20 17:59:03 MDT 2011",
  bibsource =    "http://www.fq.math.ca/13-4.html;
                 http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 http://www.math.utah.edu/pub/tex/bib/fibquart.bib",
  url =          "http://www.fq.math.ca/Scanned/13-4/webb.pdf",
  acknowledgement = ack-nhfb,
  ajournal =     "Fib. Quart",
  fjournal =     "The Fibonacci Quarterly",
  keywords =     "Benford's Law",
}

@Article{Woodroofe:1975:ZL,
  author =       "Michael Woodroofe and Bruce Hill",
  title =        "On {Zipf}'s law",
  journal =      j-J-APPL-PROBAB,
  volume =       "12",
  number =       "3",
  pages =        "425--434",
  month =        sep,
  year =         "1975",
  coden =        "JPRBAM",
  issn =         "0021-9002 (print), 1475-6072 (electronic)",
  issn-l =       "0021-9002",
  mrclass =      "62E20 (62P10)",
  mrnumber =     "0440764 (55 \#13634)",
  mrreviewer =   "I. J. Good",
  bibdate =      "Sat Nov 12 09:13:23 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  url =          "http://www.jstor.org/stable/3212857",
  zmnumber =     "Zbl 0343.60012",
  abstract =     "A Zipf's law is a probability distribution on the
                 positive integers which decays algebraically. Such laws
                 describe (approximately) a large class of phenomena. We
                 formulate a model for such phenomena and, in terms of
                 our model, give necessary and sufficient conditions for
                 a Zipf's law to hold.",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Applied Probability",
  keywords =     "classical occupancy problem; laws of large numbers:
                 weak convergence; regularly varying functions",
}

@Article{Worthen:1975:ABL,
  author =       "Dennis B. Worthen",
  title =        "The Application of {Bradford's Law} to Monographs",
  journal =      j-J-DOC,
  volume =       "31",
  number =       "1",
  pages =        "19--25",
  month =        "????",
  year =         "1975",
  coden =        "JDOCAS",
  doi =          "http://dx.doi.org/10.1108/eb026590",
  issn =         "0022-0418 (print), 1758-7379 (electronic)",
  issn-l =       "0022-0418",
  bibdate =      "Fri Nov 25 07:18:55 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Documentation",
}

@Article{Billera:1976:PSC,
  author =       "Louis J. Billera and Robert E. Bixby",
  title =        "{Pareto} Surfaces of Complexity $1$",
  journal =      j-SIAM-J-APPL-MATH,
  volume =       "30",
  number =       "1",
  pages =        "81--89",
  month =        jan,
  year =         "1976",
  coden =        "SMJMAP",
  issn =         "0036-1399 (print), 1095-712X (electronic)",
  issn-l =       "0036-1399",
  bibdate =      "Thu Oct 15 18:16:06 MDT 1998",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 http://www.math.utah.edu/pub/tex/bib/siamjapplmath.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  classification = "B0250 (Combinatorial mathematics); C1160
                 (Combinatorial mathematics)",
  corpsource =   "Dept. of Math., Cornell Univ., Ithaca, NY, USA",
  fjournal =     "SIAM Journal on Applied Mathematics",
  keywords =     "1-commodity representation; attainable sets;
                 complexity 1; game theory; graph theory; Pareto
                 surfaces; set theory",
  treatment =    "T Theoretical or Mathematical",
}

@Article{Brambilla:1976:DDA,
  author =       "Francisco Brambilla",
  title =        "La distribuzione delle aziende secondo le dimensioni.
                 {Verifica} empirica della legge logonormale e di quella
                 di {Zipf} e nuovi modelli interpretativi. ({Italian})
                 [{The} distribution of firms by size. {Empirical} test
                 of the log-normal law and {Zipf}'s law and new models
                 of interpretation]",
  journal =      "Giornale degli Economisti e Annali de Economia (Nuova
                 Serie)",
  volume =       "35",
  number =       "3--4",
  pages =        "131--153, 235",
  month =        mar # "\slash " # apr,
  year =         "1976",
  coden =        "????",
  issn =         "0017-0097",
  issn-l =       "0017-0097",
  mrclass =      "90A15",
  mrnumber =     "0452510 (56 \#10789)",
  bibdate =      "Sat Nov 12 09:13:23 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  url =          "http://www.jstor.org/stable/23242834",
  acknowledgement = ack-nhfb,
  ajournal =     "Giorn. Econom. Ann. Econom. (N.S.)",
  fjournal =     "Giornale degli Economisti e Annali de Economia",
  language =     "Italian",
}

@Article{Cohen:1976:EFD,
  author =       "Daniel I. A. Cohen",
  title =        "An explanation of the first digit phenomenon",
  journal =      j-J-COMB-THEORY-A,
  volume =       "20",
  number =       "3",
  pages =        "367--370",
  month =        may,
  year =         "1976",
  coden =        "JCBTA7",
  issn =         "0097-3165",
  issn-l =       "0097-3165",
  bibdate =      "Thu Feb 15 16:29:51 2007",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Combinatorial Theory (Series A)",
  keywords =     "Benford's Law; Law of Anomalous Numbers; Zipf's Law",
}

@Article{Davis:1976:SRI,
  author =       "Basil Davis",
  title =        "Some Remarks on Initial Digits",
  journal =      j-FIB-QUART,
  volume =       "14",
  number =       "1",
  pages =        "13--14",
  month =        feb,
  year =         "1976",
  coden =        "FIBQAU",
  issn =         "0015-0517",
  issn-l =       "0015-0517",
  bibdate =      "Thu Oct 20 17:59:05 MDT 2011",
  bibsource =    "http://www.fq.math.ca/14-1.html;
                 http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 http://www.math.utah.edu/pub/tex/bib/fibquart.bib",
  url =          "http://www.fq.math.ca/Scanned/14-1/davis.pdf",
  acknowledgement = ack-nhfb,
  ajournal =     "Fib. Quart",
  fjournal =     "The Fibonacci Quarterly",
}

@Article{Feldstein:1976:CED,
  author =       "Alan Feldstein and Richard Goodman",
  title =        "Convergence Estimates for the Distribution of Trailing
                 Digits",
  journal =      j-J-ACM,
  volume =       "23",
  number =       "2",
  pages =        "287--297",
  month =        apr,
  year =         "1976",
  coden =        "JACOAH",
  doi =          "http://doi.acm.org/10.1145/321941.321948",
  issn =         "0004-5411 (print), 1557-735X (electronic)",
  issn-l =       "0004-5411",
  bibdate =      "Wed Jan 15 18:12:53 MST 1997",
  bibsource =    "Compendex database;
                 http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  abstract =     "An analysis is made of the distribution of trailing
                 digits (tail end digits) of positive real
                 floating-point numbers represented in arbitrary base
                 $\beta$ and randomly chosen from a logarithmic
                 distribution. The analysis shows that the $n$th digit
                 for $n \geq 2$ is actually approximately uniformly
                 distributed. The approximation depends upon both $n$
                 and the base beta. It becomes better as $n$ increases,
                 and it is exact in the limit as $n \rightarrow \infty$.
                 A table of this distribution is presented for various
                 $\beta$ and $n$, along with a table of the maximum
                 digit by digit deviation $\Delta$ of the logarithmic
                 distribution from the uniform distribution. Various
                 asymptotic results for $\Delta$ are included.",
  acknowledgement = ack-nhfb,
  classification = "723",
  fjournal =     "Journal of the Association for Computing Machinery",
  journalabr =   "J Assoc Comput Mach",
  keywords =     "Benford's Law; computer arithmetic; computer
                 programming; Law of Anomalous Numbers; Zipf's Law",
}

@Article{Orlov:1976:CBP,
  author =       "Ju. K. Orlov",
  title =        "The connection between the {Pareto} distribution and
                 the generalized {Zipf--Mandelbrot} law",
  journal =      "Sakharthvelos SSR Mecnierebatha Akademiis Moambe",
  volume =       "83",
  number =       "1",
  pages =        "57--60",
  year =         "1976",
  coden =        "????",
  issn =         "????",
  mrclass =      "90A15",
  mrnumber =     "0434355 (55 \#7321)",
  mrreviewer =   "S. Krcevinac",
  bibdate =      "Sat Nov 12 09:13:23 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  ajournal =     "Sakharth. SSR Mech. Akad. Moambe",
}

@Article{Raimi:1976:FDP,
  author =       "Ralph A. Raimi",
  title =        "The first digit problem",
  journal =      j-AMER-MATH-MONTHLY,
  volume =       "83",
  number =       "7",
  pages =        "521--538",
  month =        aug # "\slash " # sep,
  year =         "1976",
  coden =        "AMMYAE",
  doi =          "http://dx.doi.org/10.2307/2319349",
  issn =         "0002-9890 (print), 1930-0972 (electronic)",
  issn-l =       "0002-9890",
  bibdate =      "Sat Nov 12 15:49:53 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  url =          "http://www.jstor.org/stable/2319349",
  acknowledgement = ack-nhfb,
  fjournal =     "American Mathematical Monthly",
  remark =       "This article surveys the literature up to 1976,
                 reports defects in several earlier mathematical
                 `explanations' of Benford's Law, and gives a 52-entry
                 bibliography of prior work. All of those entries are
                 incorporated in this bibliography. It criticizes parts
                 of \cite{Goudsmit:1944:SFN} as `dead wrong' (and the
                 author reiterates that view in \cite{Raimi:1985:FDP}.
                 See also later work \cite{Logan:1978:FDP}. On page 529,
                 Raimi writes ``If the first digits of all the tables in
                 the universe obey some fixed distribution law,
                 Stigler's or Benford's or some other, that law must
                 surely be independent of the system of units chosen,
                 since God is not known to favor either the metric
                 system or the English system. In other words, a
                 universal first digit law, if it exists, must be
                 scale-invariant.''",
  remark-2 =     "This is so far the second earliest reference that I
                 have found to \cite{Newcomb:1881:NFU}; the earliest is
                 \cite{Boring:1920:LNL}, which has only brief mention of
                 the question of digit frequencies. Raimi comments on p.
                 522: ``This assertion, whatever it may mean, will be
                 called Benford's Law because it has been thought by
                 many writers to have originated with the General
                 Electric Company physicist Frank Benford [2]. Certainly
                 Benford popularized the problem, and he may well have
                 been unaware that the polymathic Simon Newcomb,
                 primarily an astronomer but also sometime editor of The
                 American Journal of Mathematics, had also formulated
                 the same law 57 years earlier [1]. There is ample
                 precedent for naming laws and theorems for persons
                 other than their discoverers, else half of analysis
                 would be named after Euler. Besides, even Newcomb
                 implied that the observation giving rise to the Benford
                 law was an old one in his day. One would hate to change
                 the name of the law now only to find later that another
                 change was called for.''",
}

@Article{Rouault:1976:PAE,
  author =       "Alain Rouault",
  title =        "Propri{\'e}t{\'e}s asymptotiques d'un
                 {$n$}-{\'e}chantillon d'une variable al{\'e}atoire
                 d{\'e}nombrable connues sous le nom de lois de {Zipf}.
                 ({French}) [Asymptotic properties of an $n$-sample of a
                 denumerable random variable known under the name of
                 {Zipf}'s law]",
  journal =      j-C-R-ACAD-SCI-PARIS-SER-AB,
  volume =       "283",
  number =       "6",
  pages =        "Aiv, A379--A380",
  year =         "1976",
  coden =        "CHASAP",
  issn =         "0151-0509",
  issn-l =       "0151-0509",
  mrclass =      "62E20",
  mrnumber =     "0423644 (54 \#11619)",
  bibdate =      "Sat Nov 12 09:13:23 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Comptes Rendus Hebdomadaires des S{\'e}ances de
                 l'Acad{\'e}mie des Sciences. S{\'e}ries A et B",
  language =     "French",
}

@Article{Rouault:1976:SML,
  author =       "Alain Rouault",
  title =        "Sources markoviennes et lois de {Zipf}. ({French})
                 [{Markovian} source and {Zipf} laws]",
  journal =      j-C-R-ACAD-SCI-PARIS-SER-AB,
  volume =       "283",
  number =       "10",
  pages =        "Aiii, A789--A790",
  year =         "1976",
  coden =        "CHASAP",
  issn =         "0151-0509",
  issn-l =       "0151-0509",
  mrclass =      "62E20",
  mrnumber =     "0423645 (54 \#11620)",
  bibdate =      "Sat Nov 12 09:13:23 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Comptes Rendus Hebdomadaires des S{\'e}ances de
                 l'Acad{\'e}mie des Sciences. S{\'e}ries A et B",
  language =     "French",
}

@Article{Vlachy:1976:TFL,
  author =       "Jan Vlach{\'y}",
  title =        "Time Factor in {Lotka's Law}",
  journal =      "Probleme de Informare si Documentare",
  volume =       "10",
  number =       "2",
  pages =        "44--87",
  month =        "????",
  year =         "1976",
  coden =        "PIDCA6",
  issn =         "0032-924X",
  issn-l =       "0032-924X",
  bibdate =      "Fri Nov 25 07:56:00 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  ajournal =     "Prob. inf. \& doc.",
}

@Article{Brookes:1977:TBL,
  author =       "Bertram C. Brookes",
  title =        "Theory of the {Bradford Law}",
  journal =      j-J-DOC,
  volume =       "33",
  number =       "3",
  pages =        "180--209",
  month =        "????",
  year =         "1977",
  coden =        "JDOCAS",
  doi =          "http://dx.doi.org/10.1108/eb026641",
  issn =         "0022-0418 (print), 1758-7379 (electronic)",
  issn-l =       "0022-0418",
  bibdate =      "Fri Nov 25 07:16:18 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Documentation",
}

@Article{Clark:1977:ESL,
  author =       "Douglas W. Clark and C. Cordell Green",
  title =        "An Empirical Study of List Structure in {Lisp}",
  journal =      j-CACM,
  volume =       "20",
  number =       "2",
  pages =        "78--87",
  month =        feb,
  year =         "1977",
  coden =        "CACMA2",
  issn =         "0001-0782 (print), 1557-7317 (electronic)",
  issn-l =       "0001-0782",
  bibdate =      "Mon Jan 22 06:31:28 MST 2001",
  bibsource =    "Compendex database;
                 ftp://ftp.ira.uka.de/pub/bibliography/Compiler/garbage.collection.bib;
                 http://dblp.uni-trier.de/db/journals/cacm/cacm20.html#ClarkG77;
                 http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  abstract =     "Static measurements of the list structure of five
                 large Lisp programs are reported and analyzed. These
                 measurements reveal substantial regularity, or
                 predictability, among pointers to atoms and especially
                 among pointers to lists. Pointers to atoms are found to
                 obey, roughly, Zipf's law, which governs word
                 frequencies in natural languages; pointers to lists
                 usually point to a location physically nearby in
                 memory. The use of such regularities in the
                 space-efficient representation of list structure is
                 discussed.",
  acknowledgement = ack-nhfb,
  classcodes =   "C6130 (Data handling techniques); C6140D (High level
                 languages)",
  classification = "723",
  comment =      "Great paper; evidence pro CDR-coding, con fancy CONS",
  corpsource =   "Carnegie-Mellon Univ., Pittsburgh, PA, USA",
  fjournal =     "Communications of the ACM",
  journalabr =   "Commun ACM",
  keywords =     "computer programming languages; data processing ---
                 Data Structures; empirical study; LISP; list structure;
                 measurements; regularity",
  oldlabel =     "ClarkG77",
  treatment =    "P Practical",
  XMLdata =      "ftp://ftp.informatik.uni-trier.de/pub/users/Ley/bib/records.tar.gz#journals/cacm/ClarkG77",
}

@Article{Coile:1977:LFD,
  author =       "Russell C. Coile",
  title =        "{Lotka}'s Frequency Distribution of Scientific
                 Productivity",
  journal =      j-J-AM-SOC-INF-SCI,
  volume =       "28",
  number =       "6",
  pages =        "366--370",
  month =        nov,
  year =         "1977",
  coden =        "AISJB6",
  issn =         "0002-8231 (print), 1097-4571 (electronic)",
  issn-l =       "0002-8231",
  bibdate =      "Fri Nov 25 08:08:19 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of the American Society for Information
                 Science",
  keywords =     "Lotka's Law",
}

@Article{Diaconis:1977:DLD,
  author =       "Persi Diaconis",
  title =        "The distribution of leading digits and uniform
                 distribution $\bmod 1$",
  journal =      j-ANN-PROBAB,
  volume =       "5",
  number =       "1",
  pages =        "72--81",
  month =        "????",
  year =         "1977",
  coden =        "APBYAE",
  doi =          "http://dx.doi.org/10.1214/aop/1176995891",
  issn =         "0091-1798",
  issn-l =       "0091-1798",
  bibdate =      "Sat Nov 12 15:30:53 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Annals of Probability",
}

@Article{Ylvisaker:1977:TR,
  author =       "Donald Ylvisaker",
  title =        "Test Resistance",
  journal =      j-J-AM-STAT-ASSOC,
  volume =       "72",
  number =       "359",
  pages =        "551--556",
  month =        sep,
  year =         "1977",
  coden =        "JSTNAL",
  issn =         "0162-1459 (print), 1537-274X (electronic)",
  issn-l =       "0162-1459",
  bibdate =      "Wed Jan 25 08:05:48 MST 2012",
  bibsource =    "http://www.jstor.org/journals/01621459.html;
                 http://www.jstor.org/stable/i314242;
                 http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 http://www.math.utah.edu/pub/tex/bib/jamstatassoc1970.bib",
  url =          "http://www.jstor.org/stable/2286216",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of the American Statistical Association",
}

@Article{Brady:1978:MBL,
  author =       "W. G. Brady",
  title =        "More on {Benford}'s Law",
  journal =      j-FIB-QUART,
  volume =       "16",
  number =       "1",
  pages =        "51--52",
  month =        feb,
  year =         "1978",
  coden =        "FIBQAU",
  issn =         "0015-0517",
  issn-l =       "0015-0517",
  bibdate =      "Thu Oct 20 17:59:24 MDT 2011",
  bibsource =    "http://www.fq.math.ca/16-1.html;
                 http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 http://www.math.utah.edu/pub/tex/bib/fibquart.bib",
  url =          "http://www.fq.math.ca/Scanned/16-1/brady.pdf",
  acknowledgement = ack-nhfb,
  ajournal =     "Fib. Quart",
  fjournal =     "The Fibonacci Quarterly",
}

@Article{Brookes:1978:FRD,
  author =       "Bertram C. Brookes and Jos{\'e} M. Griffiths",
  title =        "Frequency-rank distributions",
  journal =      j-J-AM-SOC-INF-SCI,
  volume =       "29",
  number =       "1",
  pages =        "5--13",
  month =        jan,
  year =         "1978",
  coden =        "AISJB6",
  doi =          "http://dx.doi.org/10.1002/asi.4630290104",
  issn =         "0002-8231 (print), 1097-4571 (electronic)",
  issn-l =       "0002-8231",
  bibdate =      "Mon Feb 25 10:40:13 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  url =          "http://onlinelibrary.wiley.com/doi/10.1002/asi.4630290104/abstract",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of the American Society for Information Science",
  keywords =     "Benford's Law; Anomalous Law of Numbers",
}

@PhdThesis{Chen:1978:ZL,
  author =       "Wen-Chen Chen",
  title =        "On {Zipf}'s law",
  type =         "Thesis ({Ph.D.})",
  school =       "University of Michigan",
  address =      "Ann Arbor, MI, USA",
  pages =        "114",
  year =         "1978",
  mrclass =      "Thesis",
  mrnumber =     "2627928",
  bibdate =      "Sat Nov 12 09:13:23 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  url =          "http://gateway.proquest.com/openurl?url_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:dissertation&res_dat=xri:pqdiss&rft_dat=xri:pqdiss:7822871",
  acknowledgement = ack-nhfb,
  remark =       "Available from ProQuest LLC, Ann Arbor, MI, USA.
                 Author given name appears as Wen-Cheng in MathSciNet
                 database.",
}

@Article{Elshoff:1978:SSC,
  author =       "James L. Elshoff",
  title =        "A study of the structural composition of {PL/I}
                 programs",
  journal =      j-SIGPLAN,
  volume =       "13",
  number =       "6",
  pages =        "29--37",
  month =        jun,
  year =         "1978",
  coden =        "SINODQ",
  doi =          "http://doi.acm.org/10.1145/987515.987518",
  issn =         "0362-1340 (print), 1523-2867 (print), 1558-1160
                 (electronic)",
  issn-l =       "0362-1340",
  bibdate =      "Wed Jun 18 16:08:52 MDT 2008",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  abstract =     "Some research on a theory of the structural
                 composition of an algorithm has recently been reported.
                 The theory embodies models of operator and operand
                 distributions that have been proposed by Bayer, Zipf,
                 and Zweben. This paper reports a study in which the
                 three models of operator distributions are compared
                 with the measured distributions found in 34 PL/I
                 programs. Two of three models, one by Zipf and one by
                 Zweben, are shown to correlate highly with the measured
                 distributions. Two variations of the Zipf model are
                 then formulated and tested with good results. Also, the
                 relationship between the method of counting operators
                 and the models is investigated.",
  acknowledgement = ack-nhfb,
  classification = "C4240 (Programming and algorithm theory); C6140D
                 (High level languages)",
  corpsource =   "Computer Sci. Dept., General Motors Res. Labs.,
                 Warren, MI, USA",
  fjournal =     "ACM SIG{\-}PLAN Notices",
  keywords =     "counting operators; operator distributions; PL/1; PL/1
                 programs; programming theory; structural composition",
  treatment =    "T Theoretical or Mathematical",
}

@Book{Heaps:1978:IRC,
  author =       "Harold Stanley Heaps",
  title =        "Information retrieval, computational and theoretical
                 aspects",
  publisher =    pub-ACADEMIC,
  address =      pub-ACADEMIC:adr,
  pages =        "xii + 344",
  year =         "1978",
  isbn =         "0-12-335750-0",
  isbn-13 =      "978-0-12-335750-2",
  lccn =         "Z699 .H38",
  bibdate =      "Sat Nov 12 11:36:39 MST 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 z3950.loc.gov:7090/Voyager",
  series =       "Library and information science",
  acknowledgement = ack-nhfb,
  remark =       "Heaps's Law is given on pp. 206--208.",
  subject =      "Information storage and retrieval systems",
}

@Article{Logan:1978:FDP,
  author =       "Jonothan L. Logan and Samuel A. Goudsmit",
  title =        "The First Digit Phenomenon",
  journal =      j-PROC-AMER-PHIL-SOC,
  volume =       "122",
  number =       "4",
  pages =        "193--197",
  day =          "18",
  month =        aug,
  year =         "1978",
  coden =        "PAPCAA",
  issn =         "0003-049X",
  issn-l =       "0003-049X",
  bibdate =      "Fri Mar 30 11:20:35 2007",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  note =         "This paper contains derivations of both Stigler's Law
                 and Benford's Law, and receives strong criticism in
                 \cite{Raimi:1985:FDP}. This paper contains an important
                 historical note that is recorded in entry
                 \cite{Benford:1938:LAN}.",
  url =          "http://links.jstor.org/sici?sici=0003-049X(19780818)122%3A4%3C193%3ATFDP%3E2.0.CO%3B2-C;
                 http://www.jstor.org/stable/986530",
  abstract =     "Forty years ago an article appeared in these
                 Proceedings, which has since then attracted much
                 attention of mathematicians and some physicists. It was
                 written by Frank Benford, a physicist from the General
                 Electric Company at Schenectady. He had examined a
                 large number of numerical tables, the kind that are
                 printed in almanacs, and in scientific and technical
                 handbooks. He noticed a most unusual and unexpected
                 property of many of these tables. Consider, for
                 example, the numbers representing the populations of
                 states or all the countries in the world, or their
                 areas, their budgets, their numbers of hospital beds,
                 etc. One would expect that on the average just as many
                 of these entries would begin with the digit $1$ as with
                 $2$ or $3$ or $4$, and so on. But Benford noticed that
                 small values of the first digits occur far more
                 often.",
  acknowledgement = ack-nhfb,
  author-dates = "Samuel A. Goudsmit (July 11, 1902--December 4, 1978)",
  fjournal =     "Proceedings of the {American Philosophical Society}
                 held at {Philadelphia} for promoting useful knowledge",
  remark =       "In 1925, Samuel Goudsmit and George Uhlenbeck proposed
                 the concept of electron spin, a critical step forward
                 in the quantum mechanics of many-electron systems.
                 Surprisingly, that work did not get them the Nobel
                 Prize, but it did spur Wolfgang Pauli to present his
                 Exclusion Principle in 1925, for which he received the
                 1945 Nobel Prize in Physics. After World War II,
                 Goudsmit was the scientific head of the Alsos mission
                 to capture German nuclear scientists. In the 1950s, he
                 founded the journal Physical Review Letters. During the
                 1960s and 1970s, he was Editor-in-Chief of the main
                 American physics journal, the Physical Review.",
}

@Article{Rouault:1978:LZS,
  author =       "Alain Rouault",
  title =        "Lois de {Zipf} et sources markoviennes. ({French})
                 [{Zipf}'s law and {Markovian} sources]",
  journal =      "Ann. Inst. H. Poincar{\'e} Sect. B (N.S.)",
  volume =       "14",
  number =       "2",
  pages =        "169--188",
  year =         "1978",
  coden =        "AHPBAR",
  issn =         "0020-2347",
  issn-l =       "0020-2347",
  mrclass =      "62E99 (60J20 62P99)",
  mrnumber =     "507732 (80c:62026a)",
  mrreviewer =   "Bruce M. Hill",
  bibdate =      "Sat Nov 12 09:13:23 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Annales de l'Institut Henri Poincar{\'e}. Section B.
                 Calcul des Probabilit{\'e}s et Statistique. Nouvelle
                 S{\'e}rie",
  language =     "French",
}

@Article{Samson:1978:STU,
  author =       "W. B. Samson and R. H. Davis",
  title =        "Search Times Using Hash Tables for Records with
                 Non-Unique Keys",
  journal =      j-COMP-J,
  volume =       "21",
  number =       "3",
  pages =        "210--214",
  month =        aug,
  year =         "1978",
  coden =        "CMPJA6",
  issn =         "0010-4620 (print), 1460-2067 (electronic)",
  issn-l =       "0010-4620",
  bibdate =      "Tue Mar 25 13:51:56 MST 1997",
  bibsource =    "Compendex database;
                 http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 http://www.math.utah.edu/pub/tex/bib/hash.bib;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_21/Issue_03/",
  url =          "http://www3.oup.co.uk/computer_journal/hdb/Volume_21/Issue_03/tiff/210.tif;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_21/Issue_03/tiff/211.tif;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_21/Issue_03/tiff/212.tif;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_21/Issue_03/tiff/213.tif;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_21/Issue_03/tiff/214.tif",
  abstract =     "Recent research in hash coding has concentrated on
                 unique keys, or uniform distributions of keys. This
                 paper is intended to clarify the effect of non-unique
                 keys with various distributions on search times in the
                 hash table thus enabling recommendations to be made to
                 those who must deal with hash tables of this type. It
                 is found that extreme rank-order frequency distribution
                 of keys, such as the Zipf distribution, result in much
                 higher access times than more uniform distributions,
                 but it is possible to reduce these to some extent by
                 loading records with common keys on to the hash table
                 first.",
  acknowledgement = ack-nhfb,
  classcodes =   "C6120 (File organisation); C6130 (Data handling
                 techniques)",
  classification = "723",
  corpsource =   "Dept. of Math. and Computer Studies, Dundee Coll. of
                 Technol., Dundee, UK",
  fjournal =     "The Computer Journal",
  journalabr =   "Comput J",
  keywords =     "common keys; compiler symbol; computer programming;
                 data handling; data processing --- Data Structures;
                 direct access files; distribution; extreme; file
                 organisation; hash tables; higher access times; non
                 unique keys; overflow method; rank order frequency
                 distribution of keys; records; search times;
                 simulation; tables; uniform distributions; Zipf",
  treatment =    "T Theoretical or Mathematical",
}

@Article{Diaconis:1979:RP,
  author =       "Persi Diaconis and David Freedman",
  title =        "On Rounding Percentages",
  journal =      j-J-AM-STAT-ASSOC,
  volume =       "74",
  number =       "366",
  pages =        "359--364",
  month =        jun,
  year =         "1979",
  coden =        "JSTNAL",
  issn =         "0162-1459 (print), 1537-274X (electronic)",
  issn-l =       "0162-1459",
  bibdate =      "Wed Nov 23 11:24:59 2011",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/b/bethe-hans.bib;
                 http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 http://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 http://www.math.utah.edu/pub/tex/bib/jamstatassoc.bib",
  note =         "The authors extend prior work on correctness of sums
                 of rounded percentages \cite{Mosteller:1967:DSR}, and
                 criticize biased rounding practices in
                 \cite{Benford:1938:LAN}.",
  url =          "http://www.jstor.org/stable/2284288",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of the American Statistical Association",
  keywords =     "Benford's Law",
  remark =       "When percentage-column entries are rounded, their sum
                 may differ from 100\%. The authors use a prior proof
                 \cite{Mosteller:1967:DSR} that for $n \gg 2$ rounded
                 values, the probability of a correct sum is $\sqrt{6 /
                 (\pi n)} \approx 1.382 / \sqrt{n}$. They show that
                 rounding may produce large changes in computed
                 chi-squared values, and they conclude their article
                 with this recommendation: ``it is important to
                 calculate with many-digit accuracy when computing
                 $\chi^2$ for large sample sizes.''",
}

@Article{Mohanty:1979:MMQ,
  author =       "Siba N. Mohanty",
  title =        "Models and Measurements for Quality Assessment of
                 Software",
  journal =      j-COMP-SURV,
  volume =       "11",
  number =       "3",
  pages =        "251--275",
  month =        sep,
  year =         "1979",
  coden =        "CMSVAN",
  doi =          "http://doi.acm.org/10.1145/356778.356783",
  issn =         "0010-4892",
  issn-l =       "0360-0300",
  bibdate =      "Thu Jun 19 09:25:12 MDT 2008",
  bibsource =    "ftp://ftp.ira.uka.de/pub/bibliography/Distributed/QLD/1979.bib;
                 http://www.acm.org/pubs/contents/journals/surveys/;
                 http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  note =         "See also \cite{Dunn:1980:SFW,Mohanty:1980:SFW}.",
  acknowledgement = ack-nhfb,
  annote =       "Several software quality assessment methods which span
                 the software life cycle are discussed. The quality of a
                 system design can be estimated by measuring the system
                 entropy function or the system work function. The
                 quality improvement due to reconfiguration can be
                 determined by calculating system entropy loading
                 measures. Software science and Zipf's law are shown to
                 be useful for estimating program length and
                 implementation time.",
  country =      "USA",
  date =         "11/10/79",
  descriptors =  "Software; design; software engineering; reliability;
                 measurement; model; fundamentals in statistics;
                 performance evaluation;",
  enum =         "2189",
  fjournal =     "ACM Computing Surveys",
  references =   "65",
}

@Article{Radhakrishnan:1979:LLC,
  author =       "T. Radhakrishnan and R. Kernizan",
  title =        "{Lotka's Law} and Computer Science Literature",
  journal =      j-J-AM-SOC-INF-SCI,
  volume =       "30",
  number =       "1",
  pages =        "51--54",
  month =        jan,
  year =         "1979",
  coden =        "AISJB6",
  doi =          "http://dx.doi.org/10.1002/asi.4630300109",
  issn =         "0002-8231 (print), 1097-4571 (electronic)",
  issn-l =       "0002-8231",
  bibdate =      "Fri Nov 25 07:45:09 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of the American Society for Information
                 Science",
  onlinedate =   "6 September 2007",
  remark =       "This paper analyzes publication statistics from
                 Communications of the Association for Computing
                 Machinery (CACM) and in the Journal of the ACM
                 (JACM).",
}

@Article{Vlachy:1979:FDS,
  author =       "Jan Vlach{\'y}",
  title =        "Frequency Distribution of Scientific Performance: a
                 Bibliography of {Lotka's Law} and Related Phenomena",
  journal =      j-SCIENTOMETRICS,
  volume =       "1",
  number =       "1",
  pages =        "109--130",
  month =        sep,
  year =         "1979",
  coden =        "SCNTDX",
  doi =          "http://dx.doi.org/10.1007/BF02016844",
  issn =         "0138-9130 (print), 1588-2861 (electronic)",
  issn-l =       "0138-9130",
  bibdate =      "Fri Nov 25 07:59:34 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  url =          "http://www.springerlink.com/content/0138-9130/",
  acknowledgement = ack-nhfb,
  fjournal =     "Scientometrics",
  xxjournal =    "Scientometrics, Bibliography Section",
}

@Article{Brookes:1980:FISa,
  author =       "Bertram C. Brookes",
  title =        "The foundations of information science. {Part I}.
                 {Philosophical} aspects",
  journal =      j-J-INFO-SCI-PRINCIPLES-PRACTICE,
  volume =       "2",
  number =       "3--4",
  pages =        "125--133",
  month =        jun,
  year =         "1980",
  coden =        "JISCDI",
  doi =          "http://dx.doi.org/10.1177/016555158000200302",
  issn =         "0165-5515 (print), 1741-6485 (electronic)",
  issn-l =       "0165-5515",
  bibdate =      "Mon Feb 25 10:36:18 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  url =          "http://jis.sagepub.com/content/2/3-4/125.abstract",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Information Science, Principles and Practice",
  keywords =     "Benford's Law; Anomalous Law of Numbers",
}

@Article{Brookes:1980:FISb,
  author =       "Bertram C. Brookes",
  title =        "The foundations of information science. {Part II}.
                 {Quantitative} aspects: classes of things and the
                 challenge of human individuality",
  journal =      j-J-INFO-SCI-PRINCIPLES-PRACTICE,
  volume =       "2",
  number =       "5",
  pages =        "209--221",
  month =        oct,
  year =         "1980",
  coden =        "JISCDI",
  doi =          "http://dx.doi.org/10.1177/016555158000200502",
  issn =         "0165-5515 (print), 1741-6485 (electronic)",
  issn-l =       "0165-5515",
  bibdate =      "Mon Feb 25 11:01:20 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  url =          "http://jis.sagepub.com/content/2/5/209.abstract",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Information Science, Principles and
                 Practice",
  keywords =     "Benford's Law; Anomalous Law of Numbers",
}

@Article{Brookes:1980:FISc,
  author =       "Bertram C. Brookes",
  title =        "The foundations of information science. {Part III}.
                 {Quantitative} aspects: Objective maps and subjective
                 landscapes",
  journal =      j-J-INFO-SCI-PRINCIPLES-PRACTICE,
  volume =       "2",
  number =       "6",
  pages =        "269--275",
  month =        dec,
  year =         "1980",
  coden =        "JISCDI",
  doi =          "http://dx.doi.org/10.1177/016555158000200602 ",
  issn =         "0165-5515 (print), 1741-6485 (electronic)",
  issn-l =       "0165-5515",
  bibdate =      "Mon Feb 25 10:36:18 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  url =          "http://jis.sagepub.com/content/2/6/269.abstract",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Information Science, Principles and Practice",
  keywords =     "Benford's Law; Anomalous Law of Numbers",
}

@Article{Chen:1980:WFZ,
  author =       "Wen Chen Chen",
  title =        "On the weak form of {Zipf}'s law",
  journal =      j-J-APPL-PROBAB,
  volume =       "17",
  number =       "3",
  pages =        "611--622",
  year =         "1980",
  coden =        "JPRBAM",
  issn =         "0021-9002 (print), 1475-6072 (electronic)",
  issn-l =       "0021-9002",
  mrclass =      "62E10 (62F10)",
  mrnumber =     "580021 (81m:62021)",
  mrreviewer =   "Patrick L. Brockett",
  bibdate =      "Sat Nov 12 09:13:23 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  url =          "http://www.jstor.org/stable/3212955",
  zmnumber =     "Zbl 0435.60017",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Applied Probability",
}

@Article{Dunn:1980:SFW,
  author =       "Stanley Dunn",
  title =        "Surveyor's Forum: {Working} on Interpretations",
  journal =      j-COMP-SURV,
  volume =       "12",
  number =       "2",
  pages =        "255--255",
  month =        jun,
  year =         "1980",
  coden =        "CMSVAN",
  doi =          "http://doi.acm.org/10.1145/356810.356817",
  issn =         "0010-4892",
  issn-l =       "0360-0300",
  bibdate =      "Thu Jun 19 09:27:10 MDT 2008",
  bibsource =    "http://www.acm.org/pubs/contents/journals/surveys/;
                 http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  note =         "See \cite{Mohanty:1979:MMQ,Mohanty:1980:SFW}.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Computing Surveys",
}

@Article{Leimkuhler:1980:EFB,
  author =       "Ferdinand F. Leimkuhler",
  title =        "An Exact Formulation of {Bradford's Law}",
  journal =      j-J-DOC,
  volume =       "36",
  number =       "4",
  pages =        "285--292",
  month =        "????",
  year =         "1980",
  coden =        "JDOCAS",
  doi =          "http://dx.doi.org/10.1108/eb026699",
  issn =         "0022-0418 (print), 1758-7379 (electronic)",
  issn-l =       "0022-0418",
  bibdate =      "Fri Nov 25 07:14:04 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  abstract =     "An exact, discrete formulation of Bradford's law
                 describing the distribution of articles in journals is
                 derived by showing that Bradford's law is a special
                 case of the Zipf--Mandelbrot `rank frequency' law. A
                 relatively simple method is presented for fitting the
                 model to empirical data and estimating the number of
                 journals and articles in a subject collection. This
                 method is demonstrated with an example application.",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Documentation",
}

@Article{McKee:1980:POR,
  author =       "Arnold F. McKee",
  title =        "The {Pareto} Optimum: Reconcilable with Social
                 Thought?",
  journal =      "International Journal of Social Economics",
  volume =       "7",
  number =       "7",
  pages =        "366--375",
  month =        "????",
  year =         "1980",
  coden =        "ISLEBC",
  doi =          "http://dx.doi.org/10.1108/eb013878",
  issn =         "0306-8293 (print), 1758-6712 (electronic)",
  issn-l =       "0306-8293",
  bibdate =      "Fri Nov 25 07:01:57 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
}

@Article{Mohanty:1980:SFW,
  author =       "Siba Mohanty",
  title =        "Surveyor's Forum: {Working} on Interpretations",
  journal =      j-COMP-SURV,
  volume =       "12",
  number =       "2",
  pages =        "256--256",
  month =        jun,
  year =         "1980",
  coden =        "CMSVAN",
  doi =          "http://doi.acm.org/10.1145/356810.356818",
  issn =         "0010-4892",
  issn-l =       "0360-0300",
  bibdate =      "Thu Jun 19 09:27:10 MDT 2008",
  bibsource =    "http://www.acm.org/pubs/contents/journals/surveys/;
                 http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  note =         "See \cite{Mohanty:1979:MMQ,Dunn:1980:SFW}.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Computing Surveys",
}

@Article{Brookes:1981:FIS,
  author =       "Bertram C. Brookes",
  title =        "The foundations of information science. {Part IV}.
                 {Information} science: the changing paradigm",
  journal =      j-J-INFO-SCI-PRINCIPLES-PRACTICE,
  volume =       "3",
  number =       "1",
  pages =        "3--12",
  month =        feb,
  year =         "1981",
  coden =        "JISCDI",
  doi =          "http://dx.doi.org/10.1177/016555158100300102",
  issn =         "0165-5515 (print), 1741-6485 (electronic)",
  issn-l =       "0165-5515",
  bibdate =      "Mon Feb 25 10:36:18 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  url =          "http://jis.sagepub.com/content/3/1/3",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Information Science, Principles and
                 Practice",
  keywords =     "Benford's Law; Anomalous Law of Numbers",
}

@Article{Kennard:1981:MDF,
  author =       "Robert W. Kennard and John E. Reith",
  title =        "{M32}. On the distribution of first digits",
  journal =      j-COMMUN-STAT-SIMUL-COMPUT,
  volume =       "10",
  number =       "1",
  pages =        "97--98",
  month =        "????",
  year =         "1981",
  coden =        "CSSCDB",
  doi =          "http://dx.doi.org/10.1080/03610918108812195",
  issn =         "0361-0918",
  issn-l =       "0361-0918",
  bibdate =      "Sat Jan 07 09:27:42 2012",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  url =          "http://www.tandfonline.com/doi/abs/10.1080/03610918108812195",
  acknowledgement = ack-nhfb,
  fjournal =     "Communications in Statistics: Simulation and
                 Computation",
  keywords =     "Benford's Law",
  onlinedate =   "27 Jun 2007",
}

@Article{Pavlov:1981:DFF,
  author =       "A. I. Pavlov",
  title =        "On the distribution of fractions and {F. Benford}'s
                 law",
  journal =      j-IZV-AKAD-NAUK-SSSR-MAT,
  volume =       "45",
  number =       "4",
  pages =        "760--774, 927",
  year =         "1981",
  coden =        "IZAMAT",
  issn =         "0373-2436",
  issn-l =       "0373-2436",
  mrclass =      "10K10",
  mrnumber =     "631437 (83m:10093)",
  mrreviewer =   "Michael Keane",
  bibdate =      "Sat Nov 12 09:13:23 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Izvestiia Akademii Nauk. USSR Seriia Matematicheskaia
                 (Moscow)",
  xxtitle =      "On the distribution mod one and {Benford}'s law",
}

@Article{Peters:1981:EFB,
  author =       "James V. Peters",
  title =        "An Equivalent Form of {Benford's Law}",
  journal =      j-FIB-QUART,
  volume =       "19",
  number =       "1",
  pages =        "74--76",
  month =        feb,
  year =         "1981",
  coden =        "FIBQAU",
  issn =         "0015-0517",
  issn-l =       "0015-0517",
  mrclass =      "60C05 (10K10 60-01)",
  mrnumber =     "606117 (82k:60024)",
  mrreviewer =   "L. E. Clarke",
  bibdate =      "Sat Nov 12 09:13:23 2011",
  bibsource =    "http://www.fq.math.ca/19-1.html;
                 http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 http://www.math.utah.edu/pub/tex/bib/fibquart.bib",
  url =          "http://www.fq.math.ca/Scanned/19-1/peters.pdf",
  acknowledgement = ack-nhfb,
  ajournal =     "Fib. Quart",
  fjournal =     "The Fibonacci Quarterly. Official Organ of the
                 Fibonacci Association",
}

@Article{Peters:1981:SCC,
  author =       "James V. Peters",
  title =        "Short Communications: a combinatoric proof of
                 {Benford}'s law",
  journal =      j-AEQUATIONES-MATHEMATICAE,
  volume =       "23",
  number =       "1",
  pages =        "122--123",
  year =         "1981",
  coden =        "AEMABN",
  doi =          "http://dx.doi.org/10.1007/BF02188018",
  issn =         "0001-9054",
  issn-l =       "0001-9054",
  mrclass =      "Contributed Item",
  mrnumber =     "1553878",
  bibdate =      "Sat Nov 12 09:13:23 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Aequationes Mathematicae",
}

@Article{Potter:1981:LLR,
  author =       "William Gray Potter",
  title =        "{Lotka's Law} revisited",
  journal =      j-LIBR-TRENDS,
  volume =       "31",
  number =       "2",
  pages =        "21--39",
  month =        "Summer",
  year =         "1981",
  coden =        "LIBTA3",
  issn =         "0024-2594",
  issn-l =       "0024-2594",
  bibdate =      "Thu Nov 24 14:41:53 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  url =          "http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.172.9842",
  acknowledgement = ack-nhfb,
  fjournal =     "Library Trends",
}

@Article{Preece:1981:DFD,
  author =       "D. A. Preece",
  title =        "Distributions of Final Digits in Data",
  journal =      j-J-R-STAT-SOC-SER-D-STATISTICIAN,
  volume =       "30",
  number =       "1",
  pages =        "31--60",
  month =        mar,
  year =         "1981",
  issn =         "0039-0526 (print), 1467-9884 (electronic)",
  issn-l =       "0039-0526",
  bibdate =      "Wed Nov 23 12:19:24 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  url =          "http://www.jstor.org/stable/2987702",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of the Royal Statistical Society. Series D
                 (The Statistician)",
  remark =       "This paper extends previous work \cite{Yule:1927:RS}
                 on human bias in the recording of last digits in
                 measurements, or from roundings, or from later scale
                 conversions, and how such bias can be detected.",
}

@Article{Schatte:1981:RVL,
  author =       "Peter Schatte",
  title =        "On random variables with logarithmic mantissa
                 distribution relative to several bases",
  journal =      j-ELEK-INFO-KYBER,
  volume =       "17",
  number =       "??",
  pages =        "293--295",
  month =        "????",
  year =         "1981",
  coden =        "EIVKAX",
  issn =         "0013-5712",
  issn-l =       "0013-5712",
  bibdate =      "Sat Nov 12 15:53:03 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Elektronische Informationsverarbeitung und Kybernetik
                 (EIK)",
}

@Article{Washington:1981:BLF,
  author =       "Lawrence C. Washington",
  title =        "{Benford's Law} for {Fibonacci} and {Lucas} Numbers",
  journal =      j-FIB-QUART,
  volume =       "19",
  number =       "2",
  pages =        "175--177",
  month =        apr,
  year =         "1981",
  coden =        "FIBQAU",
  issn =         "0015-0517",
  issn-l =       "0015-0517",
  mrclass =      "10A30 (10A35)",
  mrnumber =     "614056 (82f:10009)",
  mrreviewer =   "S. P. Mohanty",
  bibdate =      "Sat Nov 12 09:13:23 2011",
  bibsource =    "http://www.fq.math.ca/19-2.html;
                 http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 http://www.math.utah.edu/pub/tex/bib/fibquart.bib",
  url =          "http://www.fq.math.ca/Scanned/19-2/washington.pdf",
  acknowledgement = ack-nhfb,
  ajournal =     "Fib. Quart",
  fjournal =     "The Fibonacci Quarterly. Official Organ of the
                 Fibonacci Association",
}

@Article{Fedorowicz:1982:TFZ,
  author =       "Jane Fedorowicz",
  title =        "The Theoretical Foundation of {Zipf's Law} and Its
                 Application to the Bibliographic Database Environment",
  journal =      j-J-AM-SOC-INF-SCI,
  volume =       "33",
  number =       "5",
  pages =        "285--293",
  year =         "1982",
  coden =        "AISJB6",
  doi =          "http://dx.doi.org/10.1002/asi.4630330507",
  issn =         "0002-8231 (print), 1097-4571 (electronic)",
  issn-l =       "0002-8231",
  bibdate =      "Mon Feb 25 06:13:56 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of the American Society for Information
                 Science",
}

@Article{Lefort:1982:LOA,
  author =       "B. Lefort",
  title =        "{L}'Emploi des Outils au Cours de Taches d'Entretien
                 et la Loi de {Zipf--Mandelbrot}. ({French}) [The Use of
                 Tools in Maintenance Tasks and the {Zipf--Mandelbrot
                 Law}]",
  journal =      j-TRAV-HUM,
  volume =       "45",
  number =       "2",
  pages =        "307--316",
  month =        "????",
  year =         "1982",
  coden =        "TRHUAH",
  issn =         "0041-1868 (print), 2104-3663 (electronic)",
  issn-l =       "0041-1868",
  bibdate =      "Mon Sep 10 07:17:32 MDT 2012",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/m/mandelbrot-benoit.bib;
                 http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  url =          "http://www.jstor.org/stable/40657805",
  acknowledgement = ack-nhfb,
  fjournal =     "Le Travail Humain",
  language =     "French",
}

@Article{Pavlov:1982:DFP,
  author =       "A. I. Pavlov",
  title =        "On the Distribution of Fractional Parts and {Benford's
                 Law}",
  journal =      "Mathematics of the {USSR}-Izvestiya",
  volume =       "19",
  number =       "1",
  pages =        "65--77",
  month =        "????",
  year =         "1982",
  coden =        "????",
  doi =          "http://dx.doi.org/10.1070/IM1982v019n01ABEH001411",
  issn =         "0025-5726",
  issn-l =       "0025-5726",
  bibdate =      "Sun Nov 13 10:46:55 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  url =          "http://stacks.iop.org/0025-5726/19/i=1/a=A05",
  abstract =     "This article investigates the distribution of the
                 first digits (from the left) in the $q$-nary expansions
                 of numerical sequences and functions ($q$ an integer
                 $\geq 2$)",
  acknowledgement = ack-nhfb,
}

@PhdThesis{Perline:1982:EVM,
  author =       "Richard K. Perline",
  title =        "An extreme value model of weakly harmonic
                 ({Pareto--Zipf} type) laws",
  type =         "Thesis ({Ph.D.})",
  school =       "Department of Behavioral Sciences, The University of
                 Chicago",
  address =      "Chicago, IL, USA",
  pages =        "129",
  month =        dec,
  year =         "1982",
  mrnumber =     "2611828",
  bibdate =      "Sat Nov 12 09:13:23 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  url =          "http://search.proquest.com/docview/251796701",
  acknowledgement = ack-nhfb,
  remark =       "Available from ProQuest LLC, Ann Arbor, MI, USA.",
}

@Article{Regazzini:1982:BFL,
  author =       "Eugenio Regazzini",
  title =        "The {Benford--Furlan} law as a statistical law",
  journal =      j-STATISTICA-BOLOGNA,
  volume =       "42",
  number =       "3",
  pages =        "351--370",
  year =         "1982",
  coden =        "STATDJ",
  issn =         "0390-590X (print), 1973-2201 (electronic)",
  issn-l =       "0390-590X",
  mrclass =      "62E99 (10K05 62A15)",
  mrnumber =     "695467 (84h:62032)",
  bibdate =      "Sat Nov 12 09:13:23 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Statistica (Bologna)",
}

@Article{Turner:1982:DLS,
  author =       "Peter R. Turner",
  title =        "The distribution of leading significant digits",
  journal =      j-IMA-J-NUMER-ANAL,
  volume =       "2",
  number =       "4",
  pages =        "407--412",
  month =        oct,
  year =         "1982",
  coden =        "IJNADH",
  doi =          "http://dx.doi.org/10.1093/imanum/2.4.407",
  issn =         "0272-4979 (print), 1464-3642 (electronic)",
  issn-l =       "0272-4979",
  mrclass =      "65G99 (60E05)",
  mrnumber =     "84f:65038",
  mrreviewer =   "Seppo Linnainmaa",
  bibdate =      "Sat Dec 23 17:06:35 MST 2000",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 http://www.math.utah.edu/pub/tex/bib/imajnumeranal.bib;
                 MathSciNet database",
  acknowledgement = ack-nhfb,
  fjournal =     "IMA Journal of Numerical Analysis",
  keywords =     "Benford's Law; Law of Anomalous Numbers; Zipf's Law",
}

@Book{Weaver:1982:LLT,
  author =       "Warren Weaver",
  title =        "{Lady Luck}: the theory of probability",
  publisher =    pub-DOVER,
  address =      pub-DOVER:adr,
  pages =        "392",
  year =         "1982",
  isbn =         "0-486-24342-7",
  isbn-13 =      "978-0-486-24342-9",
  lccn =         "QA273 .W4 1982",
  bibdate =      "Mon Nov 14 11:35:17 MST 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 z3950.loc.gov:7090/Voyager",
  url =          "http://www.loc.gov/catdir/description/dover031/82007396.html",
  acknowledgement = ack-nhfb,
  author-dates = "1894--1978",
  remark =       "Reprint of \cite{Weaver:1963:LLT}.",
  subject =      "Probabilities",
}

@Article{White:1982:FSS,
  author =       "Warren H. White",
  title =        "On the form of steady-state solutions to the
                 coagulation equations",
  journal =      j-J-COLLOID-INTERFACE-SCI,
  volume =       "87",
  number =       "1",
  pages =        "204--208",
  month =        may,
  year =         "1982",
  coden =        "JCISA5",
  doi =          "http://dx.doi.org/10.1016/0021-9797(82)90382-4",
  issn =         "0021-9797 (print), 1095-7103 (electronic)",
  issn-l =       "0021-9797",
  bibdate =      "Thu Feb 28 10:46:13 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  url =          "http://www.sciencedirect.com/science/article/pii/0021979782903824",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Colloid and Interface Science",
  keywords =     "power law; scale invariance; Zipf's law",
}

@Article{Iyengar:1983:SPL,
  author =       "S. Sitharama Iyengar and A. K. Rajagopal and V. R. R.
                 Uppuluri",
  title =        "String patterns of leading digits",
  journal =      j-APPL-MATH-COMP,
  volume =       "12",
  number =       "4",
  pages =        "321--337",
  month =        jul,
  year =         "1983",
  coden =        "AMHCBQ",
  doi =          "http://dx.doi.org/10.1016/0096-3003(83)90045-0",
  issn =         "0096-3003 (print), 1873-5649 (electronic)",
  issn-l =       "0096-3003",
  bibdate =      "Sat Feb 16 18:02:26 MST 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/applmathcomput2010.bib;
                 http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 http://www.sciencedirect.com/science/journal/00963003",
  url =          "http://www.sciencedirect.com/science/article/pii/0096300383900450",
  acknowledgement = ack-nhfb,
  fjournal =     "Applied Mathematics and Computation",
}

@Article{Montroll:1983:NOD,
  author =       "Elliott W. Montroll and Michael F. Shlesinger",
  title =        "On $ 1 / f $ noise and other distributions with long
                 tails",
  journal =      j-PROC-NATL-ACAD-SCI-USA,
  volume =       "79",
  number =       "10",
  pages =        "3380--3383",
  day =          "15",
  month =        may,
  year =         "1983",
  coden =        "PNASA6",
  doi =          "http://dx.doi.org/10.1073/pnas.79.10.3380",
  issn =         "0027-8424 (print), 1091-6490 (electronic)",
  issn-l =       "0027-8424",
  bibdate =      "Thu Feb 28 11:03:24 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  url =          "http://www.pnas.org/content/79/10/3380.abstract",
  acknowledgement = ack-nhfb,
  fjournal =     "Proceedings of the National Academy of Sciences of the
                 United States of America",
  keywords =     "power law; scale invariance; Zipf's law",
}

@Article{Orlov:1983:SSZ,
  author =       "Yu. K. Orlov and R. Ya. Chitashvili",
  title =        "The statistical significance of {Zipf}'s
                 distribution",
  journal =      "Soobshch. Akad. Nauk Gruzin. SSR",
  volume =       "109",
  number =       "3",
  pages =        "505--508",
  year =         "1983",
  coden =        "????",
  issn =         "0132-1447",
  issn-l =       "0132-1447",
  mrclass =      "62E99 (62P99)",
  mrnumber =     "723296",
  bibdate =      "Sat Nov 12 09:13:23 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Soobshcheniya Akademii Nauk Gruzinsko{\u\i} SSR",
}

@Article{Schatte:1983:AUD,
  author =       "Peter Schatte",
  title =        "On the asymptotic uniform distribution of sums reduced
                 $ \bmod 1 $",
  journal =      j-MATH-NACHR,
  volume =       "115",
  number =       "1",
  pages =        "257--281",
  month =        "????",
  year =         "1983",
  coden =        "MTMNAQ",
  doi =          "http://dx.doi.org/10.1002/mana.19841150121",
  issn =         "0025-584X",
  issn-l =       "0025-584X",
  bibdate =      "Sat Feb 16 19:12:20 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  url =          "http://onlinelibrary.wiley.com/doi/10.1002/mana.19841150121/abstract",
  acknowledgement = ack-nhfb,
  fjournal =     "Mathematische Nachrichten",
}

@Article{Schatte:1983:SUD,
  author =       "Peter Schatte",
  title =        "On {$H_\infty$}-summability and the uniform
                 distribution of sequences",
  journal =      j-MATH-NACHR,
  volume =       "113",
  number =       "1",
  pages =        "237--243",
  month =        "????",
  year =         "1983",
  coden =        "MTMNAQ",
  doi =          "http://dx.doi.org/10.1002/mana.19831130122",
  issn =         "0025-584X",
  issn-l =       "0025-584X",
  bibdate =      "Sat Feb 16 19:13:27 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  url =          "http://onlinelibrary.wiley.com/doi/10.1002/mana.19831130122/abstract",
  acknowledgement = ack-nhfb,
  fjournal =     "Mathematische Nachrichten",
}

@Article{Whittaker:1983:SID,
  author =       "James V. Whittaker",
  title =        "On Scale-Invariant Distributions",
  journal =      j-SIAM-J-APPL-MATH,
  volume =       "43",
  number =       "2",
  pages =        "257--267",
  month =        apr,
  year =         "1983",
  coden =        "SMJMAP",
  issn =         "0036-1399 (print), 1095-712X (electronic)",
  issn-l =       "0036-1399",
  mrclass =      "60E05 (10K10 62E10)",
  mrnumber =     "84h:60035",
  mrreviewer =   "K. C. Chanda",
  bibdate =      "Thu Oct 15 18:16:06 MDT 1998",
  bibsource =    "Compendex database;
                 http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 http://www.math.utah.edu/pub/tex/bib/siamjapplmath.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  affiliation =  "Univ of British Columbia, Dep of Mathematics,
                 Vancouver, BC, Can",
  classification = "922",
  fjournal =     "SIAM Journal on Applied Mathematics",
  journalabr =   "SIAM J Appl Math",
  keywords =     "probability",
}

@Article{Bennett:1984:ZLS,
  author =       "J. M. Bennett",
  title =        "{Zipf's Law}, Structured Programming and Creativity",
  journal =      j-AUSTRALIAN-COMP-J,
  volume =       "16",
  number =       "4",
  pages =        "122--129",
  year =         "1984",
  coden =        "ACMJB2",
  issn =         "0004-8917",
  issn-l =       "0004-8917",
  bibdate =      "Fri Mar 9 17:59:26 2012",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  abstract =     "As software projects increase in size, the effort
                 required to implement them increases at a greater rate.
                 The use of higher level languages and adherence to
                 various rules of ``good programming practice'' appear
                 to help only marginally in reducing the impact of this
                 non-linear effect, and progress can only be made by
                 calling on techniques for managing complexity which
                 have emerged in other fields. Hierarchical structures
                 are discussed with particular reference to software as
                 is the effect which appears to be common to a wide
                 range of human activities, and which is known as Zipf's
                 law. The effects of variation in individual programming
                 skills, the roles of creativity, invention and
                 innovation and lessons to be learned from case studies
                 of past failure are also examined.",
  acknowledgement = ack-nhfb,
  fjournal =     "Australian Computer Journal",
  keywords =     "creativity; innovation; invention; large software
                 projects; project failures; structured programming;
                 Zipf's law",
}

@Article{Boroda:1984:ZML,
  author =       "M. G. Boroda and A. A. Polikarpov",
  title =        "The {Zipf--Mandelbrot} law and units of different
                 levels of text organization",
  journal =      "Tartu Riikl. {\"U}l. Toimetised",
  volume =       "??",
  number =       "689",
  pages =        "35--60",
  year =         "1984",
  coden =        "????",
  issn =         "????",
  mrclass =      "92A25",
  mrnumber =     "781731 (86c:92030)",
  bibdate =      "Sat Nov 12 09:13:23 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Tartu Riikliku {\"U}likooli Toimetised. Uchenye
                 Zapiski Tartuskogo Gosudarstvennogo Universiteta. Acta
                 et Commentationes Universitatis Tartuensis",
}

@Article{Brookes:1984:RTE,
  author =       "Bertram C. Brookes",
  title =        "Ranking techniques and the empirical log law",
  journal =      j-INFO-PROC-MAN,
  volume =       "20",
  number =       "1--2",
  pages =        "37--46",
  month =        "????",
  year =         "1984",
  coden =        "IPMADK",
  doi =          "http://dx.doi.org/10.1016/0306-4573(84)90038-4",
  issn =         "0306-4573 (print), 1873-5371 (electronic)",
  issn-l =       "0306-4573",
  bibdate =      "Mon Feb 25 10:38:32 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  url =          "http://www.sciencedirect.com/science/article/pii/0306457384900384",
  acknowledgement = ack-nhfb,
  fjournal =     "Information Processing and Management",
  keywords =     "Benford's Law; Anomalous Law of Numbers",
}

@Article{Bunt:1984:MPL,
  author =       "Richard B. Bunt and Jennifer M. Murphy and Shikharesh
                 Majumdar",
  title =        "A measure of program locality and its application",
  journal =      j-SIGMETRICS,
  volume =       "12",
  number =       "3",
  pages =        "28--40",
  month =        aug,
  year =         "1984",
  coden =        "????",
  doi =          "http://doi.acm.org/10.1145/1031382.809311",
  issn =         "0163-5999 (print), 1557-9484 (electronic)",
  issn-l =       "0163-5999",
  bibdate =      "Thu Jun 26 11:00:50 MDT 2008",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 http://www.math.utah.edu/pub/tex/bib/sigmetrics.bib",
  abstract =     "Although the phenomenon of locality has long been
                 recognized as the single most important characteristic
                 of program behaviour, relatively little work has been
                 done in attempting to measure it. Recent work has led
                 to the development of an intrinsic measure of program
                 locality based on the Bradford--Zipf distribution.
                 Potential applications for such a measure are many, and
                 include the evaluation of program restructuring methods
                 (manual and automatic), the prediction of system
                 performance, the validation of program behaviour
                 models, and the enhanced understanding of the phenomena
                 that characterize program behaviour. A consideration of
                 each of these areas is given in connection with the
                 proposed measure, both to increase confidence in the
                 validity of the measure and to illustrate a methodology
                 for dealing with such problems.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM SIGMETRICS Performance Evaluation Review",
}

@Article{Cohen:1984:PNF,
  author =       "D. I. A. Cohen and T. M. Katz",
  title =        "Prime numbers and the first digit phenomenon",
  journal =      j-J-NUMBER-THEORY,
  volume =       "18",
  number =       "3",
  pages =        "261--268",
  month =        jun,
  year =         "1984",
  coden =        "JNUTA9",
  doi =          "http://dx.doi.org/10.1016/0022-314X(84)90061-1",
  issn =         "0022-314X (print), 1096-1658 (electronic)",
  issn-l =       "0022-314X",
  bibdate =      "Fri Nov 25 13:58:58 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Number Theory",
}

@Article{Fedorowicz:1984:DEU,
  author =       "Jane Fedorowicz",
  title =        "Database evaluation using multiple regression
                 techniques",
  journal =      j-SIGMOD,
  volume =       "14",
  number =       "2",
  pages =        "70--76",
  year =         "1984",
  coden =        "SRECD8",
  isbn =         "0-89791-128-8",
  isbn-13 =      "978-0-89791-128-3",
  issn =         "0163-5808 (print), 1943-5835 (electronic)",
  issn-l =       "0163-5808",
  bibdate =      "Mon Dec 9 07:58:51 MST 1996",
  bibsource =    "Compendex database;
                 http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  abstract =     "A model of the inverted file of an automated
                 bibliographic system is constructed using the Zipf
                 distribution of word frequency. By ascertaining the
                 parameters of the Zipfian model of the inverted file
                 system, one can estimate the minimum data storage
                 requirements of the database. In addition, given a few
                 additional system parameters, access time for a
                 specified query can be estimated. The estimation
                 procedures are accomplished using logarithmic
                 transformations and multiple regression techniques.
                 This paper introduces the Zipfian models, their
                 regression formulation, and their results and
                 interpretation for application to database
                 evaluation.",
  acknowledgement = ack-nhfb,
  affiliation =  "Northwestern Univ, Kellogg Graduate Sch of Management,
                 Evanston, IL, USA",
  affiliationaddress = "Northwestern Univ, Kellogg Graduate Sch of
                 Management, Evanston, IL, USA",
  classification = "723; 901; 922",
  conference =   "SIGMOD '84, Proceedings of Annual Meeting (ACM Special
                 Interest Group on Management of Data).",
  fjournal =     "SIGMOD Record (ACM Special Interest Group on
                 Management of Data)",
  keywords =     "access time model; bibliographic techniques; database
                 systems; evaluation; information storage systems;
                 mathematical models; multiple regression techniques;
                 Zipfian model",
  meetingaddress = "Boston, MA, USA",
  sponsor =      "ACM, Special Interest Group on Management of Data, New
                 York, NY, USA",
}

@Article{Friedberg:1984:DFD,
  author =       "Steven H. Friedberg",
  title =        "The distribution of first digits",
  journal =      j-COLLEGE-MATH-J,
  volume =       "15",
  number =       "2",
  pages =        "120--125",
  month =        mar,
  year =         "1984",
  issn =         "0746-8342 (print), 1931-1346 (electronic)",
  issn-l =       "0746-8342",
  bibdate =      "Sat Feb 16 17:38:56 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  url =          "http://www.jstor.org/stable/2686516",
  acknowledgement = ack-nhfb,
  fjournal =     "College Mathematics Journal",
}

@Article{Fuchs:1984:PDP,
  author =       "A. Fuchs and G. Letta",
  title =        "{Sur le probl{\`e}me du premier chiffre d{\'e}cimal}.
                 ({French}) [{On} the problem of the first decimal
                 digit]",
  journal =      "{Bollettino della Unione Matem{\`a}tica Italiana.
                 Serie VI. B}",
  volume =       "3",
  pages =        "451--461",
  year =         "1984",
  issn =         "0392-4041",
  issn-l =       "0392-4041",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  zmnumber =     "0557.60011",
  ajournal =     "Boll. Unione Mat. Ital., VI. Ser., B",
  keywords =     "analytical density; asymptotic density; first-digit
                 problem",
  language =     "French",
  ZMclass =      "60B99 (Probability theory on general structures)",
  ZMreviewer =   "R. Scozzafava",
}

@Article{Kohyama:1984:TIC,
  author =       "Tamotsu Kohyama and Y{\=o}ji Aizawa",
  title =        "Theory of the intermittent chaos. {$1/f$} spectrum and
                 the {Pareto--Zipf} law",
  journal =      j-PROG-THEOR-PHYS,
  volume =       "71",
  number =       "5",
  pages =        "917--929",
  year =         "1984",
  coden =        "PTPKAV",
  doi =          "http://dx.doi.org/10.1143/PTP.71.917",
  issn =         "0033-068X (print), 1347-4081 (electronic)",
  issn-l =       "0033-068X",
  mrclass =      "58F13 (76F99)",
  mrnumber =     "756214 (86a:58063)",
  mrreviewer =   "Joseph Ford",
  bibdate =      "Sat Nov 12 09:13:23 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Progress of Theoretical Physics",
}

@Article{Maia:1984:UBL,
  author =       "M. J. F. Maia and M. D. Maia",
  title =        "On the Unity of {Bradford's Law}",
  journal =      j-J-DOC,
  volume =       "40",
  number =       "3",
  pages =        "206--216",
  month =        "????",
  year =         "1984",
  coden =        "JDOCAS",
  doi =          "http://dx.doi.org/10.1108/eb026765",
  issn =         "0022-0418 (print), 1758-7379 (electronic)",
  issn-l =       "0022-0418",
  bibdate =      "Fri Nov 25 07:11:46 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Documentation",
}

@Article{McLaughlin:1984:DFI,
  author =       "William I. McLaughlin and Sylvia A. Lundy",
  title =        "Digit Functions of Integer Sequences",
  journal =      j-FIB-QUART,
  volume =       "22",
  number =       "2",
  pages =        "105--115",
  month =        may,
  year =         "1984",
  coden =        "FIBQAU",
  issn =         "0015-0517",
  issn-l =       "0015-0517",
  bibdate =      "Thu Oct 20 18:00:30 MDT 2011",
  bibsource =    "http://www.fq.math.ca/22-2.html;
                 http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 http://www.math.utah.edu/pub/tex/bib/fibquart.bib",
  url =          "http://www.fq.math.ca/Scanned/22-2/mclaughlin.pdf",
  acknowledgement = ack-nhfb,
  ajournal =     "Fib. Quart",
  fjournal =     "The Fibonacci Quarterly. Official Organ of the
                 Fibonacci Association",
}

@Article{Nagasaka:1984:BL,
  author =       "Kenji Nagasaka",
  title =        "On {Benford}'s law",
  journal =      j-ANN-INST-STAT-MATH-TOKYO,
  volume =       "36",
  number =       "2",
  pages =        "337--352",
  year =         "1984",
  coden =        "AISXAD",
  doi =          "http://dx.doi.org/10.1007/BF02481974",
  issn =         "0020-3157 (print), 1572-9052 (electronic)",
  issn-l =       "0020-3157",
  mrclass =      "60F99 (11K06 11K36 62E99)",
  mrnumber =     "758506 (86a:60052)",
  mrreviewer =   "L. Kuipers",
  bibdate =      "Sat Nov 12 09:13:23 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  ajournal =     "Ann. Inst. Statist. Math.",
  fjournal =     "Annals of the Institute of Statistical Mathematics
                 (Tokyo)",
}

@Article{Schatte:1984:AUD,
  author =       "Peter Schatte",
  title =        "On the asymptotic uniform distribution of sums reduced
                 $\bmod 1$",
  journal =      j-MATH-NACHR,
  volume =       "115",
  number =       "1",
  pages =        "275--281",
  month =        "????",
  year =         "1984",
  coden =        "MTMNAQ",
  doi =          "http://dx.doi.org/10.1002/mana.19841150121",
  issn =         "0025-584X",
  issn-l =       "0025-584X",
  bibdate =      "Sat Nov 12 15:54:14 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  url =          "http://onlinelibrary.wiley.com/doi/10.1002/mana.19841150121/abstract",
  acknowledgement = ack-nhfb,
  fjournal =     "Mathematische Nachrichten",
}

@Article{Turner:1984:FRD,
  author =       "Peter R. Turner",
  title =        "Further revelations on l.s.d",
  journal =      j-IMA-J-NUMER-ANAL,
  volume =       "4",
  number =       "2",
  pages =        "225--231",
  month =        apr,
  year =         "1984",
  coden =        "IJNADH",
  doi =          "http://dx.doi.org/10.1093/imanum/4.2.225",
  issn =         "0272-4979 (print), 1464-3642 (electronic)",
  issn-l =       "0272-4979",
  mrclass =      "65G10 (11K99)",
  mrnumber =     "85m:65039",
  mrreviewer =   "Calvin T. Long",
  bibdate =      "Sat Dec 23 17:06:35 MST 2000",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 http://www.math.utah.edu/pub/tex/bib/imajnumeranal.bib;
                 MathSciNet database",
  abstract =     "In a recent paper the author showed that the
                 distribution of leading significant digits, l.s.d.,
                 resulting from successive multiplications is
                 logarithmic. In this paper these results are extended
                 by establishing, still without any assumptions of
                 invariance to scaling, that this distribution remains
                 invariant under all further arithmetic operations ---
                 both multiplicative and additive. The fact that 30\% of
                 decimal numbers have l.s.d. 1 persists.",
  acknowledgement = ack-nhfb,
  keywords =     "l. s. d. (leading significant digits)",
}

@Article{Yuan:1984:LOC,
  author =       "Y. Yuan",
  title =        "On the least {$Q$}-order of convergence of variable
                 metric algorithms",
  journal =      j-IMA-J-NUMER-ANAL,
  volume =       "4",
  number =       "2",
  pages =        "233--239",
  month =        apr,
  year =         "1984",
  coden =        "IJNADH",
  issn =         "0272-4979 (print), 1464-3642 (electronic)",
  issn-l =       "0272-4979",
  mrclass =      "65K05",
  mrnumber =     "85h:65133",
  mrreviewer =   "A. I. \c Schiop",
  bibdate =      "Sat Dec 23 17:06:35 MST 2000",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 http://www.math.utah.edu/pub/tex/bib/imajnumeranal.bib;
                 MathSciNet database",
  acknowledgement = ack-nhfb,
  fjournal =     "IMA Journal of Numerical Analysis",
}

@Article{Barlow:1985:RED,
  author =       "J. L. Barlow and E. H. Bareiss",
  title =        "On Roundoff Error Distributions in Floating Point and
                 Logarithmic Arithmetic",
  journal =      j-COMPUTING,
  volume =       "34",
  number =       "4",
  pages =        "325--347",
  month =        dec,
  year =         "1985",
  coden =        "CMPTA2",
  issn =         "0010-485X (print), 1436-5057 (electronic)",
  issn-l =       "0010-485X",
  mrclass =      "65G05",
  mrnumber =     "87c:65045",
  mrreviewer =   "N. N. Abdelmalek",
  bibdate =      "Tue Oct 12 16:33:42 MDT 1999",
  bibsource =    "Compendex database;
                 http://springerlink.metapress.com/openurl.asp?genre=journal&issn=0010-485X;
                 http://www.math.utah.edu/pub/tex/bib/benfords-law.bib
                 http://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 MathSciNet database",
  acknowledgement = ack-nhfb,
  affiliation =  "Pennsylvania State Univ, Computer Science Dep,
                 University Park, PA, USA",
  affiliationaddress = "USA",
  classification = "723",
  fjournal =     "Computing",
  journalabr =   "Computing (Vienna/New York)",
  keywords =     "computer arithmetic; computer metatheory; floating
                 point arithmetic; logarithmic arithmetic; roundoff
                 error distributions",
}

@Article{Bradford:1985:SIS,
  author =       "Samuel C. Bradford",
  title =        "Sources of Information on Specific Subjects",
  journal =      j-J-INFO-SCI-PRINCIPLES-PRACTICE,
  volume =       "10",
  number =       "4",
  pages =        "173--180",
  month =        oct,
  year =         "1985",
  coden =        "JISCDI",
  issn =         "0165-5515 (print), 1741-6485 (electronic)",
  issn-l =       "0165-5515",
  bibdate =      "Fri Nov 25 11:49:58 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  note =         "Reprint of \cite{Bradford:1934:SIS}, the source of
                 Bradford's Law.",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Information Science, Principles and
                 Practice",
}

@Article{Egghe:1985:CLL,
  author =       "L. Egghe",
  title =        "Consequences of {Lotka's Law} for the {Law of
                 Bradford}",
  journal =      j-J-DOC,
  volume =       "41",
  number =       "3",
  pages =        "173--189",
  month =        "????",
  year =         "1985",
  coden =        "JDOCAS",
  doi =          "http://dx.doi.org/10.1108/eb026780",
  issn =         "0022-0418 (print), 1758-7379 (electronic)",
  issn-l =       "0022-0418",
  bibdate =      "Fri Nov 25 07:23:22 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Documentation",
  keywords =     "Bradford's Law",
}

@Article{Faber:1985:AML,
  author =       "Vance Faber and Andrew B. {White, Jr.} and G. Milton
                 Wing",
  title =        "Analysis of a model that leads to the {Pareto} law of
                 wealth distribution",
  journal =      j-J-MATH-ANAL-APPL,
  volume =       "112",
  number =       "2",
  pages =        "579--594",
  year =         "1985",
  coden =        "JMANAK",
  doi =          "http://dx.doi.org/10.1016/0022-247X(85)90264-1",
  issn =         "0022-247X (print), 1096-0813 (electronic)",
  issn-l =       "0022-247X",
  mrclass =      "90A14",
  mrnumber =     "813621 (87b:90027)",
  bibdate =      "Mon Feb 18 17:05:26 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Mathematical Analysis and Applications",
}

@Article{Lagarias:1985:PG,
  author =       "Jeffrey C. Lagarias",
  title =        "The $3x + 1$ Problem and Its Generalizations",
  journal =      j-AMER-MATH-MONTHLY,
  volume =       "92",
  number =       "1",
  pages =        "3--23",
  month =        jan,
  year =         "1985",
  coden =        "AMMYAE",
  issn =         "0002-9890 (print), 1930-0972 (electronic)",
  issn-l =       "0002-9890",
  mrclass =      "11K55 (11K31)",
  mrnumber =     "86i:11043",
  mrreviewer =   "A. D. Pollington",
  bibdate =      "Mon Jun 28 12:37:47 MDT 1999",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  keywords =     "Benford's Law",
}

@Article{Pao:1985:LLT,
  author =       "Miranda Lee Pao",
  title =        "{Lotka}'s law: a testing procedure",
  journal =      j-INFO-PROC-MAN,
  volume =       "21",
  number =       "4",
  pages =        "305--320",
  month =        "????",
  year =         "1985",
  coden =        "IPMADK",
  doi =          "http://dx.doi.org/10.1016/0306-4573(85)90055-X",
  issn =         "0306-4573 (print), 1873-5371 (electronic)",
  issn-l =       "0306-4573",
  bibdate =      "Fri Nov 25 08:41:41 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Information Processing and Management",
}

@Article{Raimi:1985:FDP,
  author =       "R. Raimi",
  title =        "The First Digit Phenomenon Again",
  journal =      j-PROC-AMER-PHIL-SOC,
  volume =       "129",
  number =       "2",
  pages =        "211--219",
  month =        jun,
  year =         "1985",
  coden =        "PAPCAA",
  issn =         "0003-049X",
  issn-l =       "0003-049X",
  bibdate =      "Sat Nov 12 16:56:54 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  note =         "This paper contains strong criticism of a derivation
                 of Benford's Law \cite{Logan:1978:FDP}.",
  url =          "http://www.jstor.org/stable/986989",
  acknowledgement = ack-nhfb,
  fjournal =     "Proceedings of the {American Philosophical Society}
                 held at {Philadelphia} for promoting useful knowledge",
  remark =       "This paper contains mathematical derivations of both
                 Stigler's Law and Benford's Law. Raimi comments on p.
                 217: ``the Benford law itself as a conclusion to be
                 derived is by no means as firm as Kepler's planetary
                 curves. Indeed, it has been pointed out by Diaconis and
                 Freedman [D-F] [\cite{Diaconis:1979:RP}] that a
                 statistical analysis of Benford's announced data gives
                 a high probability to the conjecture that he did a bit
                 of rounding-off here and there, always in the direction
                 of his law. The license that a physicist often takes on
                 the path from his hypotheses to verified, observable,
                 and repeatable conclusion is not justified here.''.",
}

@Article{Tichy:1985:UDD,
  author =       "Robert F. Tichy",
  title =        "Uniform distribution and diophantine inequalities",
  journal =      j-MONAT-MATH,
  volume =       "99",
  number =       "2",
  pages =        "147--152",
  month =        jun,
  year =         "1985",
  coden =        "MNMTA2",
  doi =          "http://dx.doi.org/10.1007/BF01304194",
  issn =         "0026-9255 (print), 1436-5081 (electronic)",
  issn-l =       "0026-9255",
  bibdate =      "Sun Feb 17 06:26:16 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  url =          "http://link.springer.com/article/10.1007/BF01304194",
  zmnumber =     "0538.10039",
  acknowledgement = ack-nhfb,
  fjournal =     "Monatshefte f{\"u}r Mathematik",
  keywords =     "diophantine inequalities; discrepancy; Uniformly
                 distributed sequences",
  ZMclass =      "11K06 (General theory of distribution modulo 1); 11D75
                 (Diophantine inequalities)",
}

@Article{Tuldava:1985:FST,
  author =       "Yu. A. Tuldava",
  title =        "The frequency structure of a text and {Zipf}'s law",
  journal =      "Tartu Riikl. {\"U}l. Toimetised",
  volume =       "??",
  number =       "711",
  pages =        "93--116",
  year =         "1985",
  coden =        "????",
  issn =         "????",
  mrclass =      "92A25 (94A15)",
  mrnumber =     "836129 (87c:92063)",
  bibdate =      "Sat Nov 12 09:13:23 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Tartu Riikliku {\"U}likooli Toimetised. Uchenye
                 Zapiski Tartuskogo Gosudarstvennogo Universiteta. Acta
                 et Commentationes Universitatis Tartuensis",
}

@Article{Chen:1986:RBL,
  author =       "Ye-Sho Chen and Ferdinand F. Leimkuhler",
  title =        "A relationship between {Lotka's Law}, {Bradford's
                 Law}, and {Zipf's Law}",
  journal =      j-J-AM-SOC-INF-SCI,
  volume =       "37",
  number =       "5",
  pages =        "307--314",
  year =         "1986",
  coden =        "AISJB6",
  doi =          "http://dx.doi.org/10.1002/(SICI)1097-4571(198609)37:5<307::AID-ASI5>3.0.CO;2-8",
  issn =         "0002-8231 (print), 1097-4571 (electronic)",
  issn-l =       "0002-8231",
  bibdate =      "Mon Feb 25 06:13:56 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of the American Society for Information
                 Science",
}

@Article{Feldstein:1986:OUS,
  author =       "Alan Feldstein and Peter Turner",
  title =        "Overflow, underflow, and severe loss of significance
                 in floating-point addition and subtraction",
  journal =      j-IMA-J-NUMER-ANAL,
  volume =       "6",
  number =       "2",
  pages =        "241--251",
  month =        apr,
  year =         "1986",
  coden =        "IJNADH",
  issn =         "0272-4979 (print), 1464-3642 (electronic)",
  issn-l =       "0272-4979",
  mrclass =      "65G05",
  mrnumber =     "89h:65065",
  bibdate =      "Sat Dec 23 14:52:49 2000",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  abstract =     "In this paper it is shown that, under the assumption
                 of the logarithmic distribution of numbers,
                 floating-point addition and subtraction can result in
                 overflow or underflow with alarming frequency --- a
                 frequency that increases rapidly with machine speed
                 unless the range of the exponent is also increased. If
                 numbers are assumed to be distributed in accordance
                 with Sweeney's (1965) experiments, then severe loss of
                 significance occurs with large probability in floating
                 point subtraction. These results have implications for
                 computer design and lead to the suggestion of a long
                 word format which will reduce the risks to acceptable
                 levels.",
  acknowledgement = ack-nhfb,
  fjournal =     "IMA Journal of Numerical Analysis",
  keywords =     "Benford's Law; Law of Anomalous Numbers; logarithmic
                 distribution; overflow; underflow; Zipf's Law",
}

@Article{Green:1986:BRP,
  author =       "M. W. Green",
  title =        "Book Reviews: {{\em Pareto Distributions}}, by {B. C.
                 Arnold}",
  journal =      j-APPL-STAT,
  volume =       "35",
  number =       "2",
  pages =        "215--215",
  year =         "1986",
  coden =        "APSTAG",
  issn =         "0035-9254 (print), 1467-9876 (electronic)",
  issn-l =       "0035-9254",
  bibdate =      "Sat Apr 21 10:24:36 MDT 2001",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
}

@Article{Hoare:1986:DFS,
  author =       "G. T. Q. Hoare and E. Wright",
  title =        "The distribution of first significant digits",
  journal =      j-MATH-GAZ,
  volume =       "70",
  number =       "451",
  pages =        "34--37",
  month =        mar,
  year =         "1986",
  coden =        "MAGAAS",
  issn =         "0025-5572",
  issn-l =       "0025-5572",
  bibdate =      "Sat Feb 16 17:57:52 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  url =          "http://www.jstor.org/stable/3615826",
  acknowledgement = ack-nhfb,
  fjournal =     "Mathematical Gazette",
  journal-url =  "http://www.m-a.org.uk/jsp/index.jsp?lnk=620",
}

@Article{Katz:1986:FDP,
  author =       "Talbot M. Katz and Daniel I. A. Cohen",
  title =        "The First Digit Property for Exponential Sequences is
                 Independent of the Underlying Distribution",
  journal =      j-FIB-QUART,
  volume =       "24",
  number =       "1",
  pages =        "2--7",
  month =        feb,
  year =         "1986",
  coden =        "FIBQAU",
  issn =         "0015-0517",
  issn-l =       "0015-0517",
  bibdate =      "Thu Oct 20 18:00:45 MDT 2011",
  bibsource =    "http://www.fq.math.ca/24-1.html;
                 http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 http://www.math.utah.edu/pub/tex/bib/fibquart.bib",
  url =          "http://www.fq.math.ca/Scanned/24-1/katz.pdf",
  acknowledgement = ack-nhfb,
  ajournal =     "Fib. Quart",
  fjournal =     "The Fibonacci Quarterly. Official Organ of the
                 Fibonacci Association",
}

@Article{Lemons:1986:NTD,
  author =       "Don S. Lemons",
  title =        "On the number of things and the distribution of first
                 digits",
  journal =      j-AMER-J-PHYSICS,
  volume =       "54",
  number =       "9",
  pages =        "816--817",
  month =        sep,
  year =         "1986",
  coden =        "AJPIAS",
  doi =          "http://dx.doi.org/10.1119/1.14453",
  issn =         "0002-9505",
  issn-l =       "0002-9505",
  bibdate =      "Wed Nov 23 12:03:08 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  url =          "http://ajp.aapt.org/",
  acknowledgement = ack-nhfb,
  fjournal =     "American Journal of Physics",
  keywords =     "Benford's Law",
  remark =       "Lemons gives a derivation of Benford's Law that does
                 not assume scale invariance, unlike other widely-cited
                 derivations
                 \cite{Pinkham:1961:DFS,Raimi:1976:FDP,Raimi:1985:FDP}.",
}

@Book{Lines:1986:NYT,
  author =       "Malcolm E. Lines",
  title =        "A number for your thoughts: facts and speculations
                 about numbers from {Euclid} to the latest computers",
  publisher =    pub-ADAM-HILGER,
  address =      pub-ADAM-HILGER:adr,
  pages =        "vi + 214",
  year =         "1986",
  isbn =         "0-85274-495-1 (paperback)",
  isbn-13 =      "978-0-85274-495-6 (paperback)",
  lccn =         "QA241 .L617 1986",
  bibdate =      "Wed Nov 23 11:34:02 MST 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 z3950.gbv.de:20011/gvk",
  url =          "http://www.loc.gov/catdir/enhancements/fy0668/86183277-d.html",
  acknowledgement = ack-nhfb,
  remark =       "Chapter 7 (pp. 43--52) is entitled: ``The Baffling Law
                 of Benford''.",
  subject =      "number theory",
}

@Article{Patil:1986:DFD,
  author =       "S. A. Patil and V. R. R. Uppulari",
  title =        "The distribution of first $j$ digits",
  journal =      j-COLLEGE-MATH-J,
  volume =       "17",
  number =       "3",
  pages =        "240--243",
  month =        may,
  year =         "1986",
  coden =        "????",
  issn =         "0746-8342 (print), 1931-1346 (electronic)",
  issn-l =       "0746-8342",
  bibdate =      "Sat Feb 16 19:00:24 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  url =          "http://www.jstor.org/stable/2686982",
  acknowledgement = ack-nhfb,
  fjournal =     "College Mathematics Journal",
  keywords =     "Benford's Law",
}

@Article{Schatte:1986:ALD,
  author =       "Peter Schatte",
  title =        "On the asymptotic logarithmic distribution of the
                 floating-point mantissas of sums",
  journal =      j-MATH-NACHR,
  volume =       "127",
  number =       "1",
  pages =        "7--20",
  month =        "????",
  year =         "1986",
  coden =        "MTMNAQ",
  doi =          "http://dx.doi.org/10.1002/mana.19861270102",
  issn =         "0025-584X",
  issn-l =       "0025-584X",
  bibdate =      "Sun Feb 17 06:04:23 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  url =          "http://onlinelibrary.wiley.com/doi/10.1002/mana.19861270102/abstract",
  acknowledgement = ack-nhfb,
  fjournal =     "Mathematische Nachrichten",
}

@Article{Tichy:1986:GZU,
  author =       "Robert F. Tichy",
  title =        "{Gleichverteilung und zahlentheoretische Ungleichungen
                 II}. ({German}) [{Uniform} distribution and
                 number-theoretic inequalities {II}]",
  journal =      "Anzeiger der {\"O}sterreichischen Akademie der
                 Wissenschaften. Mathematisch-Naturwissenschaftliche
                 Klasse",
  volume =       "122(1985)",
  number =       "??",
  pages =        "95--99",
  month =        "????",
  year =         "1986",
  coden =        "OSAWA8",
  doi =          "????",
  issn =         "0065-535X",
  issn-l =       "0065-535X",
  bibdate =      "Sun Feb 17 06:24:23 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  url =          "????",
  acknowledgement = ack-nhfb,
  ajournal =     "Anz. {\"O}sterr. Akad. Wiss., Math.-Naturwiss. Kl.",
  classmath =    "11K06 (General theory of distribution modulo 1); 11J25
                 (Diophantine inequalities)",
  keywords =     "diophantine inequalities; discrepancy; H infinity;
                 logarithmic mean; summation method; uniform
                 distribution",
  language =     "German",
  xxnote =       "Despite repeated searches, I have not found this
                 journal online, not even from links at the Austrian
                 Academy of Sciences, \path=http://www.oeaw.ac.at=.",
}

@Article{Bak:1987:SOC,
  author =       "Per Bak and Chao Tang and Kurt Wiesenfeld",
  title =        "Self-organized criticality: An explanation of the $ 1
                 / f $ noise",
  journal =      j-PHYS-REV-LET,
  volume =       "59",
  number =       "4",
  pages =        "381--384",
  month =        jul,
  year =         "1987",
  coden =        "PRLTAO",
  doi =          "http://dx.doi.org/10.1103/PhysRevLett.59.381",
  issn =         "0031-9007 (print), 1079-7114 (electronic), 1092-0145",
  issn-l =       "0031-9007",
  bibdate =      "Thu Feb 28 10:54:26 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  url =          "http://link.aps.org/doi/10.1103/PhysRevLett.59.381",
  acknowledgement = ack-nhfb,
  fjournal =     "Physical Review Letters",
  keywords =     "power law; scale invariance; Zipf's law",
}

@Article{Chen:1987:AZL,
  author =       "Ye-Sho Chen and Ferdinand F. Leimkuhler",
  title =        "Analysis of {Zipf}'s law: An index approach",
  journal =      j-INFO-PROC-MAN,
  volume =       "23",
  number =       "3",
  pages =        "171--182",
  day =          "1",
  month =        apr,
  year =         "1987",
  coden =        "IPMADK",
  doi =          "http://dx.doi.org/10.1016/0306-4573(87)90002-1",
  issn =         "0306-4573 (print), 1873-5371 (electronic)",
  issn-l =       "0306-4573",
  bibdate =      "Wed Feb 27 07:32:55 MST 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  url =          "http://www.sciencedirect.com/science/article/pii/0306457387900021",
  zmnumber =     "0614.62150",
  abstract =     "A rigorous analysis of Zipf's law is made using an
                 index for the sequence of observed values of the
                 variables in a Zipf-type relationship. Three important
                 properties relating rank, count, and frequency are
                 identified. Using this approach, the shape of Zipf-type
                 curves can be described in terms of three distinct
                 regions and two parameters of the Mandelbrot--Zipf law.
                 This result has considerable practical significance,
                 since it provides rigorous foundations for the
                 application of Zipf's law.",
  acknowledgement = ack-nhfb,
  classmath =    "62P99 (Appl. of statistics)",
  fjournal =     "Information Processing and Management",
  keywords =     "index approach; Mandelbrot-Zipf law; Zipf's law",
}

@Article{Fedorowicz:1987:DPE,
  author =       "Jane Fedorowicz",
  title =        "Database Performance Evaluation in an Indexed File
                 Environment",
  journal =      j-TODS,
  volume =       "12",
  number =       "1",
  pages =        "85--110",
  month =        mar,
  year =         "1987",
  coden =        "ATDSD3",
  issn =         "0362-5915 (print), 1557-4644 (electronic)",
  issn-l =       "0362-5915",
  bibdate =      "Sat Apr 14 10:34:48 MDT 2001",
  bibsource =    "Compendex database; Database/Graefe.bib;
                 Database/Wiederhold.bib; http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  url =          "http://www.acm.org/pubs/articles/journals/tods/1987-12-1/p85-fedorowicz/p85-fedorowicz.pdf;
                 http://www.acm.org/pubs/citations/journals/tods/1987-12-1/p85-fedorowicz/;
                 http://www.acm.org/pubs/toc/Abstracts/tods/13675.html",
  abstract =     "The use of database systems for managerial decision
                 making often incorporates information-retrieval
                 capabilities with numeric report generation. Of great
                 concern to the user of such a system is the response
                 time associated with issuing a query to the database.
                 This study presents a procedure for estimating response
                 time for one of the most frequently encountered
                 physical storage mechanisms, the indexed file. The
                 model provides a fairly high degree of accuracy, but is
                 simple enough so that the cost of applying the model is
                 not exorbitant. The model incorporates the knowledge
                 that the distribution of access key occurrences is
                 known to follow Zipf's law. It first estimates the
                 access time required to complete the query, which
                 includes the time needed for all input and output
                 transactions, and CPU time used in performing the
                 search. The effects of multiple users on an
                 individual's response time are then assessed using a
                 simple regression estimation technique. The two-step
                 procedure allows for the separation of access time from
                 multiuser influences.",
  acknowledgement = ack-nhfb,
  affiliation =  "Boston Univ, Boston, MA, USA",
  affiliationaddress = "Boston Univ, Boston, MA, USA",
  annote =       "a procedure for estimating response time; distribution
                 of access key occurrences follow Zipf's law. Early
                 version with Kellogg, J. L. Model provides a fairly
                 high degree of accuracy but is simple. The effects of
                 multiple users are assessed using simple regression
                 estimation.",
  classification = "723; 912; 922",
  fjournal =     "ACM Transactions on Database Systems",
  generalterms = "Design; Performance",
  keywords =     "data processing --- File organization; database
                 performance; database systems; indexed file
                 environment; MANAGEMENT --- Information Systems;
                 multiple users, design; Performance; performance;
                 response time; statistical methods --- regression
                 analysis; Zipf's law",
  subject =      "{\bf D.4.3}: Software, OPERATING SYSTEMS, File Systems
                 Management, File organization. {\bf H.2.2}: Information
                 Systems, DATABASE MANAGEMENT, Physical Design, Access
                 methods. {\bf H.3.2}: Information Systems, INFORMATION
                 STORAGE AND RETRIEVAL, Information Storage, File
                 organization. {\bf H.3.3}: Information Systems,
                 INFORMATION STORAGE AND RETRIEVAL, Information Search
                 and Retrieval, Retrieval models.",
}

@Article{Hosking:1987:PQE,
  author =       "J. R. M. Hosking and J. R. Wallis",
  title =        "Parameter and Quantile Estimation for the Generalized
                 {Pareto} Distribution",
  journal =      j-TECHNOMETRICS,
  volume =       "29",
  number =       "3",
  pages =        "339--349",
  month =        "????",
  year =         "1987",
  coden =        "TCMTA2",
  issn =         "0040-1706 (print), 1537-2723 (electronic)",
  issn-l =       "0040-1706",
  bibdate =      "Fri Nov 25 16:39:38 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Technometrics",
}

@Article{Kunoff:1987:FDP,
  author =       "Sharon Kunoff",
  title =        "{$N!$} has the First Digit Property",
  journal =      j-FIB-QUART,
  volume =       "25",
  number =       "4",
  pages =        "365--367",
  month =        nov,
  year =         "1987",
  coden =        "FIBQAU",
  issn =         "0015-0517",
  issn-l =       "0015-0517",
  bibdate =      "Thu Oct 20 18:01:00 MDT 2011",
  bibsource =    "http://www.fq.math.ca/25-4.html;
                 http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 http://www.math.utah.edu/pub/tex/bib/fibquart.bib",
  url =          "http://www.fq.math.ca/Scanned/25-4/kunoff.pdf",
  acknowledgement = ack-nhfb,
  ajournal =     "Fib. Quart",
  fjournal =     "The Fibonacci Quarterly. Official Organ of the
                 Fibonacci Association",
}

@Article{Nagasaka:1987:BLL,
  author =       "Kenji Nagasaka and Jau-Shyong Shiue",
  title =        "{Benford}'s law for linear recurrence sequences",
  journal =      "Tsukuba J. Math.",
  volume =       "11",
  number =       "2",
  pages =        "341--351",
  year =         "1987",
  coden =        "????",
  issn =         "0387-4982",
  issn-l =       "0387-4982",
  mrclass =      "60E99 (11B37)",
  mrnumber =     "926460 (88m:60047)",
  mrreviewer =   "L. Kuipers",
  bibdate =      "Sat Nov 12 09:13:23 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Tsukuba Journal of Mathematics",
}

@Article{Nicholls:1987:EZP,
  author =       "Paul Travis Nicholls",
  title =        "Estimation of {Zipf} parameters",
  journal =      j-J-AM-SOC-INF-SCI,
  volume =       "38",
  number =       "6",
  pages =        "443--445",
  year =         "1987",
  coden =        "AISJB6",
  doi =          "http://dx.doi.org/10.1002/(SICI)1097-4571(198711)38:6<443::AID-ASI4>3.0.CO;2-E",
  issn =         "0002-8231 (print), 1097-4571 (electronic)",
  issn-l =       "0002-8231",
  bibdate =      "Mon Feb 25 06:13:56 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of the American Society for Information
                 Science",
}

@Article{Sanders:1987:PPUa,
  author =       "Robert Sanders",
  title =        "The {Pareto Principle}: Its Use and Abuse",
  journal =      "Journal of Consumer Marketing",
  volume =       "4",
  number =       "1",
  pages =        "47--50",
  month =        "????",
  year =         "1987",
  coden =        "????",
  doi =          "http://dx.doi.org/10.1108/eb008188",
  issn =         "0736-3761",
  issn-l =       "0736-3761",
  bibdate =      "Fri Nov 25 06:56:30 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
}

@Article{Sanders:1987:PPUb,
  author =       "Robert Sanders",
  title =        "The {Pareto Principle}: Its Use and Abuse",
  journal =      "Journal of Services Marketing",
  volume =       "1",
  number =       "2",
  pages =        "37--40",
  month =        "????",
  year =         "1987",
  coden =        "????",
  doi =          "http://dx.doi.org/10.1108/eb024706",
  issn =         "0887-6045",
  issn-l =       "0887-6045",
  bibdate =      "Fri Nov 25 06:56:30 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
}

@Article{Schatte:1987:ABM,
  author =       "Peter Schatte",
  title =        "On the asymptotic behaviour of the mantissa
                 distribution of sums",
  journal =      j-J-INFO-PROC-CYBERNETICS-EIK,
  volume =       "23",
  number =       "??",
  pages =        "353--360",
  month =        "????",
  year =         "1987",
  coden =        "JICYE5",
  issn =         "0863-0593",
  issn-l =       "0863-0593",
  bibdate =      "Sat Nov 12 15:58:50 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  ajournal =     "J. Inform. Process. Cybern. EIK",
  fjournal =     "Journal of Information Processing and Cybernetics:
                 EIK",
}

@Article{Schatte:1987:SEU,
  author =       "Peter Schatte",
  title =        "Some estimates of the {$\mathcal{H}_\infty$}-uniform
                 distribution",
  journal =      j-MONAT-MATH,
  volume =       "103",
  number =       "3",
  pages =        "233--249",
  month =        sep,
  year =         "1987",
  coden =        "MNMTA2",
  doi =          "http://dx.doi.org/10.1007/BF01364342",
  issn =         "0026-9255 (print), 1436-5081 (electronic)",
  issn-l =       "0026-9255",
  bibdate =      "Sat Nov 12 15:57:05 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  url =          "http://link.springer.com/article/10.1007/BF01364342",
  acknowledgement = ack-nhfb,
  fjournal =     "Monatshefte f{\"u}r Mathematik",
}

@Article{Tague:1987:MVZ,
  author =       "Jean Tague and Paul Nicholls",
  title =        "The maximal value of a {Zipf} size variable: Sampling
                 properties and relationship to other parameters",
  journal =      j-INFO-PROC-MAN,
  volume =       "23",
  number =       "3",
  pages =        "155--170",
  day =          "7",
  month =        jun,
  year =         "1987",
  coden =        "IPMADK",
  doi =          "http://dx.doi.org/10.1016/0306-4573(87)90001-X",
  issn =         "0306-4573 (print), 1873-5371 (electronic)",
  issn-l =       "0306-4573",
  bibdate =      "Wed Feb 27 07:32:55 MST 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  url =          "http://www.sciencedirect.com/science/article/pii/030645738790001X",
  acknowledgement = ack-nhfb,
  fjournal =     "Information Processing and Management",
  keywords =     "Zipf's Law",
}

@Article{Tichy:1987:GS,
  author =       "Robert F. Tichy",
  title =        "{Gleichverteilung zum Summierungsverfahren
                 {$H_\infty$}}. ({German}) [{Uniform} distribution to
                 the {$ H_\infty$} summation method]",
  journal =      j-MATH-NACHR,
  volume =       "131",
  number =       "??",
  pages =        "119--125",
  month =        "????",
  year =         "1987",
  coden =        "MTMNAQ",
  doi =          "http://dx.doi.org/10.1002/mana.19871310112",
  issn =         "0025-584X",
  issn-l =       "0025-584X",
  bibdate =      "Mon Feb 18 06:44:11 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  url =          "????",
  zmnumber =     "0626.10044",
  acknowledgement = ack-nhfb,
  fjournal =     "Mathematische Nachrichten",
  keywords =     "$H_\infty$-discrepancy; difference sequences; real
                 sequences; uniform distribution",
  language =     "German",
  ZMclass =      "11K06 (General theory of distribution modulo 1); 40J05
                 (Summability in abstract structures)",
  ZMreviewer =   "D. Leitmann",
}

@Article{Turner:1987:DDI,
  author =       "Peter R. Turner",
  title =        "The Distribution of l.s.d. and Its Implications for
                 Computer Design",
  journal =      j-MATH-GAZ,
  volume =       "71",
  number =       "455",
  pages =        "26--31",
  month =        mar,
  year =         "1987",
  coden =        "MAGAAS",
  doi =          "http://dx.doi.org/10.2307/3616283",
  issn =         "0025-5572",
  issn-l =       "0025-5572",
  bibdate =      "Tue Oct 30 23:36:58 2007",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  note =         "[l.s.d. = least significant digits]. The topic is
                 variously known as Benford's Law, the Law of Anomalous
                 Numbers, and Zipf's Law.",
  acknowledgement = ack-nhfb,
  fjournal =     "Mathematical Gazette",
  journal-url =  "http://www.m-a.org.uk/jsp/index.jsp?lnk=620",
  keywords =     "Benford's Law; Law of Anomalous Numbers; logarithmic
                 distribution; overflow; underflow; Zipf's Law",
}

@Article{Belevitch:1988:PQD,
  author =       "Vitold Belevitch",
  title =        "{\`A} propos de la queue de la distribution de {Zipf}.
                 ({French}) [{On} the tail of the {Zipf} distribution]",
  journal =      "Ann. Soc. Sci. Bruxelles S{\'e}r. I",
  volume =       "102",
  number =       "3",
  pages =        "73--85 (1989)",
  year =         "1988",
  coden =        "ASSBAH",
  issn =         "0037-959X",
  issn-l =       "0037-959X",
  mrclass =      "92A90",
  mrnumber =     "1016850 (90g:92114)",
  bibdate =      "Sat Nov 12 09:13:23 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Annales de la Societ{\'e} Scientifique de Bruxelles.
                 S{\'e}rie I. Sciences Math{\'e}matiques, Astronomiques
                 et Physiques",
  language =     "French",
}

@Article{Carslow:1988:AIN,
  author =       "C. Carslow",
  title =        "Anomalies in Income Numbers. {Evidence} of Goal
                 Oriented Behavior",
  journal =      j-ACCOUNT-REV,
  volume =       "63",
  number =       "2",
  pages =        "321--327",
  month =        apr,
  year =         "1988",
  coden =        "ACRVAS",
  issn =         "0001-4826 (print), 1558-7967 (electronic)",
  issn-l =       "0001-4826",
  bibdate =      "Sat Dec 10 11:19:33 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  url =          "http://www.jstor.org/stable/248109",
  acknowledgement = ack-nhfb,
  fjournal =     "The Accounting Review",
  keywords =     "Benford's Law",
  remark =       "This paper references neither Newcomb nor Benford, but
                 it uses their digit-frequency formula from
                 \cite{Feller:1966:IPT} to compare with data on revenues
                 of New Zealand companies.",
}

@Article{Hill:1988:RNG,
  author =       "Theodore Hill",
  title =        "Random number guessing and the first digit
                 phenomenon",
  journal =      j-PSYCHOL-REP,
  volume =       "62",
  number =       "3",
  pages =        "967--971",
  month =        jun,
  year =         "1988",
  coden =        "PYRTAZ",
  doi =          "http://dx.doi.org/10.2466/pr0.1988.62.3.967",
  issn =         "0033-2941 (print), 1558-691X (electronic)",
  issn-l =       "0033-2941",
  bibdate =      "Fri Feb 15 06:41:31 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  url =          "http://www.amsciepub.com/doi/abs/10.2466/pr0.1988.62.3.967",
  acknowledgement = ack-nhfb,
  ajournal =     "Psychol. rep.",
  fjournal =     "Psychological Reports",
}

@InCollection{Kanemitsu:1988:BLF,
  author =       "Shigeru Kanemitsu and Kenji Nagasaka and G{\'e}rard
                 Rauzy and Jau-Shyong Shiue",
  booktitle =    "Probability theory and mathematical statistics
                 ({Kyoto}, 1986)",
  title =        "On {Benford}'s law: the first digit problem",
  volume =       "1299",
  publisher =    pub-SV,
  address =      pub-SV:adr,
  pages =        "158--169",
  year =         "1988",
  doi =          "http://dx.doi.org/10.1007/BFb0078471",
  mrclass =      "11K06 (60E99)",
  mrnumber =     "935987 (89d:11059)",
  mrreviewer =   "Peter Schatte",
  bibdate =      "Sat Nov 12 09:13:23 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  series =       "Lecture Notes in Math.",
  acknowledgement = ack-nhfb,
}

@InCollection{Nicolis:1988:PBZ,
  author =       "John S. Nicolis",
  booktitle =    "Synergetics, order and chaos ({Madrid}, 1987)",
  title =        "On the parallel between {Zipf}'s law and {$1 / f$}
                 processes in chaotic systems possessing coexisting
                 attractors",
  publisher =    "World Sci. Publ.",
  address =      "Teaneck, NJ, USA",
  pages =        "723--734",
  year =         "1988",
  mrclass =      "58F13 (00A69)",
  mrnumber =     "1115922 (92g:58087)",
  mrreviewer =   "Dieter H. Mayer",
  bibdate =      "Sat Nov 12 09:13:23 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
}

@Article{Prather:1988:CET,
  author =       "R. E. Prather",
  title =        "Comparison and Extension of Theories of {Zipf} and
                 {Halstead}",
  journal =      j-COMP-J,
  volume =       "31",
  number =       "3",
  pages =        "248--252",
  month =        jun,
  year =         "1988",
  coden =        "CMPJA6",
  issn =         "0010-4620 (print), 1460-2067 (electronic)",
  issn-l =       "0010-4620",
  bibdate =      "Tue Mar 25 13:51:56 MST 1997",
  bibsource =    "Compendex database;
                 http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_31/Issue_03/",
  url =          "http://www3.oup.co.uk/computer_journal/hdb/Volume_31/Issue_03/tiff/248.tif;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_31/Issue_03/tiff/249.tif;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_31/Issue_03/tiff/250.tif;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_31/Issue_03/tiff/251.tif;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_31/Issue_03/tiff/252.tif",
  acknowledgement = ack-nhfb,
  affiliation =  "Trinity Univ, San Antonio, TX, USA",
  affiliationaddress = "Trinity Univ, San Antonio, TX, USA",
  classcodes =   "C6110B (Software engineering techniques)",
  classification = "723",
  corpsource =   "Comput. and Inf. Sci., Trinity Univ., San Antonio, TX,
                 USA",
  fjournal =     "The Computer Journal",
  keywords =     "behavioural psychology; computer programming; computer
                 software; empirical law; Halstead metrics; Halstead's
                 hypothesis; length estimates; Measurements;
                 probabilistic hypothesis; process; programming;
                 software engineering; software metrication; software
                 science; Zipf metrics; Zipf's law",
  treatment =    "T Theoretical or Mathematical",
}

@Article{Sanders:1988:PPU,
  author =       "Robert Sanders",
  title =        "The {Pareto Principle}: Its Use and Abuse",
  journal =      "Journal of Business \& Industrial Marketing",
  volume =       "3",
  number =       "2",
  pages =        "37--40",
  month =        "????",
  year =         "1988",
  coden =        "????",
  doi =          "http://dx.doi.org/10.1108/eb006057",
  issn =         "0885-8624",
  issn-l =       "0885-8624",
  bibdate =      "Fri Nov 25 07:04:53 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
}

@Article{Schatte:1988:ASC,
  author =       "Peter Schatte",
  title =        "On the Almost Sure Convergence of Floating-Point
                 Mantissas and {Benford's Law}",
  journal =      j-MATH-NACHR,
  volume =       "135",
  number =       "1",
  pages =        "79--83",
  month =        "????",
  year =         "1988",
  coden =        "MTMNAQ",
  doi =          "http://dx.doi.org/10.1002/mana.19881350108",
  issn =         "0025-584X",
  issn-l =       "0025-584X",
  mrclass =      "60F15 (11K31)",
  mrnumber =     "944219 (89g:60114)",
  mrreviewer =   "S. A. Book",
  bibdate =      "Sat Nov 12 09:13:23 2011",
  bibsource =    "http://onlinelibrary.wiley.com/;
                 http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Mathematische Nachrichten",
  keywords =     "Benford's Law; Law of Anomalous Numbers; Zipf's Law",
  onlinedate =   "12 Nov 2006",
  reviewer =     "S. A. Book",
}

@Article{Schatte:1988:LIL,
  author =       "Peter Schatte",
  title =        "On a law of the iterated logarithm for sums {$\bmod
                 1$} with application to {Benford}'s law",
  journal =      j-PROBAB-THEORY-RELAT-FIELDS,
  volume =       "77",
  number =       "2",
  pages =        "167--178",
  year =         "1988",
  coden =        "PTRFEU",
  doi =          "http://dx.doi.org/10.1007/BF00334035",
  issn =         "0178-8051 (print), 1432-2064 (electronic)",
  issn-l =       "0178-8051",
  mrclass =      "60F15 (11K31)",
  mrnumber =     "927235 (89b:60081)",
  mrreviewer =   "L. Kuipers",
  bibdate =      "Sat Nov 12 09:13:23 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Probability Theory and Related Fields",
}

@Article{Schatte:1988:MDC,
  author =       "Peter Schatte",
  title =        "On Mantissa Distribution in Computing and {Benford}'s
                 Law",
  journal =      j-J-INFO-PROC-CYBERNETICS-EIK,
  volume =       "24",
  number =       "9",
  pages =        "443--455",
  month =        "????",
  year =         "1988",
  coden =        "JICYE5",
  issn =         "0863-0593",
  issn-l =       "0863-0593",
  mrclass =      "60E05 (11K06 11K31 65G99)",
  mrnumber =     "984516 (90g:60016)",
  mrreviewer =   "F. Schweiger",
  bibdate =      "Sat Nov 12 09:13:23 2011",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb # "\slash " # ack-nj,
  fjournal =     "Journal of Information Processing and Cybernetics:
                 EIK",
  keywords =     "Benford's Law; Law of Anomalous Numbers; Zipf's Law",
}

@Article{Schatte:1988:UDC,
  author =       "Peter Schatte",
  title =        "On the uniform distribution of certain sequences and
                 {Benford}'s law",
  journal =      j-MATH-NACHR,
  volume =       "136",
  number =       "1",
  pages =        "271--273",
  year =         "1988",
  coden =        "MTMNAQ",
  doi =          "http://dx.doi.org/10.1002/mana.19881360119",
  issn =         "0025-584X",
  issn-l =       "0025-584X",
  mrclass =      "11K06 (11K31)",
  mrnumber =     "952478 (89j:11075)",
  mrreviewer =   "O. P. Stackelberg",
  bibdate =      "Sat Nov 12 09:13:23 2011",
  bibsource =    "http://onlinelibrary.wiley.com/;
                 http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Mathematische Nachrichten",
  onlinedate =   "11 Nov 2006",
}

@Article{Tichy:1988:SRC,
  author =       "Robert F. Tichy",
  title =        "{Statistische Resultate {\"u}ber computergerechte
                 Darstellungen von Zahlen}. ({German}) [Statistical
                 results on computer-oriented representations of
                 numbers]",
  journal =      "Anzeiger der {\"O}sterreichischen Akademie der
                 Wissenschaften. Mathematisch-Naturwissenschaftliche
                 Klasse",
  volume =       "1987",
  number =       "??",
  pages =        "1--8",
  month =        "????",
  year =         "1988",
  coden =        "OSAWA8",
  doi =          "????",
  issn =         "0065-535X",
  issn-l =       "0065-535X",
  bibdate =      "Mon Feb 18 06:45:27 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  url =          "????",
  zmnumber =     "0625.10041",
  acknowledgement = ack-nhfb,
  ajournal =     "Anz. {\"O}sterr. Akad. Wiss., Math.-Naturwiss. Kl.",
  xxnote =       "Despite repeated searches, I have not found this
                 journal online, not even from links at the Austrian
                 Academy of Sciences, \path=http://www.oeaw.ac.at=.",
  ZMclass =      "11K16 (Normal numbers, etc.); 11J71 (Distribution
                 modulo one); 11K38 (Irregularities of distribution)",
}

@Article{Arnold:1989:BEP,
  author =       "Barry C. Arnold and S. James Press",
  title =        "{Bayesian} estimation and prediction for {Pareto}
                 data",
  journal =      j-J-AM-STAT-ASSOC,
  volume =       "84",
  number =       "408",
  pages =        "1079--1084",
  month =        "????",
  year =         "1989",
  coden =        "JSTNAL",
  issn =         "0162-1459 (print), 1537-274X (electronic)",
  issn-l =       "0162-1459",
  mrclass =      "62F15 (62F10)",
  mrnumber =     "92f:62034",
  bibdate =      "Mon May 5 12:36:01 MDT 1997",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 http://www.math.utah.edu/pub/tex/bib/jamstatassoc.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of the American Statistical Association",
}

@Article{Chen:1989:ZLT,
  author =       "Ye-Sho Chen",
  title =        "{Zipf}'s laws in text modeling",
  journal =      "International Journal of General Systems. Methodology,
                 Applications, Education",
  volume =       "15",
  number =       "3",
  pages =        "233--252",
  year =         "1989",
  coden =        "IJGSAX",
  doi =          "http://dx.doi.org/10.1080/03081078908935048",
  issn =         "0308-1079, 1026-7492, 1563-5104",
  issn-l =       "0308-1079",
  mrclass =      "92A90",
  mrnumber =     "1015844",
  bibdate =      "Sat Nov 12 09:13:23 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  ajournal =     "Internat. J. Gen. Systems",
  fjournal =     "International Journal of General Systems. Methodology,
                 Applications, Education",
}

@Article{Family:1989:KDG,
  author =       "Fereydoon Family and Paul Meakin",
  title =        "Kinetics of droplet growth processes: Simulations,
                 theory, and experiments",
  journal =      j-PHYS-REV-A,
  volume =       "40",
  number =       "7",
  pages =        "3836--3854",
  month =        oct,
  year =         "1989",
  coden =        "PLRAAN",
  doi =          "http://dx.doi.org/10.1103/PhysRevA.40.3836",
  issn =         "1050-2947 (print), 1094-1622, 1538-4446, 1538-4519",
  issn-l =       "1050-2947",
  bibdate =      "Thu Feb 28 10:49:20 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  url =          "http://link.aps.org/doi/10.1103/PhysRevA.40.3836",
  acknowledgement = ack-nhfb,
  fjournal =     "Physical Review A (Atomic, Molecular, and Optical
                 Physics)",
}

@InProceedings{Kitsuregawa:1989:EBS,
  author =       "Masaru Kitsuregawa and Masaya Nakayama and Mikio
                 Takagi",
  title =        "The Effect of Bucket Size Tuning in the Dynamic Hybrid
                 {GRACE} Hash Join Method",
  crossref =     "Apers:1989:VLD",
  pages =        "257--266",
  month =        aug,
  year =         "1989",
  coden =        "VLDBDP",
  bibdate =      "Sat Jan 25 17:38:12 MST 1997",
  bibsource =    "Compendex database;
                 http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 http://www.math.utah.edu/pub/tex/bib/hash.bib",
  abstract =     "In this paper, we show detailed analysis and
                 performance evaluation of the Dynamic Hybrid GRACE Hash
                 Join Method (DHGH Method) when the tuple distribution
                 in buckets is unbalanced. The conventional Hash Join
                 Methods specify the tuple distribution in buckets
                 statically. However it may differ from estimation since
                 join operations are applied with selection operations.
                 When the tuple distribution in buckets is unbalanced,
                 the processing cost of join operation becomes more
                 costly than the ideal case when you use Hybrid Hash
                 Join Method (HH Method). On the other hand, when you
                 use the DHGH Method, the destaging buckets are selected
                 dynamically, gives the same performance as the ideal
                 case even if the tuple distribution in buckets is
                 unbalanced such as Zipf-like distributions.",
  acknowledgement = ack-nhfb,
  affiliation =  "Univ of Tokyo",
  affiliationaddress = "Tokyo, Jpn",
  classification = "723",
  journalabr =   "Very Large Data Bases Int Conf Very Large Data Bases",
  keywords =     "Computer Metatheory --- Programming Theory; Computer
                 Programming --- Algorithms; Database Systems; Query
                 Processing; Relational; Relational Algebra; VLDB",
}

@Article{Lang:1989:UAB,
  author =       "Sheau-Dong Lang and James R. Driscoll and Jiann H.
                 Jou",
  title =        "A Unified Analysis of Batched Searching of Sequential
                 and Tree-Structured Files",
  journal =      j-TODS,
  volume =       "14",
  number =       "4",
  pages =        "604--618",
  month =        dec,
  year =         "1989",
  coden =        "ATDSD3",
  issn =         "0362-5915 (print), 1557-4644 (electronic)",
  issn-l =       "0362-5915",
  mrclass =      "68P10 (68P20)",
  mrnumber =     "1 073 204",
  bibdate =      "Sat Apr 14 10:34:48 MDT 2001",
  bibsource =    "Database/Graefe.bib; Database/Wiederhold.bib;
                 http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  url =          "http://www.acm.org/pubs/articles/journals/tods/1989-14-4/p604-lang/p604-lang.pdf;
                 http://www.acm.org/pubs/citations/journals/tods/1989-14-4/p604-lang/;
                 http://www.acm.org/pubs/toc/Abstracts/tods/76908.html",
  abstract =     "A direct and unified approach is used to analyze the
                 efficiency of batched searching of sequential and
                 tree-structured files. The analysis is applicable to
                 arbitrary search distributions, and closed-form
                 expressions are obtained for the expected batched
                 searching cost and savings. In particular, we consider
                 a search distribution satisfying Zipf's law for
                 sequential files and four types of uniform (random)
                 search distribution for sequential and tree-structured
                 files. These results unify and extend earlier research
                 on batched searching and estimating block accesses for
                 database systems.",
  acknowledgement = ack-nhfb,
  affiliation =  "Central Florida Univ., Orlando, FL, USA",
  annote =       "closed-form expressions for the number of accesses
                 needed given arbitrary search distributions.",
  fjournal =     "ACM Transactions on Database Systems",
  generalterms = "Algorithms; Design; Performance; Theory",
  keywords =     "algorithms; design; performance; theory",
  subject =      "{\bf H.3.3}: Information Systems, INFORMATION STORAGE
                 AND RETRIEVAL, Information Search and Retrieval, Search
                 process. {\bf H.3.2}: Information Systems, INFORMATION
                 STORAGE AND RETRIEVAL, Information Storage, File
                 organization. {\bf H.2.2}: Information Systems,
                 DATABASE MANAGEMENT, Physical Design, Access methods.",
}

@Article{Nicolis:1989:CDM,
  author =       "G. Nicolis and C. Nicolis and John S. Nicolis",
  title =        "Chaotic dynamics, {Markov} partitions, and {Zipf}'s
                 law",
  journal =      j-J-STAT-PHYS,
  volume =       "54",
  number =       "3--4",
  pages =        "915--924",
  year =         "1989",
  coden =        "JSTPSB",
  issn =         "0022-4715 (print), 1572-9613 (electronic)",
  issn-l =       "0022-4715",
  mrclass =      "58F13 (58F14 58F20)",
  mrnumber =     "988565 (90b:58184)",
  mrreviewer =   "Shi Hai Li",
  bibdate =      "Sat Nov 12 09:13:23 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Statistical Physics",
}

@Article{Nicolis:1989:PBZ,
  author =       "John S. Nicolis and Ichiro Tsuda",
  title =        "On the parallel between {Zipf}'s law and {$1 / f$}
                 processes in chaotic systems possessing coexisting
                 attractors",
  journal =      j-PROG-THEOR-PHYS,
  volume =       "82",
  number =       "2",
  pages =        "254--274",
  year =         "1989",
  coden =        "PTPKAV",
  issn =         "0033-068X (print), 1347-4081 (electronic)",
  issn-l =       "0033-068X",
  mrclass =      "58F13 (92K20)",
  mrnumber =     "1023357 (91d:58165)",
  mrreviewer =   "Nima Geffen",
  bibdate =      "Sat Nov 12 09:13:23 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Progress of Theoretical Physics",
}

@Article{Schatte:1989:MUD,
  author =       "Peter Schatte",
  title =        "On measures of uniformly distributed sequences and
                 {Benford}'s law",
  journal =      j-MONAT-MATH,
  volume =       "107",
  number =       "3",
  pages =        "245--256",
  year =         "1989",
  coden =        "MNMTA2",
  doi =          "http://dx.doi.org/10.1007/BF01300347",
  issn =         "0026-9255 (print), 1436-5081 (electronic)",
  issn-l =       "0026-9255",
  mrclass =      "11K36 (60F99)",
  mrnumber =     "1008683 (90k:11097)",
  mrreviewer =   "Kazuo Goto",
  bibdate =      "Sat Nov 12 09:13:23 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Monatshefte f{\"u}r Mathematik",
}

@Article{Shieh:1989:BZE,
  author =       "Yeung-Nan Shieh",
  title =        "The {Beckmann--Zipf} effect and plant location under
                 uniform pricing",
  journal =      j-ECONOM-LETT,
  volume =       "30",
  number =       "1",
  pages =        "89--92",
  day =          "1",
  month =        jan,
  year =         "1989",
  coden =        "ECLEDS",
  doi =          "http://dx.doi.org/10.1016/0165-1765(89)90162-6",
  issn =         "0165-1765 (print), 1873-7374 (electronic)",
  issn-l =       "0165-1765",
  mrclass =      "90A12 (90B05)",
  mrnumber =     "1010312",
  bibdate =      "Wed Feb 27 07:32:55 MST 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  url =          "http://www.sciencedirect.com/science/article/pii/0165176589901626",
  acknowledgement = ack-nhfb,
  fjournal =     "Economics Letters",
  keywords =     "Zipf's Law",
}

@Article{Thomas:1989:UPR,
  author =       "Jacob K. Thomas",
  title =        "Unusual patterns in reported earnings",
  journal =      j-ACCOUNT-REV,
  volume =       "59",
  number =       "4",
  pages =        "773--787",
  month =        oct,
  year =         "1989",
  coden =        "ACRVAS",
  issn =         "0001-4826 (print), 1558-7967 (electronic)",
  issn-l =       "0001-4826",
  bibdate =      "Fri Feb 15 06:49:18 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  url =          "http://www.jstor.org/stable/247861",
  acknowledgement = ack-nhfb,
  fjournal =     "The Accounting Review",
  keywords =     "Benford's Law; distribution of first digits;
                 distribution of second digits",
}

@Article{Katsikas:1990:CDG,
  author =       "A. A. Katsikas and J. S. Nicolis",
  title =        "Chaotic dynamics of generating {Markov} partitions and
                 linguistic sequences mimicking {Zipf}'s law",
  journal =      "Nuovo Cimento D (1)",
  volume =       "12",
  number =       "2",
  pages =        "177--195",
  year =         "1990",
  coden =        "NCSDDN",
  doi =          "http://dx.doi.org/10.1007/BF02450454",
  issn =         "0392-6737 (print), 1826-9893 (electronic)",
  issn-l =       "0392-6737",
  mrclass =      "92A90 (58F13 92A08 94A15)",
  mrnumber =     "1049338 (90m:92114)",
  bibdate =      "Sat Nov 12 09:13:23 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Societ{\`a} Italiana di Fisica. Il Nuovo Cimento. D.
                 Serie 1",
}

@InCollection{Nagasaka:1990:BLL,
  author =       "Kenji Nagasaka and Shigeru Kanemitsu and Jau-Shyong
                 Shiue",
  booktitle =    "Number theory, {Vol}.\ {I} ({Budapest}, 1987)",
  title =        "{Benford}'s law: the logarithmic law of first digit",
  volume =       "51",
  publisher =    pub-NORTH-HOLLAND,
  address =      pub-NORTH-HOLLAND:adr,
  pages =        "361--391",
  year =         "1990",
  mrclass =      "11K06",
  mrnumber =     "1058225 (92b:11048)",
  mrreviewer =   "Peter Schatte",
  bibdate =      "Sat Nov 12 09:13:23 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  series =       "Colloq. Math. Soc. J{\'a}nos Bolyai",
  acknowledgement = ack-nhfb,
}

@Article{Schatte:1990:BLC,
  author =       "Peter Schatte",
  title =        "On {Benford}'s law for continued fractions",
  journal =      j-MATH-NACHR,
  volume =       "148",
  pages =        "137--144",
  year =         "1990",
  coden =        "MTMNAQ",
  issn =         "0025-584X",
  issn-l =       "0025-584X",
  mrclass =      "11K50 (11K06)",
  mrnumber =     "1127337 (92m:11077)",
  mrreviewer =   "Harald Niederreiter",
  bibdate =      "Sat Nov 12 09:13:23 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Mathematische Nachrichten",
}

@Book{Szekely:1990:PKN,
  author =       "G{\'a}bor J. Sz{\'e}kely",
  title =        "{Paradoxa: klassische und neue {\"U}berraschungen aus
                 Wahrscheinlichkeitsrechnung und mathematischer
                 Statistik}. (German) [{Paradoxes}: traditional and new
                 surprises in probability and mathematical statistics]",
  publisher =    "Deutsch",
  address =      "Thun, Switzerland",
  pages =        "239",
  year =         "1990",
  isbn =         "3-87144-850-8",
  isbn-13 =      "978-3-87144-850-8",
  lccn =         "????",
  bibdate =      "Thu Nov 17 19:26:05 MST 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 z3950.gbv.de:20011/gvk",
  note =         "Translation by Ulrike Leitner from the Hungarian
                 original.",
  url =          "http://www.gbv.de/dms/hbz/toc/ht003363686.pdf;
                 http://www.zentralblatt-math.org/zmath/en/search/?an=0743.60004",
  acknowledgement = ack-nhfb,
  language =     "German",
}

@Article{VandenBroeck:1990:LFB,
  author =       "C. {Van den Broeck} and R. Kawai",
  title =        "Learning in feedforward {Boolean} networks",
  journal =      j-PHYS-REV-A,
  volume =       "42",
  number =       "??",
  pages =        "6210--??",
  day =          "15",
  month =        nov,
  year =         "1990",
  coden =        "PLRAAN",
  doi =          "http://dx.doi.org/10.1103/PhysRevA.42.6210",
  issn =         "1050-2947 (print), 1094-1622, 1538-4446, 1538-4519",
  issn-l =       "1050-2947",
  bibdate =      "Tue Feb 26 06:40:57 MST 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  url =          "http://link.aps.org/doi/10.1103/PhysRevA.42.6210",
  acknowledgement = ack-nhfb,
  fjournal =     "Physical Review A (Atomic, Molecular, and Optical
                 Physics)",
  keywords =     "Zipf's Law",
}

@Article{Yeh:1990:ODT,
  author =       "Hsiaw-Chan Yeh",
  title =        "One discrete time series model for fat-tailed integer
                 random variables: {Zipf} process",
  journal =      "Bulletin of the Institute of Mathematics. Academia
                 Sinica",
  volume =       "18",
  number =       "1",
  pages =        "19--33",
  year =         "1990",
  coden =        "BIMSDG",
  issn =         "0304-9825",
  issn-l =       "0304-9825",
  mrclass =      "60J10 (62M10)",
  mrnumber =     "1072827 (91i:60175)",
  mrreviewer =   "Ed McKenzie",
  bibdate =      "Sat Nov 12 09:13:23 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  ajournal =     "Bull. Inst. Math. Acad. Sinica",
  fjournal =     "Bulletin of the Institute of Mathematics. Academia
                 Sinica",
}

@Article{Antonini:1991:NUD,
  author =       "Rita Giuliano Antonini",
  title =        "On the Notion of Uniform Distribution Mod $1$",
  journal =      j-FIB-QUART,
  volume =       "29",
  number =       "3",
  pages =        "230--234",
  month =        aug,
  year =         "1991",
  coden =        "FIBQAU",
  issn =         "0015-0517",
  issn-l =       "0015-0517",
  bibdate =      "Thu Oct 20 18:01:34 MDT 2011",
  bibsource =    "http://www.fq.math.ca/29-3.html;
                 http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 http://www.math.utah.edu/pub/tex/bib/fibquart.bib",
  url =          "http://www.fq.math.ca/Scanned/29-3/antonini.pdf",
  acknowledgement = ack-nhfb,
  ajournal =     "Fib. Quart",
  fjournal =     "The Fibonacci Quarterly. Official Organ of the
                 Fibonacci Association",
  keywords =     "Benford's Law",
}

@Article{Burke:1991:BLP,
  author =       "John Burke and Eric Kincanon",
  title =        "{Benford}'s law and physical constants: The
                 distribution of initial digits",
  journal =      j-AMER-J-PHYSICS,
  volume =       "59",
  number =       "10",
  pages =        "952--952",
  month =        oct,
  year =         "1991",
  coden =        "AJPIAS",
  doi =          "http://dx.doi.org/10.1119/1.16838",
  issn =         "0002-9505",
  issn-l =       "0002-9505",
  bibdate =      "Mon Nov 14 17:31:11 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  url =          "http://adsabs.harvard.edu/abs/1991AmJPh..59..952B;
                 http://ajp.aapt.org/resource/1/ajpias/v59/i10/p952_s1",
  acknowledgement = ack-nhfb,
  fjournal =     "American Journal of Physics",
}

@Article{Chen:1991:ZLN,
  author =       "Ye-Sho Chen",
  title =        "{Zipf}'s law in natural languages, programming
                 languages, and command languages: the {Simon--Yule}
                 approach",
  journal =      j-INT-J-SYST-SCI,
  volume =       "22",
  number =       "11",
  pages =        "2299--2312",
  year =         "1991",
  coden =        "IJSYA9",
  doi =          "http://dx.doi.org/10.1080/00207729108910791",
  issn =         "0020-7721",
  issn-l =       "0020-7721",
  bibdate =      "Sat Nov 12 10:50:55 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  zmnumber =     "0793.68020",
  abstract =     "Zipf's law and issues in natural languages,
                 programming languages and command languages related to
                 it, are reviewed. We point out the need for a unified
                 theory to resolve the issues. Based on Herbert Simon's
                 creative process for scientific discovery, we evaluate
                 four leading theories of language generation. As a
                 result, the Simon--Yule model of text generation is
                 selected as a promising theory. The implications of the
                 theory related to the issues in natural languages,
                 programming languages and command languages are
                 discussed.",
  acknowledgement = ack-nhfb,
  classmath =    "68N15 (Programming languages) 68T50 (Natural language
                 processing)",
  fjournal =     "International Journal of Systems Science",
  keywords =     "command languages; natural languages; programming
                 languages; Simon-Yule model; text generation; Zipf's
                 law",
}

@Book{Durrett:1991:PTE,
  author =       "Richard Durrett",
  title =        "Probability: theory and examples",
  publisher =    "Wadsworth and Brooks\slash Cole Advanced Books and
                 Software",
  address =      "Pacific Grove, CA, USA",
  pages =        "ix + 453",
  year =         "1991",
  isbn =         "0-534-13206-5",
  isbn-13 =      "978-0-534-13206-4",
  lccn =         "QA273 .D865 1991",
  bibdate =      "Mon Nov 21 10:06:18 MST 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 z3950.loc.gov:7090/Voyager",
  price =        "US\$49.95",
  series =       "The Wadsworth and Brooks\slash Cole statistics\slash
                 probability series",
  acknowledgement = ack-nhfb,
  remark =       "Benford's Law is treated on pp. 300ff. Hill \cite[page
                 893]{Hill:1995:BII} reports that Durrett has a proof
                 that the $k$-th digit of powers of integers follows
                 Benford's Law.",
  subject =      "Probabilities",
}

@Book{Hardy:1991:DS,
  author =       "G. H. (Godfrey Harold) Hardy",
  title =        "Divergent series",
  publisher =    "Chelsea Pub. Co.",
  address =      "New York, NY, USA",
  edition =      "Second",
  pages =        "xvi + 396",
  year =         "1991",
  isbn =         "0-8284-0334-1",
  isbn-13 =      "978-0-8284-0334-4",
  lccn =         "QA295 .H29 1991",
  bibdate =      "Wed Nov 16 08:17:27 MST 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 z3950.loc.gov:7090/Voyager",
  acknowledgement = ack-nhfb,
  author-dates = "1877--1947",
  remark =       "Unaltered reprint of \cite{Hardy:1949:DS}, despite
                 label of second edition.",
  subject =      "Divergent series",
}

@Article{Katsikas:1991:CDG,
  author =       "A. A. Katsikas and J. S. Nicolis",
  title =        "Chaotic Dynamics of Generating {Markov} Partitions,
                 and Linguistic Sequences Mimicking {Zipf}'s Law",
  journal =      j-LECT-NOTES-COMP-SCI,
  volume =       "565",
  pages =        "335--??",
  year =         "1991",
  coden =        "LNCSD9",
  issn =         "0302-9743 (print), 1611-3349 (electronic)",
  issn-l =       "0302-9743",
  bibdate =      "Mon May 13 08:51:55 MDT 1996",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Lecture Notes in Computer Science",
}

@Article{Schatte:1991:NBL,
  author =       "P. Schatte and K. Nagasaka",
  title =        "A note on {Benford}'s law for second order linear
                 recurrences with periodical coefficients",
  journal =      j-Z-ANAL-ANWEND,
  volume =       "10",
  number =       "2",
  pages =        "251--254",
  year =         "1991",
  coden =        "????",
  issn =         "0232-2064",
  issn-l =       "0232-2064",
  mrclass =      "11K31",
  mrnumber =     "1155374 (93b:11101)",
  mrreviewer =   "F. Schweiger",
  bibdate =      "Sat Nov 12 09:13:23 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "{Zeitschrift f{\"u}r Analysis und ihre Anwendungen}",
}

@Article{Schatte:1991:ULI,
  author =       "P. Schatte",
  title =        "On a uniform law of the iterated logarithm for sums
                 mod {$1$} and {Benford}'s law",
  journal =      "Litovsk. Mat. Sb.",
  volume =       "31",
  number =       "1",
  pages =        "205--217",
  year =         "1991",
  coden =        "????",
  doi =          "http://dx.doi.org/10.1007/BF00972327",
  issn =         "0132-2818",
  issn-l =       "0132-2818",
  mrclass =      "60F15 (11K99)",
  mrnumber =     "1161363 (93g:60067)",
  mrreviewer =   "O. P. Stackelberg",
  bibdate =      "Sat Nov 12 09:13:23 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Lietuvos TSR Moksl\polhk u Akademija. Lietuvos TSR
                 Auk\v stosios Mokyklos. Lietuvos Matematikos Rinkinys.
                 Akademiya Nauk Litovsko{\u\i} SSR. Vysshie Uchebnye
                 Zavedeniya Litovsko{\u\i} SSR. Litovski\u\i\
                 Matematicheski{\u\i} Sbornik",
  xxnote =       "Check pages: reprinted in two version of this
                 journal??",
}

@Article{Trubnikov:1991:SDZ,
  author =       "B. A. Trubnikov and I. A. Rumynski{\u\i}",
  title =        "A simple derivation of the {Zipf--Krylov} law for
                 words and the possibility of its ``evolution''
                 interpretation",
  journal =      j-DOKL-AKAD-NAUK,
  volume =       "321",
  number =       "2",
  pages =        "270--275",
  year =         "1991",
  coden =        "DANKAS",
  issn =         "0002-3264",
  issn-l =       "0002-3264",
  mrclass =      "00A69 (92K20)",
  mrnumber =     "1153554",
  bibdate =      "Sat Nov 12 09:13:23 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Doklady Akademii Nauk SSSR",
}

@TechReport{Busta:1992:TRN,
  author =       "B. Busta and R. Sundheim",
  title =        "Tax return numbers tend to obey {Benford}'s law",
  type =         "Working Paper",
  number =       "W93-106-94",
  institution =  "Center for Business Research, St. Cloud State
                 University",
  address =      "St. Cloud, MN, USA",
  year =         "1992",
  bibdate =      "Sat Feb 16 17:29:47 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
}

@Article{Goto:1992:SEB,
  author =       "Kazuo Got{\^o}",
  title =        "Some examples of {Benford} sequences",
  journal =      "Math. J. Okayama Univ.",
  volume =       "34",
  pages =        "225--232 (1994)",
  year =         "1992",
  coden =        "MJOKAP",
  issn =         "0030-1566",
  issn-l =       "0030-1566",
  mrclass =      "11K36",
  mrnumber =     "1272624 (95c:11097)",
  bibdate =      "Sat Nov 12 09:13:23 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Mathematical Journal of Okayama University",
}

@Article{Gunther:1992:PCZ,
  author =       "R. G{\"u}nther and B. Schapiro and P. Wagner",
  title =        "Physical complexity and {Zipf}'s law",
  journal =      j-INT-J-THEOR-PHYS,
  volume =       "31",
  number =       "3",
  pages =        "525--543",
  year =         "1992",
  coden =        "IJTPBM",
  doi =          "http://dx.doi.org/10.1007/BF00740003",
  issn =         "0020-7748 (print), 1572-9575 (electronic)",
  issn-l =       "0020-7748",
  mrclass =      "58F40",
  mrnumber =     "1154668 (92k:58252)",
  bibdate =      "Sat Nov 12 09:13:23 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Theoretical Physics",
}

@Article{Jech:1992:LDL,
  author =       "Thomas Jech",
  title =        "The logarithmic distribution of leading digits and
                 finitely additive measures",
  journal =      j-DISCRETE-MATH,
  volume =       "108",
  number =       "1--3",
  pages =        "53--57",
  month =        "????",
  year =         "1992",
  coden =        "DSMHA4",
  issn =         "0012-365X (print), 1872-681X (electronic)",
  issn-l =       "0012-365X",
  bibdate =      "Fri Nov 18 12:12:57 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Discrete Mathematics",
}

@Article{Lagarias:1992:PTS,
  author =       "J. C. Lagarias and A. Weiss",
  title =        "The {$3 X + 1$} problem: two stochastic models",
  journal =      j-ANN-APPL-PROBAB,
  volume =       "2",
  number =       "??",
  pages =        "329--361",
  month =        "????",
  year =         "1992",
  issn =         "1050-5164",
  issn-l =       "1050-5164",
  bibdate =      "Mon Nov 21 07:49:35 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Annals of applied probability",
}

@Article{Li:1992:RTE,
  author =       "W. Li",
  title =        "Random texts exhibit {Zipf}'s-law-like word frequency
                 distribution",
  journal =      j-IEEE-TRANS-INF-THEORY,
  volume =       "38",
  number =       "6",
  pages =        "1842--1845",
  month =        "????",
  year =         "1992",
  coden =        "IETTAW",
  doi =          "http://dx.doi.org/10.1109/18.165464",
  issn =         "0018-9448 (print), 1557-9654 (electronic)",
  issn-l =       "0018-9448",
  bibdate =      "Fri Nov 18 12:32:19 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Information Theory",
}

@PhdThesis{Nigrini:1992:DIE,
  author =       "Mark John Nigrini",
  title =        "The detection of income tax evasion through an
                 analysis of digital distributions",
  type =         "{Ph.D.} Dissertation",
  school =       "Department of Accounting\slash Business Law,
                 University of Cincinnati",
  address =      "Cincinnati, OH, USA",
  pages =        "xvi + 309",
  day =          "28",
  month =        aug,
  year =         "1992",
  bibdate =      "Sat Nov 12 15:47:41 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  url =          "http://search.proquest.com/docview/304052348",
  acknowledgement = ack-nhfb,
  advisor =      "Wallace R. Wood",
  remark =       "There are more than 230 mentions of Frank Benford, and
                 8 of Simon Newcomb, but no mention of Pareto or Zipf.",
}

@Article{Sanders:1992:PPU,
  author =       "Robert Sanders",
  title =        "The {Pareto Principle}: its Use and Abuse",
  journal =      j-J-PROD-BRAND-MANAG,
  volume =       "1",
  number =       "2",
  pages =        "37--40",
  month =        "????",
  year =         "1992",
  coden =        "????",
  doi =          "http://dx.doi.org/10.1108/10610429210036762",
  issn =         "1061-0421",
  issn-l =       "1061-0421",
  bibdate =      "Fri Nov 25 06:50:32 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Product \& Brand Management",
  keywords =     "80/20 rule",
}

@Article{Too:1992:UDM,
  author =       "Yeu-Hua Too",
  title =        "On the uniform distribution modulo one of some
                 log-like sequences",
  journal =      "Proceedings of the Japan Academy, Series A.
                 Mathematical Sciences",
  volume =       "68",
  number =       "9",
  pages =        "269--272",
  month =        "????",
  year =         "1992",
  doi =          "http://dx.doi.org/10.3792/pjaa.68.269",
  issn =         "0021-4280",
  issn-l =       "0021-4280",
  bibdate =      "Mon Feb 18 06:55:06 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  url =          "http://projecteuclid.org/euclid.pja/1195511634",
  acknowledgement = ack-nhfb,
}

@Article{Trachtenberg:1992:WFR,
  author =       "M. Trachtenberg",
  title =        "Why failure rates observe {Zipf}'s law in operational
                 software",
  journal =      j-IEEE-TRANS-RELIAB,
  volume =       "41",
  number =       "3",
  pages =        "386--389",
  year =         "1992",
  coden =        "IEERAJ",
  doi =          "http://dx.doi.org/10.1109/24.159803",
  issn =         "0018-9529 (print), 1558-1721 (electronic)",
  issn-l =       "0018-9529",
  bibdate =      "Sat Nov 12 10:50:55 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  zmnumber =     "0825.68222",
  acknowledgement = ack-nhfb,
  classmath =    "68M15 (Reliability and testing of computer systems)
                 68N01 (General)",
  fjournal =     "IEEE Transactions on Reliability",
}

@Article{Anonymous:1993:WFR,
  author =       "Anonymous",
  title =        "Why failure rates observe {Zipf}'s law in operational
                 software: {M. Trachtenberg. IEEE Transactions on
                 Reliability, {\bf 41}(3), 386 (1992)}",
  journal =      j-MICROELECT-RELIABILITY,
  volume =       "33",
  number =       "13",
  pages =        "2062--2062",
  month =        oct,
  year =         "1993",
  coden =        "MCRLAS",
  doi =          "http://dx.doi.org/10.1016/0026-2714(93)90406-O",
  issn =         "0026-2714 (print), 1872-941X (electronic)",
  issn-l =       "0026-2714",
  bibdate =      "Wed Feb 27 07:32:55 MST 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  url =          "http://www.sciencedirect.com/science/article/pii/002627149390406O",
  acknowledgement = ack-nhfb,
  fjournal =     "Microelectronics and Reliability",
  keywords =     "Zipf's Law",
}

@Article{Buck:1993:IBF,
  author =       "B. Buck and A. C. Merchant and S. M. Perez",
  title =        "An illustration of {Benford}'s first digit law using
                 alpha decay half lives",
  journal =      j-EUR-J-PHYS,
  volume =       "14",
  number =       "2",
  pages =        "59--63",
  month =        "????",
  year =         "1993",
  coden =        "EJPHD4",
  issn =         "0143-0807 (print), 1361-6404 (electronic)",
  issn-l =       "0143-0807",
  bibdate =      "Mon Nov 14 17:32:53 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  url =          "http://adsabs.harvard.edu/abs/1993EJPh...14...59B",
  acknowledgement = ack-nhfb,
  fjournal =     "European Journal of Physics",
}

@Article{Deakin:1993:ADB,
  author =       "Michael A. B. Deakin",
  title =        "Another derivation of {Benford}'s law",
  journal =      j-AUSTRALIAN-MATH-SOC-GAZ,
  volume =       "20",
  number =       "5",
  pages =        "162--163",
  year =         "1993",
  coden =        "????",
  issn =         "0311-0729",
  issn-l =       "0311-0729",
  mrclass =      "11K36",
  mrnumber =     "1268513 (95j:11072)",
  mrreviewer =   "Jean-Loup Mauclaire",
  bibdate =      "Sat Nov 12 09:13:23 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Australian Mathematical Society Gazette",
}

@Article{Nigrini:1993:CBL,
  author =       "Mark Nigrini",
  title =        "Can {Benford's Law} be used in Forensic Accounting?",
  journal =      "The Balance Sheet",
  volume =       "??",
  number =       "??",
  pages =        "7--8",
  month =        jun,
  year =         "1993",
  coden =        "????",
  issn =         "????",
  bibdate =      "Mon Nov 21 22:03:06 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
}

@TechReport{Sundheim:1993:FNT,
  author =       "R. Sundheim and B. Busta",
  title =        "{Fibonacci} numbers tend to obey {Benford's Law}: an
                 extension of {Wlodarski} and {Sentance}",
  type =         "Working Paper",
  institution =  "St. Cloud State University",
  address =      "St. Cloud, MN, USA",
  month =        "????",
  year =         "1993",
  bibdate =      "Mon Feb 18 06:37:56 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
}

@Article{Sury:1993:FPD,
  author =       "B. Sury",
  title =        "Fractional parts of $ \log p $ and a digit function",
  journal =      j-EXPO-MATH,
  volume =       "11",
  number =       "4",
  pages =        "381--384",
  month =        "????",
  year =         "1993",
  doi =          "????",
  issn =         "0723-0869 (print), 1878-0792 (electronic)",
  issn-l =       "0723-0869",
  bibdate =      "Mon Feb 18 06:39:02 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  url =          "????",
  zmnumber =     "0787.11003",
  acknowledgement = ack-nhfb,
  ajournal =     "Expo. Math.",
  fjournal =     "Expositiones Mathematicae",
  journal-url =  "http://www.sciencedirect.com/science/journal/07230869",
  keywords =     "decimal expansion; sum of digits",
  ZMclass =      "11A63 (Radix representation; digital problems)",
  ZMreviewer =   "G. Larcher (Salzburg)",
}

@Article{Wolf:1993:PHJ,
  author =       "Joel L. Wolf and Philip S. Yu and John Turek and
                 Daniel M. Dias",
  title =        "A parallel hash join algorithm for managing data
                 skew",
  journal =      j-IEEE-TRANS-PAR-DIST-SYS,
  volume =       "4",
  number =       "12",
  pages =        "1355--1371",
  month =        dec,
  year =         "1993",
  coden =        "ITDSEO",
  doi =          "http://dx.doi.org/10.1109/71.250117",
  issn =         "1045-9219 (print), 1558-2183 (electronic)",
  issn-l =       "1045-9219",
  bibdate =      "Fri Apr 11 15:20:39 MDT 1997",
  bibsource =    "Compendex database;
                 http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 http://www.math.utah.edu/pub/tex/bib/ieeetranspardistsys.bib",
  acknowledgement = ack-nhfb,
  affiliation =  "IBM T. J. Watson Research Cent",
  affiliationaddress = "Yorktown Heights, NY, USA",
  classification = "721.1; 722.4; 723.1; 723.2; 723.3; 921.4; C4240P
                 (Parallel programming and algorithm theory); C4250
                 (Database theory); C6160D (Relational DBMS)",
  corpsource =   "IBM Thomas J. Watson Res. Center, Yorktown Heights,
                 NY, USA",
  fjournal =     "IEEE Transactions on Parallel and Distributed
                 Systems",
  journalabr =   "IEEE Trans Parallel Distrib Syst",
  keywords =     "Algorithms; combinatorial; Combinatorial mathematics;
                 Combinatorial optimization; Complex queries; complex
                 queries; Computational complexity; Data handling; Data
                 skew; data skew; database theory; hash; Hash joins;
                 hashing; heuristic optimization; hierarchical; join
                 column; joins; load balancing; Load balancing;
                 optimization; parallel algorithms; parallel hash join
                 algorithm; Parallel processing systems; Program
                 processors; Query languages; query processing;
                 Relational database systems; relational databases;
                 resource allocation; scheduling; Zipf-like
                 distribution",
  treatment =    "T Theoretical or Mathematical",
}

@Article{Wolf:1993:PSM,
  author =       "Joel L. Wolf and Daniel M. Dias and Philip S. Yu",
  title =        "Parallel sort merge join algorithm for managing data
                 skew",
  journal =      j-IEEE-TRANS-PAR-DIST-SYS,
  volume =       "4",
  number =       "1",
  pages =        "70--86",
  month =        jan,
  year =         "1993",
  coden =        "ITDSEO",
  doi =          "http://dx.doi.org/10.1109/71.205654",
  issn =         "1045-9219 (print), 1558-2183 (electronic)",
  issn-l =       "1045-9219",
  bibdate =      "Fri Apr 11 15:20:39 MDT 1997",
  bibsource =    "Compendex database;
                 http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 http://www.math.utah.edu/pub/tex/bib/ieeetranspardistsys.bib",
  acknowledgement = ack-nhfb,
  affiliation =  "IBM",
  affiliationaddress = "Yorktown Heights, NY, USA",
  classification = "723.1; 723.3; 921.5; C4240P (Parallel programming
                 and algorithm theory); C4250 (Database theory); C6130
                 (Data handling techniques); C6160B (Distributed DBMS);
                 C6160D (Relational DBMS)",
  corpsource =   "IBM T. J. Watson Res. Center. Yorktown Heights, NY,
                 USA",
  fjournal =     "IEEE Transactions on Parallel and Distributed
                 Systems",
  journalabr =   "IEEE Trans Parallel Distrib Syst",
  keywords =     "Algorithms; Computer systems programming; Data skew;
                 data skew management; distributed databases; Divide and
                 conquer approach; divide-and-conquer; join phases; load
                 balancing; merging; multiple processors;
                 Multiprocessing programs; Optimization; parallel;
                 Parallel algorithms; parallel algorithms; Parallel sort
                 merge join algorithm; parallelizable optimization
                 algorithm; phase; Query processing; relational algebra;
                 Relational database systems; relational databases;
                 scheduling; Scheduling; sort merge join algorithm; sort
                 phase; sorting; Sorting; transfer phase; Zipf-like
                 distribution",
  treatment =    "T Theoretical or Mathematical",
}

@Book{Arthur:1994:IRP,
  author =       "W. Brian Arthur",
  title =        "Increasing returns and path dependence in the
                 economy",
  publisher =    pub-U-MICHIGAN,
  address =      pub-U-MICHIGAN:adr,
  pages =        "xx + 201",
  year =         "1994",
  isbn =         "0-472-09496-3 , 0-472-06496-7 (paperback)",
  isbn-13 =      "978-0-472-09496-7, 978-0-472-06496-0 (paperback)",
  lccn =         "HD69.S5 A77 1994",
  bibdate =      "Wed Feb 27 07:08:40 MST 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 z3950.loc.gov:7090/Voyager",
  note =         "With a foreword by Kenneth J. Arrow.",
  series =       "Economics, cognition, and society",
  acknowledgement = ack-nhfb,
  keywords =     "Zipf's Law",
  subject =      "Economies of scale; Mathematical models; Economic
                 development; Economics, Mathematical",
}

@Article{Boyle:1994:AFS,
  author =       "Jeff Boyle",
  title =        "An application of {Fourier} series to the most
                 significant digit problem",
  journal =      j-AMER-MATH-MONTHLY,
  volume =       "101",
  number =       "9",
  pages =        "879--886",
  month =        nov,
  year =         "1994",
  coden =        "AMMYAE",
  issn =         "0002-9890 (print), 1930-0972 (electronic)",
  issn-l =       "0002-9890",
  mrclass =      "60F99",
  mrnumber =     "1 300 493",
  bibdate =      "Wed Dec 3 17:17:33 MST 1997",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
}

@Article{Fuchs:1994:PDP,
  author =       "Aim{\'e} Fuchs and Giorgio Letta",
  title =        "Le probl{\`e}me du premier chiffre d{\'e}cimal pour
                 les nombres premiers. ({French}) [The problem for the
                 first decimal digit of prime numbers",
  journal =      "Rendiconti della Accademia Nazionale delle Scienze
                 detta dei XL. Serie V. Memorie di Matem{\`a}tica",
  volume =       "18",
  number =       "1",
  pages =        "81--87",
  month =        "????",
  year =         "1994",
  bibdate =      "Sat Feb 16 17:40:01 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  url =          "http://www.combinatorics.org/ojs/index.php/eljc/article/download/v3i2r25/pdf",
  zmnumber =     "0838.11004",
  acknowledgement = ack-nhfb,
  ajournal =     "Rend. Accad. Naz. Sci. XL, V. Ser., Mem. Mat.",
  keywords =     "asymptotic densities; logarithmic density; primes;
                 relative densities",
  language =     "French",
  xxjournal =    "Rend. Acad. Naz. Sci. Detta",
  xxvolume =     "XL",
  ZMclass =      "11B05 (Topology etc. of sets of numbers); 11K16
                 (Normal numbers, etc.)",
  ZMreviewer =   "I. Z. Ruzsa (Budapest)",
}

@Article{Ley:1994:TPB,
  author =       "Eduadro Ley and Hal R. Varian",
  title =        "Are there psychological barriers in the {Dow--Jones}
                 index?",
  journal =      j-APPL-FINANC-ECON,
  volume =       "4",
  number =       "3",
  pages =        "217--224",
  month =        "????",
  year =         "1994",
  coden =        "????",
  doi =          "http://dx.doi.org/10.1080/758526902",
  issn =         "0960-3107 (print), 1466-4305 (electronic)",
  issn-l =       "0960-3107",
  bibdate =      "Sat Feb 16 18:29:52 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  url =          "http://www.tandfonline.com/doi/abs/10.1080/758526902",
  acknowledgement = ack-nhfb,
  fjournal =     "Applied Financial Economics",
}

@Article{Mantegna:1994:LFN,
  author =       "R. N. Mantegna and S. V. Buldyrev and A. L. Goldberger
                 and S. Havlin and C. K. Peng and M. Simons and H. E.
                 Stanley",
  title =        "Linguistic Features of Noncoding {DNA} Sequences",
  journal =      j-PHYS-REV-LET,
  volume =       "73",
  number =       "??",
  pages =        "3169--??",
  day =          "5",
  month =        dec,
  year =         "1994",
  coden =        "PRLTAO",
  doi =          "http://dx.doi.org/10.1103/PhysRevLett.73.3169",
  issn =         "0031-9007 (print), 1079-7114 (electronic), 1092-0145",
  issn-l =       "0031-9007",
  bibdate =      "Tue Feb 26 06:40:57 MST 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  url =          "http://link.aps.org/doi/10.1103/PhysRevLett.73.3169",
  acknowledgement = ack-nhfb,
  fjournal =     "Physical Review Letters",
  keywords =     "Zipf's Law",
}

@Article{Nigrini:1994:UDF,
  author =       "Mark J. Nigrini",
  title =        "Using digital frequencies to detect fraud",
  journal =      "The White Paper",
  volume =       "??",
  number =       "??",
  pages =        "3--6",
  month =        apr # "\slash " # may,
  year =         "1994",
  bibdate =      "Sat Feb 16 18:53:08 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  remark =       "The White Paper is the precursor to Fraud Magazine; I
                 cannot find it in the Library of Congress catalog.",
}

@Article{Pedrotti:1994:ALU,
  author =       "A. Pedrotti",
  title =        "Analysis of a list-update strategy",
  journal =      j-INFO-PROC-LETT,
  volume =       "52",
  number =       "3",
  pages =        "115--121",
  day =          "11",
  month =        nov,
  year =         "1994",
  coden =        "IFPLAT",
  issn =         "0020-0190 (print), 1872-6119 (electronic)",
  issn-l =       "0020-0190",
  bibdate =      "Wed Nov 11 12:16:26 MST 1998",
  bibsource =    "Compendex database;
                 http://www.elsevier.com:80/inca/publications/store/5/0/5/6/1/2/;
                 http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  affiliation =  "Scuola Normale Superiore",
  affiliationaddress = "Pisa, Italy",
  classification = "721.1; 723.2; 921.6; 922.1; 922.2; C4240C
                 (Computational complexity); C6130 (Data handling
                 techniques)",
  corpsource =   "Scuola Normale Superiore, Pisa, Italy",
  fjournal =     "Information Processing Letters",
  journalabr =   "Inf Process Lett",
  keywords =     "Algorithms; analysis of algorithms; average-case
                 complexity; BIT; competitive algorithms; Computational
                 complexity; computational complexity; convergence;
                 Convergence of numerical methods; Data handling;
                 Function evaluation; Heuristic methods; list
                 processing; list update; Markov chains; Move to front
                 algorithm; move-to-front; Probability; Random number
                 generation; searching; Theorem proving; transpose;
                 Zipf's law",
  treatment =    "T Theoretical or Mathematical",
}

@Article{Berton:1995:HGT,
  author =       "L. Berton",
  title =        "He's Got their Number. {Scholar} Uses Math to Foil
                 Financial Fraud",
  journal =      j-WALL-ST-J,
  volume =       "??",
  number =       "??",
  pages =        "??--??",
  day =          "10",
  month =        jul,
  year =         "1995",
  coden =        "WSJOAF",
  issn =         "0099-9660",
  issn-l =       "0099-9660",
  bibdate =      "Sat Dec 10 11:17:37 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Wall Street Journal",
}

@Book{Bologna:1995:FAF,
  author =       "Jack Bologna and Robert J. Lindquist",
  title =        "Fraud auditing and forensic accounting: new tools and
                 techniques",
  publisher =    pub-WILEY,
  address =      pub-WILEY:adr,
  edition =      "Second",
  pages =        "xv + 249",
  year =         "1995",
  isbn =         "0-471-10646-1 (hardcover)",
  isbn-13 =      "978-0-471-10646-3 (hardcover)",
  lccn =         "HV8079.W47 B65 1995",
  bibdate =      "Tue Nov 22 10:31:53 MST 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 z3950.loc.gov:7090/Voyager",
  url =          "http://www.loc.gov/catdir/bios/wiley042/95005510.html;
                 http://www.loc.gov/catdir/description/wiley033/95005510.html;
                 http://www.loc.gov/catdir/toc/onix04/95005510.html",
  acknowledgement = ack-nhfb,
  remark =       "This book does not discuss Benford's Law, but may be
                 helpful background for application of that law to the
                 detection of fraud.",
  subject =      "white collar crime investigation; United States;
                 forensic accounting; fraud investigation",
}

@Article{Czirok:1995:CBS,
  author =       "Andras Czir{\'o}k and Rosario N. Mantegna and Shlomo
                 Havlin and H. Eugene Stanley",
  title =        "Correlations in binary sequences and a generalized
                 {Zipf} analysis",
  journal =      j-PHYS-REV-E,
  volume =       "52",
  number =       "??",
  pages =        "446--??",
  day =          "1",
  month =        jul,
  year =         "1995",
  coden =        "PLEEE8",
  doi =          "http://dx.doi.org/10.1103/PhysRevE.52.446",
  issn =         "1539-3755 (print), 1550-2376 (electronic)",
  issn-l =       "1539-3755",
  bibdate =      "Tue Feb 26 06:40:57 MST 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  url =          "http://link.aps.org/doi/10.1103/PhysRevE.52.446",
  acknowledgement = ack-nhfb,
  fjournal =     "Physical Review E (Statistical physics, plasmas,
                 fluids, and related interdisciplinary topics)",
  keywords =     "Zipf's Law",
}

@Article{Filipponi:1995:SPA,
  author =       "Piero Filipponi and Renato Menicocci",
  title =        "Some Probabilistic Aspects of the Terminal Digits of
                 {Fibonacci} Numbers",
  journal =      j-FIB-QUART,
  volume =       "33",
  number =       "4",
  pages =        "325--331",
  month =        aug,
  year =         "1995",
  coden =        "FIBQAU",
  issn =         "0015-0517",
  issn-l =       "0015-0517",
  bibdate =      "Thu Oct 20 18:02:19 MDT 2011",
  bibsource =    "http://www.fq.math.ca/33-4.html;
                 http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 http://www.math.utah.edu/pub/tex/bib/fibquart.bib",
  url =          "http://www.fq.math.ca/Scanned/33-4/filipponi.pdf",
  acknowledgement = ack-nhfb,
  ajournal =     "Fib. Quart",
  fjournal =     "The Fibonacci Quarterly. Official Organ of the
                 Fibonacci Association",
}

@Article{Havlin:1995:DBZ,
  author =       "Shlomo Havlin",
  title =        "The distance between {Zipf} plots",
  journal =      j-PHYSICA-A,
  volume =       "216",
  number =       "1--2",
  pages =        "148--150",
  day =          "1",
  month =        jun,
  year =         "1995",
  coden =        "PHYADX",
  doi =          "http://dx.doi.org/10.1016/0378-4371(95)00069-J",
  issn =         "0378-4371 (print), 1873-2119 (electronic)",
  issn-l =       "0378-4371",
  bibdate =      "Wed Feb 27 07:32:55 MST 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  url =          "http://www.sciencedirect.com/science/article/pii/037843719500069J",
  acknowledgement = ack-nhfb,
  fjournal =     "Physica A. Statistical Mechanics and its
                 Applications",
  keywords =     "Zipf's Law",
}

@Article{Hill:1995:BII,
  author =       "Theodore P. Hill",
  title =        "Base-invariance implies {Benford's Law}",
  journal =      j-PROC-AM-MATH-SOC,
  volume =       "123",
  number =       "3",
  pages =        "887--895",
  month =        mar,
  year =         "1995",
  coden =        "PAMYAR",
  doi =          "http://dx.doi.org/10.2307/2160815",
  issn =         "0002-9939 (print), 1088-6826 (electronic)",
  issn-l =       "0002-9939",
  mrclass =      "60A10 (28D05)",
  mrnumber =     "1233974 (95d:60006)",
  mrreviewer =   "Peter Schatte",
  bibdate =      "Sat Nov 12 09:13:23 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  url =          "http://www.jstor.org/stable/2160815",
  acknowledgement = ack-nhfb,
  fjournal =     "Proceedings of the American Mathematical Society",
}

@Article{Hill:1995:SDP,
  author =       "Theodore P. Hill",
  title =        "The significant-digit phenomenon",
  journal =      j-AMER-MATH-MONTHLY,
  volume =       "102",
  number =       "4",
  pages =        "322--327",
  month =        apr,
  year =         "1995",
  coden =        "AMMYAE",
  doi =          "http://dx.doi.org/10.2307/2974952",
  issn =         "0002-9890 (print), 1930-0972 (electronic)",
  issn-l =       "0002-9890",
  mrclass =      "11K99 (60E99)",
  mrnumber =     "96f:11101",
  mrreviewer =   "Jean-Loup Mauclaire",
  bibdate =      "Wed Dec 3 17:17:33 MST 1997",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "American Mathematical Monthly",
}

@Article{Hill:1995:SDS,
  author =       "Theodore P. Hill",
  title =        "A statistical derivation of the significant-digit
                 law",
  journal =      j-STAT-SCI,
  volume =       "10",
  number =       "4",
  pages =        "354--363",
  year =         "1995",
  coden =        "STSCEP",
  issn =         "0883-4237",
  issn-l =       "0883-4237",
  mrclass =      "60E99 (60A10 62E99)",
  mrnumber =     "1421567 (98a:60021)",
  mrreviewer =   "Peter Schatte",
  bibdate =      "Sat Nov 12 10:09:36 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  url =          "2-P&origin=MSN;
                 http://links.jstor.org/sici?sici=0883-4237(199511)10:4<354:ASDOTS>2.0.CO",
  zmnumber =     "Zbl 0955.60509",
  acknowledgement = ack-nhfb,
  fjournal =     "Statistical Science. A Review Journal of the Institute
                 of Mathematical Statistics",
}

@Article{Kanter:1995:MPL,
  author =       "I. Kanter and D. A. Kessler",
  title =        "{Markov} Processes: Linguistics and {Zipf's Law}",
  journal =      j-PHYS-REV-LET,
  volume =       "74",
  number =       "??",
  pages =        "4559--??",
  day =          "29",
  month =        may,
  year =         "1995",
  coden =        "PRLTAO",
  doi =          "http://dx.doi.org/10.1103/PhysRevLett.74.4559",
  issn =         "0031-9007 (print), 1079-7114 (electronic), 1092-0145",
  issn-l =       "0031-9007",
  bibdate =      "Tue Feb 26 06:40:57 MST 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  url =          "http://link.aps.org/doi/10.1103/PhysRevLett.74.4559",
  acknowledgement = ack-nhfb,
  fjournal =     "Physical Review Letters",
  keywords =     "Zipf's Law",
}

@Article{Makse:1995:MUG,
  author =       "Hern{\'a}n A. Makse and Shlomo Havlin and H. Eugene
                 Stanley",
  title =        "Modelling urban growth patterns",
  journal =      j-NATURE,
  volume =       "377",
  number =       "6550",
  pages =        "608--612",
  day =          "19",
  month =        oct,
  year =         "1995",
  coden =        "NATUAS",
  doi =          "http://dx.doi.org/10.1038/377608a0",
  issn =         "0028-0836 (print), 1476-4687 (electronic)",
  issn-l =       "0028-0836",
  bibdate =      "Wed Feb 27 06:06:25 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  url =          "http://www.nature.com/nature/journal/v377/n6550/abs/377608a0.html",
  acknowledgement = ack-nhfb,
  fjournal =     "Nature",
  keywords =     "Berlin (Germany) population; London (UK) population;
                 Zipf's Law",
}

@Article{Mantegna:1995:SAC,
  author =       "R. N. Mantegna and S. V. Buldyrev and A. L. Goldberger
                 and S. Havlin and C.-K. Peng and M. Simons and H. E.
                 Stanley",
  title =        "Systematic analysis of coding and noncoding {DNA}
                 sequences using methods of statistical linguistics",
  journal =      j-PHYS-REV-E,
  volume =       "52",
  number =       "??",
  pages =        "2939--??",
  day =          "1",
  month =        sep,
  year =         "1995",
  coden =        "PLEEE8",
  doi =          "http://dx.doi.org/10.1103/PhysRevE.52.2939",
  issn =         "1539-3755 (print), 1550-2376 (electronic)",
  issn-l =       "1539-3755",
  bibdate =      "Tue Feb 26 06:40:57 MST 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  url =          "http://link.aps.org/doi/10.1103/PhysRevE.52.2939",
  acknowledgement = ack-nhfb,
  fjournal =     "Physical Review E (Statistical physics, plasmas,
                 fluids, and related interdisciplinary topics)",
  keywords =     "Zipf's Law",
}

@Article{Mosimann:1995:DFC,
  author =       "James E. Mosimann and Claire V. Wiseman and Ruth E.
                 Edelman",
  title =        "Data Fabrication: Can People Generate Random Digits?",
  journal =      j-ACCOUNT-RES,
  volume =       "4",
  number =       "1",
  pages =        "31--55",
  month =        "????",
  year =         "1995",
  coden =        "ARQAEZ",
  issn =         "0898-9621 (print), 1545-5815 (electronic)",
  issn-l =       "0898-9621",
  bibdate =      "Sat Dec 10 11:56:38 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  url =          "http://www.tandfonline.com/doi/abs/10.1080/08989629508573866",
  acknowledgement = ack-nhfb,
  fjournal =     "Accountability in Research",
  keywords =     "Benford's Law",
  remark =       "The abstract ends with: ``The difficulty that people
                 have in creating random error digits supports the
                 utility of examining such digits in investigations of
                 scientific misconduct.''",
}

@Article{Stanley:1995:ZPS,
  author =       "Michael H. R. Stanley and Sergey V. Buldyrev and
                 Shlomo Havlin and Rosario N. Mantegna and Michael A.
                 Salinger and H. Eugene Stanley",
  title =        "{Zipf} plots and the size distribution of firms",
  journal =      j-ECONOM-LETT,
  volume =       "49",
  number =       "4",
  pages =        "453--457",
  day =          "15",
  month =        oct,
  year =         "1995",
  coden =        "ECLEDS",
  doi =          "http://dx.doi.org/10.1016/0165-1765(95)00696-D",
  issn =         "0165-1765 (print), 1873-7374 (electronic)",
  issn-l =       "0165-1765",
  bibdate =      "Wed Feb 27 07:32:55 MST 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  url =          "http://www.sciencedirect.com/science/article/pii/016517659500696D",
  acknowledgement = ack-nhfb,
  fjournal =     "Economics Letters",
  keywords =     "Zipf's Law",
}

@Article{Wagner-Dobler:1995:DLL,
  author =       "Roland Wagner-D{\"o}bler and Jan Berg",
  title =        "The Dependence of {Lotka's Law} on the Selection of
                 Time Periods in the Development of Scientific Areas and
                 Authors",
  journal =      j-J-DOC,
  volume =       "51",
  number =       "1",
  pages =        "28--43",
  month =        "????",
  year =         "1995",
  coden =        "JDOCAS",
  doi =          "http://dx.doi.org/10.1108/eb026941",
  issn =         "0022-0418 (print), 1758-7379 (electronic)",
  issn-l =       "0022-0418",
  bibdate =      "Fri Nov 25 07:29:22 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Documentation",
}

@Article{Zornig:1995:URZ,
  author =       "Peter Z{\"o}rnig and Gabriel Altmann",
  title =        "Unified representation of {Zipf} distributions",
  journal =      j-COMPUT-STAT-DATA-ANAL,
  volume =       "19",
  number =       "4",
  pages =        "461--473",
  day =          "1",
  month =        apr,
  year =         "1995",
  coden =        "CSDADW",
  doi =          "http://dx.doi.org/10.1016/0167-9473(94)00009-8",
  issn =         "0167-9473 (print), 1872-7352 (electronic)",
  issn-l =       "0167-9473",
  mrclass =      "62E10 (62F10)",
  mrnumber =     "1333065 (96f:62029)",
  mrreviewer =   "Friedrich Liese",
  bibdate =      "Wed Feb 27 07:32:55 MST 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  url =          "http://www.sciencedirect.com/science/article/pii/0167947394000098",
  acknowledgement = ack-nhfb,
  fjournal =     "Computational Statistics \& Data Analysis",
  keywords =     "Zipf's Law",
}

@Book{Bak:1996:HNW,
  author =       "Per Bak",
  title =        "How nature works: the science of self-organized
                 criticality",
  publisher =    "Copernicus",
  address =      "New York, NY, USA",
  pages =        "xiii + 212 + 8",
  year =         "1996",
  isbn =         "0-387-94791-4 (hardcover)",
  isbn-13 =      "978-0-387-94791-4 (hardcover)",
  lccn =         "QC173.4.C74 B34 1996",
  bibdate =      "Thu Nov 24 13:34:22 MST 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 z3950.loc.gov:7090/Voyager",
  acknowledgement = ack-nhfb,
  keywords =     "Zipf's Law",
  subject =      "Critical phenomena (Physics); Complexity (Philosophy);
                 Physics; Philosophy",
}

@Article{Beirlant:1996:TIE,
  author =       "Jan Beirlant and Petra Vynckier and Jozef L. Teugels",
  title =        "Tail Index Estimation, {Pareto} Quantile Plots, and
                 Regression Diagnostics",
  journal =      j-J-AM-STAT-ASSOC,
  volume =       "91",
  number =       "436",
  pages =        "1659--??",
  month =        "????",
  year =         "1996",
  coden =        "JSTNAL",
  issn =         "0162-1459 (print), 1537-274X (electronic)",
  issn-l =       "0162-1459",
  bibdate =      "Mon May 5 08:26:17 MDT 1997",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 http://www.math.utah.edu/pub/tex/bib/jamstatassoc.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of the American Statistical Association",
}

@Article{Burgos:1996:ZSB,
  author =       "Javier D. Burgos and Pedro Moreno-Tovar",
  title =        "{Zipf}-scaling behavior in the immune system",
  journal =      j-BIOSYSTEMS,
  volume =       "39",
  number =       "3",
  pages =        "227--232",
  day =          "15",
  month =        nov,
  year =         "1996",
  coden =        "BSYMBO",
  doi =          "http://dx.doi.org/10.1016/0303-2647(96)01618-8",
  issn =         "0303-2647 (print), 1872-8324 (electronic)",
  issn-l =       "0303-2647",
  bibdate =      "Wed Feb 27 07:32:55 MST 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  url =          "http://www.sciencedirect.com/science/article/pii/0303264796016188",
  acknowledgement = ack-nhfb,
  fjournal =     "Biosystems (A6E)",
  keywords =     "Zipf's Law",
}

@Article{Campanino:1996:IIM,
  author =       "Massimo Campanino and Stefano Isola",
  title =        "Infinite invariant measures for non-uniformly
                 expanding transformations of $[0, 1]$: Weak law of
                 large numbers with anomalous scaling",
  journal =      j-FORUM-MATH,
  volume =       "8",
  number =       "1",
  pages =        "71--92",
  year =         "1996",
  coden =        "FOMAEF",
  doi =          "http://dx.doi.org/10.1515/form.1996.8.71",
  issn =         "0933-7741 (print), 1435-5337 (electronic)",
  issn-l =       "0933-7741",
  bibdate =      "Sat Nov 12 10:33:06 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  zmnumber =     "0837.60022",
  abstract =     "We consider a class of maps of $[0, 1]$ with an
                 indifferent fixed point at 0 and expanding everywhere
                 else. Using the invariant ergodic probability measure
                 of a suitable, everywhere expanding, induced
                 transformation we are able to study the infinite
                 invariant measure of the original map in some detail.
                 Given a continuous function with compact support in
                 $]0, 1]$, we prove that its time averages satisfy a
                 `weak law of large numbers' with anomalous scaling $n /
                 \log n$ and give an upper bound for the decay of
                 correlations.",
  acknowledgement = ack-nhfb,
  ajournal =     "Forum Math.",
  classmath =    "60F05 (Weak limit theorems) 28D05 (Measure-preserving
                 transformations) 37A99 (Ergodic theory)",
  fjournal =     "Forum Mathematicum",
  keywords =     "decay of correlations; invariant ergodic probability
                 measure; weak law of large numbers",
}

@Article{Czirok:1996:POP,
  author =       "Andr{\'a}s Czir{\'o}k and H. Eugene Stanley and
                 Tam{\'a}s Vicsek",
  title =        "Possible origin of power-law behavior in $n$-tuple
                 {Zipf} analysis",
  journal =      j-PHYS-REV-E,
  volume =       "53",
  number =       "??",
  pages =        "6371--??",
  day =          "1",
  month =        jun,
  year =         "1996",
  coden =        "PLEEE8",
  doi =          "http://dx.doi.org/10.1103/PhysRevE.53.6371",
  issn =         "1539-3755 (print), 1550-2376 (electronic)",
  issn-l =       "1539-3755",
  bibdate =      "Tue Feb 26 06:40:57 MST 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  url =          "http://link.aps.org/doi/10.1103/PhysRevE.53.6371",
  acknowledgement = ack-nhfb,
  fjournal =     "Physical Review E (Statistical physics, plasmas,
                 fluids, and related interdisciplinary topics)",
  keywords =     "Zipf's Law",
}

@Article{Fuchs:1996:PDP,
  author =       "Aim{\'e} Fuchs and Giorgio Letta",
  title =        "Le probl{\`e}me du premier chiffre d{\'e}cimal pour
                 les nombres premiers. ({French}) [The problem for the
                 first decimal digit of prime numbers",
  journal =      j-ELECT-J-COMB,
  volume =       "3",
  number =       "2",
  pages =        "R25:1--R25:7",
  month =        "????",
  year =         "1996",
  issn =         "1077-8926 (print), 1097-1440 (electronic)",
  issn-l =       "1077-8926",
  bibdate =      "Sat Feb 16 17:40:01 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  note =         "The Foata Festschrift volume.",
  url =          "http://www.combinatorics.org/ojs/index.php/eljc/article/download/v3i2r25/pdf",
  zmnumber =     "0853.11006",
  acknowledgement = ack-nhfb,
  fjournal =     "Electronic Journal of Combinatorics",
  language =     "French",
  xxpages =      "601--607",
}

@Article{Gunther:1996:ZLE,
  author =       "R. G{\"u}nther and L. Levitin and B. Schapiro and P.
                 Wagner",
  title =        "{Zipf}'s law and the effect of ranking on probability
                 distributions",
  journal =      j-INT-J-THEOR-PHYS,
  volume =       "35",
  number =       "2",
  pages =        "395--417",
  year =         "1996",
  coden =        "IJTPBM",
  doi =          "http://dx.doi.org/10.1007/BF02083823",
  issn =         "0020-7748 (print), 1572-9575 (electronic)",
  issn-l =       "0020-7748",
  bibdate =      "Sat Nov 12 10:53:57 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  zmnumber =     "0843.60002",
  abstract =     "Ranking procedures are widely used in the description
                 of many different types of complex systems. Zipf's law
                 is one of the most remarkable frequency-rank
                 relationships and has been observed independently in
                 physics, linguistics, biology, demography, etc. We show
                 that ranking plays a crucial role in making it possible
                 to detect empirical relationships in systems that exist
                 in one realization only, even when the statistical
                 ensemble to which the systems belong has a very broad
                 probability distribution. Analytical results and
                 numerical simulations are presented which clarify the
                 relations between the probability distributions and the
                 behavior of expected values for unranked and ranked
                 random variables. This analysis is performed, in
                 particular, for the evolutionary model presented in our
                 previous papers which leads to Zipf's law and reveals
                 the underlying mechanism of this phenomenon in terms of
                 a system with interdependent and interacting components
                 as opposed to the ``ideal gas'' models suggested by
                 previous researchers. The ranking procedure applied to
                 this model leads to a new, unexpected phenomenon: a
                 characteristic ``staircase'' behavior of the mean
                 values of the ranked variables (ranked occupation
                 numbers). This result is due to the broadness of the
                 probability distributions for the occupation numbers
                 and does not follow from the ``ideal gas'' model. Thus,
                 it provides an opportunity, by comparison with
                 empirical data, to obtain evidence as to which model
                 relates to reality.",
  acknowledgement = ack-nhfb,
  classmath =    "60A99 (Foundations of probability theory)",
  fjournal =     "International Journal of Theoretical Physics",
  keywords =     "numerical simulations; ranking procedures; Zipf's
                 law",
}

@TechReport{Hill:1996:NDT,
  author =       "Theodore P. Hill",
  title =        "A note on distributions of true versus fabricated
                 data",
  type =         "Preprint",
  institution =  "Department of Mathematics, Georgia Institute of
                 Technology",
  address =      "Atlanta, GA, USA",
  pages =        "4",
  year =         "1996",
  bibdate =      "Sat Feb 16 17:47:27 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  url =          "http://digitalcommons.calpoly.edu/cgi/viewcontent.cgi?article=1046&context=rgp_rsr",
  acknowledgement = ack-nhfb,
}

@Article{Israeloff:1996:CZD,
  author =       "N. E. Israeloff and M. Kagalenko and K. Chan",
  title =        "Can {Zipf} Distinguish Language From Noise in
                 Noncoding {DNA}?",
  journal =      j-PHYS-REV-LET,
  volume =       "76",
  number =       "??",
  pages =        "1976--??",
  day =          "11",
  month =        mar,
  year =         "1996",
  coden =        "PRLTAO",
  doi =          "http://dx.doi.org/10.1103/PhysRevLett.76.1976",
  issn =         "0031-9007 (print), 1079-7114 (electronic), 1092-0145",
  issn-l =       "0031-9007",
  bibdate =      "Tue Feb 26 06:40:57 MST 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  url =          "http://link.aps.org/doi/10.1103/PhysRevLett.76.1976",
  acknowledgement = ack-nhfb,
  fjournal =     "Physical Review Letters",
  keywords =     "Zipf's Law",
}

@Article{Krugman:1996:CMU,
  author =       "Paul Krugman",
  title =        "Confronting the Mystery of Urban Hierarchy",
  journal =      j-J-JPN-INT-ECON,
  volume =       "10",
  number =       "4",
  pages =        "399--418",
  month =        dec,
  year =         "1996",
  coden =        "JJIEBD",
  doi =          "http://dx.doi.org/10.1006/jjie.1996.0023",
  issn =         "0889-1583 (print), 1095-8681 (electronic)",
  issn-l =       "0889-1583",
  bibdate =      "Wed Feb 27 06:15:55 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  url =          "http://www.sciencedirect.com/science/article/pii/S0889158396900234",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of the {Japanese} and International Economies",
  keywords =     "Zipf's Law",
}

@Book{Krugman:1996:SOE,
  author =       "Paul R. Krugman",
  title =        "The Self-Organizing Economy",
  publisher =    "Blackwell Publishers",
  address =      "Cambridge, MA, USA",
  pages =        "vi + 122",
  year =         "1996",
  isbn =         "1-55786-699-6 (paperback)",
  isbn-13 =      "978-1-55786-699-8 (paperback)",
  lccn =         "HB199 .K75 1996",
  bibdate =      "Wed Feb 27 07:08:14 MST 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 z3950.loc.gov:7090/Voyager",
  acknowledgement = ack-nhfb,
  keywords =     "Zipf's Law",
  subject =      "Economics; Self-organizing systems",
}

@Article{Ley:1996:PDU,
  author =       "Eduardo Ley",
  title =        "On the Peculiar Distribution of the {U.S.} Stock
                 Indexes' Digits",
  journal =      j-AMER-STAT,
  volume =       "50",
  number =       "4",
  pages =        "311--313",
  month =        nov,
  year =         "1996",
  coden =        "ASTAAJ",
  issn =         "0003-1305 (print), 1537-2731 (electronic)",
  issn-l =       "0003-1305",
  bibdate =      "Mon Nov 14 15:09:04 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/amstat.bib;
                 http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 http://www.math.utah.edu/pub/tex/bib/fparith.bib",
  url =          "http://www.jstor.org/stable/2684926",
  acknowledgement = ack-nhfb,
  fjournal =     "The American Statistician",
}

@Article{Newman:1996:ASC,
  author =       "M. E. J. Newman and Kim Sneppen",
  title =        "Avalanches, scaling, and coherent noise",
  journal =      j-PHYS-REV-E,
  volume =       "54",
  number =       "6",
  pages =        "6226--6231",
  month =        dec,
  year =         "1996",
  coden =        "PLEEE8",
  doi =          "http://dx.doi.org/10.1103/PhysRevE.54.6226",
  issn =         "1539-3755 (print), 1550-2376 (electronic)",
  issn-l =       "1539-3755",
  bibdate =      "Thu Feb 28 10:44:51 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  url =          "http://link.aps.org/doi/10.1103/PhysRevE.54.6226",
  acknowledgement = ack-nhfb,
  fjournal =     "Physical Review E (Statistical physics, plasmas,
                 fluids, and related interdisciplinary topics)",
  keywords =     "power law; scale invariance; Zipf's law",
}

@Article{Nigrini:1996:TCA,
  author =       "M. Nigrini",
  title =        "A Taxpayer Compliance Application of {Benford's Law}",
  journal =      "Journal of the American Taxation Association",
  volume =       "18",
  number =       "1",
  pages =        "72--91",
  month =        "????",
  year =         "1996",
  coden =        "????",
  issn =         "0198-9073 (print), 1558-8017 (electronic)",
  issn-l =       "0198-9073",
  bibdate =      "Mon Nov 14 16:30:42 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  ajournal =     "J. Amer. Tax. Assoc.",
  fjournal =     "Journal of the American Taxation Association",
}

@Article{Perline:1996:ZLC,
  author =       "Richard Perline",
  title =        "{Zipf}'s law, the {Central Limit Theorem}, and the
                 random division of the unit interval",
  journal =      j-PHYS-REV-E,
  volume =       "54",
  number =       "1",
  pages =        "220--223",
  day =          "1",
  month =        jul,
  year =         "1996",
  coden =        "PLEEE8",
  doi =          "http://dx.doi.org/10.1103/PhysRevE.54.220",
  issn =         "1539-3755 (print), 1550-2376 (electronic)",
  issn-l =       "1539-3755",
  bibdate =      "Tue Feb 26 06:40:57 MST 2013",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/m/mandelbrot-benoit.bib;
                 http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  url =          "http://link.aps.org/doi/10.1103/PhysRevE.54.220",
  acknowledgement = ack-nhfb,
  fjournal =     "Physical Review E (Statistical physics, plasmas,
                 fluids, and related interdisciplinary topics)",
  keywords =     "Mandelbrot's monkey-at-the-typewriter model of Zipf's
                 inverse power law; Zipf's Law",
}

@Article{Sole:1996:ESO,
  author =       "Ricard V. Sol{\'e} and Susanna C. Manrubia",
  title =        "Extinction and self-organized criticality in a model
                 of large-scale evolution",
  journal =      j-PHYS-REV-E,
  volume =       "54",
  number =       "1",
  pages =        "R42--R45",
  month =        jul,
  year =         "1996",
  coden =        "PLEEE8",
  doi =          "http://dx.doi.org/10.1103/PhysRevE.54.R42",
  issn =         "1539-3755 (print), 1550-2376 (electronic)",
  issn-l =       "1539-3755",
  bibdate =      "Thu Feb 28 10:32:32 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  url =          "http://link.aps.org/doi/10.1103/PhysRevE.54.R42",
  acknowledgement = ack-nhfb,
  fjournal =     "Physical Review E (Statistical physics, plasmas,
                 fluids, and related interdisciplinary topics)",
  keywords =     "power law; scale invariance; Zipf's law",
}

@Article{Solomon:1996:SSE,
  author =       "Sorin Solomon and Moshe Levy",
  title =        "Spontaneous Scaling Emergence in Generic Stochastic
                 Systems",
  journal =      j-INT-J-MOD-PHYS-C,
  volume =       "7",
  number =       "5",
  pages =        "745--752",
  month =        oct,
  year =         "1996",
  coden =        "IJMPEO",
  doi =          "http://dx.doi.org/10.1142/S0129183196000624",
  issn =         "0129-1831 (print), 1793-6586 (electronic)",
  bibdate =      "Thu Feb 28 10:20:02 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  url =          "http://www.worldscientific.com/doi/abs/10.1142/S0129183196000624",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Modern Physics C [Physics and
                 Computers]",
  journal-url =  "http://www.worldscientific.com/loi/ijmpc",
}

@Article{Watanabe:1996:EZL,
  author =       "Makoto S. Watanabe",
  title =        "Erratum: {Zipf}'s law in percolation",
  journal =      j-PHYS-REV-E,
  volume =       "54",
  number =       "??",
  pages =        "4483--??",
  day =          "1",
  month =        oct,
  year =         "1996",
  coden =        "PLEEE8",
  doi =          "http://dx.doi.org/10.1103/PhysRevE.54.4483",
  issn =         "1539-3755 (print), 1550-2376 (electronic)",
  issn-l =       "1539-3755",
  bibdate =      "Tue Feb 26 06:40:57 MST 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  note =         "See \cite {Watanabe:1996:ZLP}.",
  url =          "http://link.aps.org/doi/10.1103/PhysRevE.54.4483",
  acknowledgement = ack-nhfb,
  fjournal =     "Physical Review E (Statistical physics, plasmas,
                 fluids, and related interdisciplinary topics)",
  keywords =     "Zipf's Law",
}

@Article{Watanabe:1996:ZLP,
  author =       "Makoto S. Watanabe",
  title =        "{Zipf}'s law in percolation",
  journal =      j-PHYS-REV-E,
  volume =       "53",
  number =       "??",
  pages =        "4187--??",
  day =          "1",
  month =        apr,
  year =         "1996",
  coden =        "PLEEE8",
  doi =          "http://dx.doi.org/10.1103/PhysRevE.53.4187",
  issn =         "1539-3755 (print), 1550-2376 (electronic)",
  issn-l =       "1539-3755",
  bibdate =      "Tue Feb 26 06:40:57 MST 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  note =         "See erratum \cite {Watanabe:1996:EZL}.",
  url =          "http://link.aps.org/doi/10.1103/PhysRevE.53.4187",
  acknowledgement = ack-nhfb,
  fjournal =     "Physical Review E (Statistical physics, plasmas,
                 fluids, and related interdisciplinary topics)",
  keywords =     "Zipf's Law",
}

@Article{Allaart:1997:ISC,
  author =       "Pieter C. Allaart",
  title =        "An Invariant-Sum Characterization of {Benford's Law}",
  journal =      j-J-APPL-PROBAB,
  volume =       "34",
  number =       "1",
  pages =        "288--291",
  month =        mar,
  year =         "1997",
  coden =        "JPRBAM",
  doi =          "http://dx.doi.org/10.2307/3215195",
  issn =         "0021-9002 (print), 1475-6072 (electronic)",
  issn-l =       "0021-9002",
  mrclass =      "60E05",
  mrnumber =     "1429075 (98d:60029)",
  mrreviewer =   "Peter Schatte",
  bibdate =      "Sat Nov 12 09:13:23 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  url =          "http://www.jstor.org/stable/3215195",
  abstract =     "The accountant Nigrini remarked that in tables of data
                 distributed according to Benford's law, the sum of all
                 elements with first digit $d (d = 1, 2, \ldots, 9)$ is
                 approximately constant. In this note, a mathematical
                 formulation of Nigrini's observation is given and it is
                 shown that Benford's law is the unique probability
                 distribution such that the expected sum of all elements
                 with first digits $d_{1}, \ldots, d_{k}$ is constant
                 for every fixed $k$.",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Applied Probability",
  keywords =     "Benford's Law; Law of Anomalous Numbers; Zipf's Law",
}

@Article{Castillo:1997:FGP,
  author =       "Enrique Castillo and Ali S. Hadi",
  title =        "Fitting the Generalized {Pareto} Distribution to
                 Data",
  journal =      j-J-AM-STAT-ASSOC,
  volume =       "92",
  number =       "440",
  pages =        "1609--1620",
  month =        dec,
  year =         "1997",
  coden =        "JSTNAL",
  issn =         "0162-1459 (print), 1537-274X (electronic)",
  issn-l =       "0162-1459",
  bibdate =      "Mon Oct 30 06:57:36 MST 2000",
  bibsource =    "http://www.amstat.org/publications/jasa/;
                 http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 http://www.math.utah.edu/pub/tex/bib/jamstatassoc.bib",
  url =          "http://www.amstat.org/publications/jasa/abstracts_97/december/CASTILLO.HTM;
                 http://www.jstor.org/stable/2965432",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of the American Statistical Association",
}

@Article{Chen:1997:NHS,
  author =       "Weishing Chen and Tai-Hsi Wu",
  title =        "A non-homogeneous software reliability model based on
                 {Zipf}'s law",
  journal =      "International Journal of Quality \& Reliability
                 Management",
  volume =       "14",
  number =       "4",
  pages =        "409--431",
  month =        "????",
  year =         "1997",
  doi =          "http://dx.doi.org/10.1108/02656719710170666",
  issn =         "0265-671X (print), 1758-6682 (electronic)",
  issn-l =       "0265-671X",
  bibdate =      "Fri Nov 25 07:08:17 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
}

@Article{Denisov:1997:FBS,
  author =       "S. Denisov",
  title =        "Fractal binary sequences: {Tsallis} thermodynamics and
                 the {Zipf} law",
  journal =      j-PHYS-LET-A,
  volume =       "235",
  number =       "5",
  pages =        "447--451",
  day =          "17",
  month =        nov,
  year =         "1997",
  coden =        "PYLAAG",
  doi =          "http://dx.doi.org/10.1016/S0375-9601(97)00688-9",
  issn =         "0375-9601 (print), 1873-2429 (electronic)",
  issn-l =       "0375-9601",
  bibdate =      "Wed Feb 27 07:32:55 MST 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  url =          "http://www.sciencedirect.com/science/article/pii/S0375960197006889",
  acknowledgement = ack-nhfb,
  fjournal =     "Physics Letters A",
  keywords =     "Zipf's Law",
}

@InCollection{Hill:1997:BL,
  author =       "Theodore Hill",
  editor =       "Michiel Hazewinkel",
  booktitle =    "Encyclopedia of Mathematics, Supplement {I}",
  title =        "{Benford's Law}",
  volume =       "1",
  publisher =    pub-SV,
  address =      pub-SV:adr,
  pages =        "102--103",
  year =         "1997",
  isbn =         "90-481-4896-0",
  isbn-13 =      "978-90-481-4896-7",
  lccn =         "????",
  bibdate =      "Wed Nov 16 10:29:23 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
}

@Article{Irmay:1997:RBZ,
  author =       "Shragga Irmay",
  title =        "The relationship between {Zipf}'s law and the
                 distribution of first digits",
  journal =      j-J-APPL-STAT,
  volume =       "24",
  number =       "4",
  pages =        "383--393",
  day =          "1",
  month =        aug,
  year =         "1997",
  coden =        "????",
  issn =         "0266-4763 (print), 1360-0532 (electronic)",
  issn-l =       "0266-4763",
  mrclass =      "62E15",
  mrnumber =     "1491308 (98h:62015)",
  bibdate =      "Sat Nov 12 09:13:23 2011",
  bibsource =    "http://www.catchword.co.uk/titles/carfax/02664763/;
                 http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 http://www.tandf.co.uk/journals/routledge/02664763.html",
  url =          "http://www.tandfonline.com/doi/abs/10.1080/02664769723594",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Applied Statistics",
  keywords =     "Benford's Law; Zipf's Law",
  xxpages =      "383--394",
}

@Book{Knuth:1997:SA,
  author =       "Donald E. Knuth",
  title =        "Seminumerical Algorithms",
  volume =       "2",
  publisher =    pub-AW,
  address =      pub-AW:adr,
  edition =      "Third",
  pages =        "xiii + 762",
  year =         "1997",
  isbn =         "0-201-89684-2",
  isbn-13 =      "978-0-201-89684-8",
  lccn =         "QA76.6 .K64 1997",
  bibdate =      "Fri Jul 11 15:41:22 1997",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 http://www.math.utah.edu/pub/tex/bib/master.bib",
  note =         "See section 4.2.4V, The Fraction Parts, pages
                 254--262, for a discussion of Benford's Law.",
  price =        "US\$52.75",
  series =       "The Art of Computer Programming",
  acknowledgement = ack-nhfb,
}

@Manual{Nigrini:1997:DAT,
  author =       "Mark J. Nigrini",
  title =        "Digital Analysis Tests and Statistics",
  organization = "The Nigrini Institute, Inc.",
  address =      "Allen, TX, USA",
  month =        "????",
  year =         "1997",
  bibdate =      "Sat Feb 16 18:55:18 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  url =          "http://www.nigrini.com/data_software/Program_Details_2009.docx",
  acknowledgement = ack-nhfb,
}

@Article{Nigrini:1997:UBL,
  author =       "M. J. Nigrini and L. J. Mittermaier",
  title =        "The Use of {Benford's Law} as an Aid in Analytical
                 Procedures",
  journal =      j-AUDITING,
  volume =       "16",
  number =       "2",
  pages =        "52--67",
  month =        "????",
  year =         "1997",
  coden =        "????",
  issn =         "0278-0380 (print), 1558-7991 (electronic)",
  issn-l =       "0278-0380",
  bibdate =      "Sun Nov 13 11:37:48 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  url =          "http://aaapubs.org/loi/ajpt",
  acknowledgement = ack-nhfb,
  fjournal =     "Auditing: A Journal of Practice \& Theory",
}

@Article{Salsburg:1997:DPB,
  author =       "David Salsburg",
  title =        "Digit Preferences in the {Bible}",
  journal =      j-CHANCE,
  volume =       "10",
  number =       "4",
  pages =        "46--48",
  month =        "????",
  year =         "1997",
  coden =        "CNDCE4",
  doi =          "http://dx.doi.org/10.1080/09332480.1997.10542065",
  issn =         "0933-2480 (print), 1867-2280 (electronic)",
  issn-l =       "0933-2480",
  bibdate =      "Sat Feb 16 19:08:02 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  url =          "http://amstat.tandfonline.com/doi/full/10.1080/09332480.1997.10542065",
  acknowledgement = ack-nhfb,
  fjournal =     "Chance: a magazine for people interested in the
                 analysis of data",
}

@Article{Tsonis:1997:ZLS,
  author =       "A. A. Tsonis and C. Schultz and P. A. Tsonis",
  title =        "{Zipf's Law} and the structure and evolution of
                 languages",
  journal =      j-COMPLEXITY,
  volume =       "2",
  number =       "5",
  pages =        "12--13",
  year =         "1997",
  coden =        "COMPFS",
  doi =          "http://dx.doi.org/10.1002/(SICI)1099-0526(199705/06)2:5<12::AID-CPLX3>3.0.CO;2-C",
  issn =         "1076-2787 (print), 1099-0526 (electronic)",
  issn-l =       "1076-2787",
  bibdate =      "Mon Feb 25 06:13:56 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Complexity",
}

@Article{Zanette:1997:RIU,
  author =       "Dami{\'a}n H. Zanette and Susanna C. Manrubia",
  title =        "Role of Intermittency in Urban Development: A Model of
                 Large-Scale City Formation",
  journal =      j-PHYS-REV-LET,
  volume =       "79",
  number =       "3",
  pages =        "523--526",
  day =          "3",
  month =        jul,
  year =         "1997",
  coden =        "PRLTAO",
  doi =          "http://dx.doi.org/10.1103/PhysRevLett.79.523",
  issn =         "0031-9007 (print), 1079-7114 (electronic), 1092-0145",
  issn-l =       "0031-9007",
  bibdate =      "Thu Feb 28 10:40:44 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  url =          "http://link.aps.org/doi/10.1103/PhysRevLett.79.523",
  acknowledgement = ack-nhfb,
  fjournal =     "Physical Review Letters",
  keywords =     "power law; scale invariance; Zipf's law",
}

@Article{Bach:1998:EPM,
  author =       "Eric Bach",
  title =        "Efficient prediction of {Marsaglia--Zaman} random
                 number generators",
  journal =      j-IEEE-TRANS-INF-THEORY,
  volume =       "44",
  number =       "3",
  pages =        "1253--1257",
  year =         "1998",
  coden =        "IETTAW",
  doi =          "http://dx.doi.org/10.1109/18.669305",
  issn =         "0018-9448 (print), 1557-9654 (electronic)",
  issn-l =       "0018-9448",
  mrclass =      "65C10",
  mrnumber =     "99b:65007",
  bibdate =      "Thu Dec 22 07:42:24 2011",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib;
                 http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 http://www.math.utah.edu/pub/tex/bib/prng.bib",
  zmnumber =     "0915.65003",
  abstract =     "This paper presents two properties of the random
                 number generator by {\it G. Marsaglia} and {\it A.
                 Zaman} [Ann. Appl. Probab. 1, No. 3, 462-480 (1991; Zbl
                 0733.65005)]. First, it is shown that its successive
                 digits are digits of certain rational $b$-adic numbers.
                 Then, an efficient algorithm is derived to predict an
                 unknown pseudorandom sequence of this type. Two
                 examples of the prediction are given.",
  acknowledgement = ack-nhfb,
  classmath =    "*65C10 Random number generation 11K45 Pseudo-random
                 numbers, etc.",
  fjournal =     "IEEE Transactions on Information Theory",
  keywords =     "$b$-adic number; algorithm; continued fraction;
                 pseudo-random number generator",
  ZMreviewer =   "K. Uosaki (Tottori)",
}

@Article{Browne:1998:FBL,
  author =       "Malcolm W. Browne",
  title =        "Following {Benford's Law}, or Looking Out for {No.
                 1}",
  journal =      j-NY-TIMES,
  volume =       "??",
  number =       "??",
  pages =        "F4--F4",
  day =          "4",
  month =        aug,
  year =         "1998",
  coden =        "NYTIAO",
  issn =         "0362-4331 (print), 1542-667X, 1553-8095",
  issn-l =       "0362-4331",
  bibdate =      "Sat Feb 16 14:29:48 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  note =         "Science section.",
  url =          "http://search.proquest.com/hnpnewyorktimes/docview/109868161/13C4AACC02923FE97A/1",
  acknowledgement = ack-nhfb,
  fjournal =     "New York Times",
}

@Article{Busta:1998:UBL,
  author =       "Bruce Busta and Randy Weinberg",
  title =        "Using {Benford's Law} and Neural Networks as a Review
                 Procedure",
  journal =      "Managerial Auditing Journal",
  volume =       "13",
  number =       "6",
  pages =        "356--366",
  month =        "????",
  year =         "1998",
  coden =        "????",
  doi =          "http://dx.doi.org/10.1108/02686909810222375",
  issn =         "0268-6902 (print), 1758-7735 (electronic)",
  issn-l =       "0268-6902",
  bibdate =      "Tue Nov 22 18:50:49 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
}

@Article{DeCeuster:1998:HPB,
  author =       "M. J. K. DeCeuster and G. Dhaene and T. Schatteman",
  title =        "On the hypothesis of psychological barriers in stock
                 markets and {Benford}'s law",
  journal =      j-J-EMPIR-FINANCE,
  volume =       "5",
  number =       "3",
  pages =        "263--279",
  month =        sep,
  year =         "1998",
  coden =        "JEFIEC",
  doi =          "http://dx.doi.org/10.1016/S0927-5398(97)00024-8",
  issn =         "0927-5398 (print), 1879-1727 (electronic)",
  issn-l =       "0927-5398",
  bibdate =      "Sun Nov 13 11:33:46 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  url =          "http://www.sciencedirect.com/science/article/pii/S0927539897000248",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Empirical Finance",
}

@Article{Hill:1998:FDP,
  author =       "Theodore P. Hill",
  title =        "The First Digit Phenomenon",
  journal =      j-AM-SCI,
  volume =       "86",
  number =       "4",
  pages =        "358--363",
  month =        jul # "\slash " # aug,
  year =         "1998",
  coden =        "AMSCAC",
  doi =          "http://dx.doi.org/10.1511/1998.4.358",
  issn =         "0003-0996 (print), 1545-2786 (electronic)",
  issn-l =       "0003-0996",
  bibdate =      "Sat Dec 10 11:54:49 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  url =          "http://people.math.gatech.edu/~hill/publications/PAPER%20PDFS/TheFirstDigitPhenomenonAmericanScientist1996.pdf;
                 http://www.math.gatech.edu/~hill/publications/cv.dir/1st-dig.pdf",
  abstract =     "A century ago, Simon Newcomb observed an unexpected
                 pattern in the first digits of logarithm tables: The
                 digit $1$ is significantly more likely to occur than
                 $2$, $2$ than $3$, and so on. More than a half-century
                 later, Frank Benford rediscovered the first-digit
                 phenomenon and found that it applied to many tables of
                 numerical data, including the stock market, census
                 statistics and accounting figures. New mathematical
                 insights establish the empirical law developed by
                 Newcomb and Benford as part of modern probability
                 theory, and recent applications include testing of
                 mathematical models, design of computers and detection
                 of fraud in accounting.",
  acknowledgement = ack-nhfb,
  fjournal =     "American Scientist",
  keywords =     "Benford's Law; Law of Anomalous Numbers; Zipf's Law",
}

@Article{Manrubia:1998:IMU,
  author =       "Susanna C. Manrubia and Dami{\'a}n H. Zanette",
  title =        "Intermittency model for urban development",
  journal =      j-PHYS-REV-E,
  volume =       "58",
  number =       "1",
  pages =        "295--302",
  month =        jul,
  year =         "1998",
  coden =        "PLEEE8",
  doi =          "http://dx.doi.org/10.1103/PhysRevE.58.295",
  issn =         "1539-3755 (print), 1550-2376 (electronic)",
  issn-l =       "1539-3755",
  bibdate =      "Thu Feb 28 10:42:23 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  url =          "http://link.aps.org/doi/10.1103/PhysRevE.58.295",
  acknowledgement = ack-nhfb,
  fjournal =     "Physical Review E (Statistical physics, plasmas,
                 fluids, and related interdisciplinary topics)",
  keywords =     "power law; scale invariance; Zipf's law",
}

@Article{Marsili:1998:IIL,
  author =       "Matteo Marsili and Yi-Cheng Zhang",
  title =        "Interacting Individuals Leading to {Zipf's Law}",
  journal =      j-PHYS-REV-LET,
  volume =       "80",
  number =       "??",
  pages =        "2741--??",
  day =          "23",
  month =        mar,
  year =         "1998",
  coden =        "PRLTAO",
  doi =          "http://dx.doi.org/10.1103/PhysRevLett.80.2741",
  issn =         "0031-9007 (print), 1079-7114 (electronic), 1092-0145",
  issn-l =       "0031-9007",
  bibdate =      "Tue Feb 26 06:40:57 MST 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  url =          "http://link.aps.org/doi/10.1103/PhysRevLett.80.2741",
  acknowledgement = ack-nhfb,
  fjournal =     "Physical Review Letters",
  keywords =     "Zipf's Law",
}

@Article{Nigrini:1998:DIB,
  author =       "Mark J. Nigrini",
  title =        "{Dow} Illustrates {Benford's Law}",
  journal =      j-NY-TIMES,
  volume =       "??",
  number =       "??",
  pages =        "F4--F4",
  day =          "4",
  month =        aug,
  year =         "1998",
  coden =        "NYTIAO",
  issn =         "0362-4331 (print), 1542-667X, 1553-8095",
  issn-l =       "0362-4331",
  bibdate =      "Sat Feb 16 15:46:43 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  url =          "http://search.proquest.com/hnpnewyorktimes/docview/109901848/13C4AB0BB5661D397CE/1",
  acknowledgement = ack-nhfb,
  fjournal =     "New York Times",
}

@Article{NunesAmaral:1998:PLS,
  author =       "Lu{\'\is} A. {Nunes Amaral} and Sergey V. Buldyrev and
                 Shlomo Havlin and Michael A. Salinger and H. Eugene
                 Stanley",
  title =        "Power Law Scaling for a System of Interacting Units
                 with Complex Internal Structure",
  journal =      j-PHYS-REV-LET,
  volume =       "80",
  number =       "7",
  pages =        "1385--1388",
  day =          "16",
  month =        feb,
  year =         "1998",
  coden =        "PRLTAO",
  doi =          "http://dx.doi.org/10.1103/PhysRevLett.80.1385",
  issn =         "0031-9007 (print), 1079-7114 (electronic), 1092-0145",
  issn-l =       "0031-9007",
  bibdate =      "Thu Feb 28 11:09:02 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  url =          "http://link.aps.org/doi/10.1103/PhysRevLett.80.1385",
  acknowledgement = ack-nhfb,
  fjournal =     "Physical Review Letters",
  keywords =     "power law; scale invariance; Zipf's law",
}

@Article{Pietronero:1998:UDN,
  author =       "L. Pietronero and E. Tosatti and V. Tosatti and A.
                 Vespignani",
  title =        "The Uneven Distribution of Numbers in Nature",
  journal =      "ArXiv e-prints",
  pages =        "9",
  day =          "27",
  month =        aug,
  year =         "1998",
  bibdate =      "Mon Nov 21 06:58:45 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  url =          "http://arxiv.org/abs/cond-mat/9808305",
  abstract =     "Suppose you look at today's stock prices and bet on
                 the value of the first digit. One could guess that a
                 fair bet should correspond to the frequency of $1/9 =
                 11.11\%$ for each digit from 1 to 9. This is by no
                 means the case, and one can easily observe a strong
                 prevalence of the small values over the large ones. The
                 first three integers 1, 2 and 3 alone have globally a
                 frequency of 60\% while the other six values 4, 5, 6,
                 7, 8 and 9 appear only in 40\% of the cases. This
                 situation is actually much more general than the stock
                 market and it occurs in a variety of number catalogs
                 related to natural phenomena. The first observation of
                 this property traces back to S. Newcomb in 1881 but a
                 more precise account was given by F. Benford in 1938.
                 In this note we illustrate these observations with the
                 enlightening specific example of the stock market. We
                 also identify the general mechanism for the origin of
                 this uneven distribution in the multiplicative nature
                 of fluctuations in economics and in many natural
                 phenomena. This provides a natural explanation for the
                 ubiquitous presence of the Benford's law in many
                 different phenomena with the common element that their
                 fluctuations refer to a fraction of their values. This
                 brings us close to the problem of the spontaneous
                 origin of scale invariant properties in various
                 phenomena which is a debated question at the frontier
                 of different fields.",
  acknowledgement = ack-nhfb,
}

@Article{Pocheau:1998:SRS,
  author =       "A. Pocheau",
  title =        "Scale ratios, statistical symmetries and
                 intermittency",
  journal =      j-EUROPHYS-LETT,
  volume =       "43",
  number =       "4",
  pages =        "410--415",
  month =        aug,
  year =         "1998",
  coden =        "EULEEJ",
  doi =          "http://dx.doi.org/10.1209/epl/i1998-00103-6",
  issn =         "0295-5075 (print), 1286-4854 (electronic)",
  issn-l =       "0295-5075",
  bibdate =      "Sat Feb 16 16:02:17 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Europhysics Letters",
}

@Article{Ramsden:1998:ZLB,
  author =       "J. J. Ramsden and J. Vohradsk{\'y}",
  title =        "{Zipf}-like behavior in procaryotic protein
                 expression",
  journal =      j-PHYS-REV-E,
  volume =       "58",
  number =       "??",
  pages =        "7777--??",
  day =          "1",
  month =        dec,
  year =         "1998",
  coden =        "PLEEE8",
  doi =          "http://dx.doi.org/10.1103/PhysRevE.58.7777",
  issn =         "1539-3755 (print), 1550-2376 (electronic)",
  issn-l =       "1539-3755",
  bibdate =      "Tue Feb 26 06:40:57 MST 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  url =          "http://link.aps.org/doi/10.1103/PhysRevE.58.7777",
  acknowledgement = ack-nhfb,
  fjournal =     "Physical Review E (Statistical physics, plasmas,
                 fluids, and related interdisciplinary topics)",
  keywords =     "Zipf's Law",
}

@Article{Schatte:1998:BLV,
  author =       "P. Schatte",
  title =        "On {Benford}'s law to variable base",
  journal =      j-STAT-PROB-LETT,
  volume =       "37",
  number =       "4",
  pages =        "391--397",
  day =          "30",
  month =        mar,
  year =         "1998",
  coden =        "SPLTDC",
  doi =          "http://dx.doi.org/10.1016/S0167-7152(97)00142-9",
  issn =         "0167-7152 (print), 1879-2103 (electronic)",
  issn-l =       "0167-7152",
  mrclass =      "60F05 (60E15)",
  mrnumber =     "1624423 (99e:60072)",
  mrreviewer =   "Theodore P. Hill",
  bibdate =      "Tue Nov 22 11:28:19 MST 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 http://www.sciencedirect.com/",
  url =          "http://www.sciencedirect.com/science/article/pii/S0167715297001429",
  abstract =     "Benford's law is studied in dependence on the base $b
                 > 1$. It can hold to large bases $b$ only
                 approximately. The quality of approximation is
                 estimated in cases of products and sums of random
                 variables, respectively, and in case of some
                 deterministic sequences. Always the approximation by
                 Benford's law becomes worse as $b \to \infty$, but as a
                 rule also as $b \to 1 + 0$",
  acknowledgement = ack-nhfb,
  fjournal =     "Statistics \& Probability Letters",
  keywords =     "Benford's Law",
}

@Article{Slijepcevic:1998:NID,
  author =       "Sini{\v{s}}a Slijep{\v{c}}evi{\'c}",
  title =        "A Note on Initial Digits of Recurrence Sequences",
  journal =      j-FIB-QUART,
  volume =       "36",
  number =       "4",
  pages =        "305--308",
  month =        aug,
  year =         "1998",
  coden =        "FIBQAU",
  issn =         "0015-0517",
  issn-l =       "0015-0517",
  bibdate =      "Thu Oct 20 18:02:49 MDT 2011",
  bibsource =    "http://www.fq.math.ca/36-4.html;
                 http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 http://www.math.utah.edu/pub/tex/bib/fibquart.bib",
  url =          "http://www.fq.math.ca/Scanned/36-4/slijepcevic.pdf",
  acknowledgement = ack-nhfb,
  ajournal =     "Fib. Quart",
  fjournal =     "The Fibonacci Quarterly. Official Organ of the
                 Fibonacci Association",
}

@Article{Troll:1998:ZLC,
  author =       "G. Troll and P. beim Graben",
  title =        "{Zipf}'s law is not a consequence of the {Central
                 Limit Theorem}",
  journal =      j-PHYS-REV-E,
  volume =       "57",
  number =       "3",
  pages =        "1347--1355",
  day =          "1",
  month =        feb,
  year =         "1998",
  coden =        "PLEEE8",
  doi =          "http://dx.doi.org/10.1103/PhysRevE.57.1347",
  issn =         "1539-3755 (print), 1550-2376 (electronic)",
  issn-l =       "1539-3755",
  bibdate =      "Tue Feb 26 06:40:57 MST 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  url =          "http://link.aps.org/doi/10.1103/PhysRevE.57.1347;
                 http://pre.aps.org/abstract/PRE/v57/i2/p1347_1",
  abstract =     "It has been observed that the rank statistics of
                 string frequencies of many symbolic systems (e.g., word
                 frequencies of natural languages) follows Zipf's law in
                 good approximation. We show that, contrary to claims in
                 the literature, Zipf's law cannot be realized by the
                 central limit theorem(s). The observation that a
                 log-normal distribution of string frequencies yields an
                 approximately Zipf-like rank statistics is actually
                 misleading. Indeed, Zipf's law for the rank statistics
                 is strictly equivalent to a power law distribution of
                 frequencies. There are two natural ways to perform the
                 infinite size limit for the vocabulary. The first one
                 is the method of choice in the literature; it makes the
                 upper word length bound tend to infinity and leads in
                 the case of a multistate Bernoulli process via a
                 central limit theorem to a log-normal frequency
                 distribution. An alternative and for text samples
                 actually better realizable way is to make the lower
                 frequency bound tend to zero. This limit procedure
                 leads to a power law distribution and hence to Zipf's
                 law --- at least for Bernoulli processes and to a very
                 good approximation for natural languages where it
                 passes the $\chi^2$ test. For the Bernoulli case we
                 will give a heuristic proof.",
  acknowledgement = ack-nhfb,
  fjournal =     "Physical Review E (Statistical physics, plasmas,
                 fluids, and related interdisciplinary topics)",
  keywords =     "Zipf's Law",
}

@Book{Wirsching:1998:DSG,
  author =       "G{\"u}nther J. Wirsching",
  title =        "The dynamical system generated by the $3 n + 1$
                 function",
  volume =       "1681",
  publisher =    pub-SV,
  address =      pub-SV:adr,
  pages =        "vii + 158",
  year =         "1998",
  isbn =         "3-540-63970-5 (softcover)",
  isbn-13 =      "978-3-540-63970-1 (softcover)",
  issn =         "0075-8434 (print), 1617-9692 (electronic)",
  lccn =         "QA3 .L28 no. 1681",
  bibdate =      "Mon Nov 21 08:00:54 MST 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 z3950.loc.gov:7090/Voyager",
  series =       ser-LNM,
  url =          "http://www.loc.gov/catdir/enhancements/fy0818/97051329-d.html;
                 http://www.loc.gov/catdir/enhancements/fy0818/97051329-t.html",
  acknowledgement = ack-nhfb,
  keywords =     "Benford's Law",
  subject =      "Sequences (Mathematics); Combinatorial probabilities;
                 Convergence",
}

@Article{Ausloos:1999:PMK,
  author =       "M. Ausloos and K. Ivanova",
  title =        "Precise $ (m, k) $-{Zipf} diagram analysis of
                 mathematical and financial time series when $ m = 6 $,
                 $ k = 2 $",
  journal =      j-PHYSICA-A,
  volume =       "270",
  number =       "3--4",
  pages =        "526--542",
  day =          "15",
  month =        aug,
  year =         "1999",
  coden =        "PHYADX",
  doi =          "http://dx.doi.org/10.1016/S0378-4371(99)00178-8",
  issn =         "0378-4371 (print), 1873-2119 (electronic)",
  issn-l =       "0378-4371",
  bibdate =      "Wed Feb 27 07:32:55 MST 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  url =          "http://www.sciencedirect.com/science/article/pii/S0378437199001788",
  acknowledgement = ack-nhfb,
  fjournal =     "Physica A. Statistical Mechanics and its
                 Applications",
  keywords =     "Zipf's Law",
}

@Article{AyllonBurguillo:1999:PDS,
  author =       "Juan David {Ayll{\'o}n Burguillo} and Manuel {Perera
                 Dom{\'\i}nguez}",
  title =        "El primer d{\'\i}gito significativo. ({Spanish}) [The
                 first significant digit]",
  journal =      "{Epsilon}: Revista de la {Sociedad Andaluza de
                 Educaci{\'o}n Matem{\'a}tica ``Thales''}",
  volume =       "15",
  number =       "3(45)",
  pages =        "339--352",
  month =        "????",
  year =         "1999",
  issn =         "1131-9321",
  issn-l =       "1131-9321",
  bibdate =      "Sat Feb 16 14:32:14 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  zmnumber =     "MATHEDUC.02332710",
  acknowledgement = ack-nhfb,
  ajournal =     "{Rev. Epsil{\'o}n SAEM `Thales'}",
  journal-url =  "http://thales.cica.es/epsilon/;
                 http://dialnet.unirioja.es/servlet/revista?codigo=504",
  language =     "Spanish",
  msc2010 =      "K60xx",
  remark =       "Reported in \cite{Torres:2007:HDN} to contain an
                 extensive bibliography on Benford's Law. The publisher
                 does not have issues before 2003, and no electronic
                 copy has yet been found on the Internet. Attempts to
                 get this paper via Interlibrary Loan failed on the
                 grounds that ``We are unable to verify any owning
                 libraries within the United States or those that we
                 have ILL privileges.''",
  xxauthor =     "M. P. Dominguez and J. D. A. Burguillo",
  xxauthor =     "Manuel {Perera Dom{\'\i}nguez} and Juan David
                 {Ayll{\'o}n Burguillo}",
}

@Article{Barabasi:1999:ESR,
  author =       "Albert-L{\'a}szl{\'o} Barab{\'a}si and R{\'e}ka
                 Albert",
  title =        "Emergence of scaling in random networks",
  journal =      j-SCIENCE,
  volume =       "286",
  number =       "5439",
  pages =        "509--512",
  day =          "15",
  month =        oct,
  year =         "1999",
  coden =        "SCIEAS",
  doi =          "http://dx.doi.org/10.1126/science.286.5439.509",
  issn =         "0036-8075 (print), 1095-9203 (electronic)",
  issn-l =       "0036-8075",
  bibdate =      "Tue Nov 15 09:57:42 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  url =          "http://www.sciencemag.org/content/286/5439/509",
  acknowledgement = ack-nhfb,
  fjournal =     "Science",
  keywords =     "power-law distribution; Zipf's Law",
}

@Article{Bolton:1999:SFD,
  author =       "R. J. Bolton and D. J. Hand",
  title =        "Statistical Fraud Detection: a review",
  journal =      j-STAT-SCI,
  volume =       "17",
  number =       "3",
  pages =        "235--255",
  month =        "????",
  year =         "1999",
  coden =        "STSCEP",
  issn =         "0883-4237",
  issn-l =       "0883-4237",
  bibdate =      "Sat Feb 16 17:26:25 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Statistical Science",
}

@Article{Brakman:1999:RZT,
  author =       "Steven Brakman and Harry Garretsen and Charles {Van
                 Marrewijk} and Marianne {Van Den Berg}",
  title =        "The Return of {Zipf}: Towards a Further Understanding
                 of the Rank--Size Distribution",
  journal =      j-J-REG-SCI,
  volume =       "39",
  number =       "1",
  pages =        "183--213",
  year =         "1999",
  doi =          "http://dx.doi.org/10.1111/1467-9787.00129",
  issn =         "0022-4146 (print), 1467-9787 (electronic)",
  issn-l =       "0022-4146",
  bibdate =      "Mon Feb 25 06:13:56 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Regional Science",
}

@Article{Coderre:1999:FDU,
  author =       "David Coderre",
  title =        "Fraud Detection Using Digital Analysis",
  journal =      j-EDPACS,
  volume =       "27",
  number =       "3",
  pages =        "1--8",
  month =        "????",
  year =         "1999",
  coden =        "EDPCDF",
  doi =          "http://dx.doi.org/10.1201/1079/43249.27.3.19990901/30268.1",
  issn =         "0736-6981 (print), 1936-1009 (electronic)",
  issn-l =       "0736-6981",
  bibdate =      "Sat Jan 07 09:20:49 2012",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  url =          "http://www.tandfonline.com/doi/abs/10.1201/1079/43249.27.3.19990901/30268.1",
  acknowledgement = ack-nhfb,
  fjournal =     "EDPACS",
  keywords =     "Benford's Law",
  onlinedate =   "21 Dec 2006",
}

@Article{Egghe:1999:LZM,
  author =       "L. Egghe",
  title =        "On the law of {Zipf--Mandelbrot} for multi-word
                 phrases",
  journal =      j-J-AM-SOC-INF-SCI,
  volume =       "50",
  number =       "3",
  pages =        "233--241",
  month =        "????",
  year =         "1999",
  coden =        "AISJB6",
  doi =          "http://dx.doi.org/10.1002/(SICI)1097-4571(1999)50:3<233::AID-ASI6>3.0.CO;2-8",
  issn =         "0002-8231 (print), 1097-4571 (electronic)",
  issn-l =       "0002-8231",
  bibdate =      "Mon Sep 10 06:09:31 2012",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/m/mandelbrot-benoit.bib;
                 http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of the American Society for Information
                 Science",
  onlinedate =   "17 Feb 1999",
}

@Article{Gabaix:1999:ZLC,
  author =       "Xavier Gabaix",
  title =        "{Zipf}'s law for cities: An explanation",
  journal =      j-Q-J-ECON,
  volume =       "114",
  number =       "3",
  pages =        "739--767",
  year =         "1999",
  coden =        "QJECAT",
  doi =          "http://dx.doi.org/10.1162/003355399556133",
  issn =         "0033-5533 (print), 1531-4650 (electronic)",
  issn-l =       "0033-5533",
  bibdate =      "Sat Nov 12 10:57:19 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  zmnumber =     "0952.91059",
  abstract =     "Zipf's law is a very tight constraint on the class of
                 admissible models of local growth. It says that for
                 most countries the size distribution of cities
                 strikingly fits a power law: the number of cities with
                 populations greater than $S$ is proportional to $1/S$.
                 Suppose that, at least in the upper tail, all cities
                 follow some proportional growth process (this appears
                 to be verified empirically). This automatically leads
                 their distribution to converge to Zipf's law.",
  acknowledgement = ack-nhfb,
  ajournal =     "Q. J. Econ.",
  classmath =    "91B62 (Dynamic economic models etc.) 91B72 (Spatial
                 models)",
  fjournal =     "The Quarterly Journal of Economics",
  keywords =     "local growth; Zipf's law",
}

@Article{Hill:1999:DFD,
  author =       "Theodore P. Hill",
  title =        "The Difficulty of Faking Data",
  journal =      j-CHANCE,
  volume =       "12",
  number =       "3",
  pages =        "27--31",
  month =        "????",
  year =         "1999",
  coden =        "CNDCE4",
  doi =          "http://dx.doi.org/10.1080/09332480.1999.10542154",
  issn =         "0933-2480 (print), 1867-2280 (electronic)",
  issn-l =       "0933-2480",
  bibdate =      "Tue Nov 22 18:54:44 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  url =          "http://amstat.tandfonline.com/doi/abs/10.1080/09332480.1999.10542154",
  acknowledgement = ack-nhfb,
  fjournal =     "Chance: a magazine for people interested in the
                 analysis of data",
  journal-url =  "http://chance.amstat.org/",
  keywords =     "Benford's Law",
  xxnote =       "Check: Hurlimann bibliography says v26 pp. 8--13??;
                 that is wrong!",
}

@Article{Hill:1999:PCS,
  author =       "Theodore P. Hill",
  title =        "Le premier chiffre significatif fait sa loi.
                 ({French}) [{The} first significant digit makes its
                 law]",
  journal =      "La Recherche: L'actualit{\'e} des sciences",
  volume =       "2",
  number =       "316",
  pages =        "72--76",
  month =        jan,
  year =         "1999",
  coden =        "RCCHBV",
  issn =         "0029-5671 (print), 1625-9955 (electronic)",
  issn-l =       "0029-5671",
  bibdate =      "Sat Feb 16 17:51:25 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  url =          "http://www.larecherche.fr/savoirs/autre/premier-chiffre-significatif-fait-sa-loi-01-01-1999-70970",
  acknowledgement = ack-nhfb,
  xxjournal =    "La Recherche Hors S{\'e}rie",
}

@Article{Huberman:1999:IGD,
  author =       "Bernardo A. Huberman and Lada A. Adamic",
  title =        "{Internet}: Growth dynamics of the {World-Wide Web}",
  journal =      j-NATURE,
  volume =       "401",
  number =       "6749",
  pages =        "131--131",
  day =          "9",
  month =        sep,
  year =         "1999",
  coden =        "NATUAS",
  doi =          "http://dx.doi.org/10.1038/43604",
  issn =         "0028-0836 (print), 1476-4687 (electronic)",
  issn-l =       "0028-0836",
  bibdate =      "Tue Nov 15 09:52:36 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Nature",
  keywords =     "Zipf's Law",
}

@TechReport{Lowe:1999:FDL,
  author =       "Tomas Lowe and Sally Murphy and Justin Hayward",
  title =        "The First Digit Law",
  type =         "Report",
  number =       "??",
  institution =  "Department of Computing, Imperial College",
  address =      "London, UK",
  month =        jun,
  year =         "1999",
  bibdate =      "Wed Nov 23 16:59:50 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  url =          "http://users.isr.ist.utl.pt/~jmrs/research/TopicsLinks/Benford/hayward.pdf;
                 http://www.doc.ic.ac.uk/~jjh97/suprema/main_page.html",
  acknowledgement = ack-nhfb,
  lastaccess =   "23 November 2011",
}

@Article{Malcai:1999:PLD,
  author =       "Ofer Malcai and Ofer Biham and Sorin Solomon",
  title =        "Power-law distributions and {L{\'e}vy}-stable
                 intermittent fluctuations in stochastic systems of many
                 autocatalytic elements",
  journal =      j-PHYS-REV-E,
  volume =       "60",
  number =       "2",
  pages =        "1299--1303",
  month =        aug,
  year =         "1999",
  coden =        "PLEEE8",
  doi =          "http://dx.doi.org/10.1103/PhysRevE.60.1299",
  issn =         "1539-3755 (print), 1550-2376 (electronic)",
  issn-l =       "1539-3755",
  bibdate =      "Thu Feb 28 10:25:38 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  url =          "http://link.aps.org/doi/10.1103/PhysRevE.60.1299",
  acknowledgement = ack-nhfb,
  fjournal =     "Physical Review E (Statistical physics, plasmas,
                 fluids, and related interdisciplinary topics)",
}

@Article{Manrubia:1999:SMP,
  author =       "Susanna C. Manrubia and Dami{\'a}n H. Zanette",
  title =        "Stochastic multiplicative processes with reset
                 events",
  journal =      j-PHYS-REV-E,
  volume =       "59",
  number =       "5",
  pages =        "4945--4948",
  month =        may,
  year =         "1999",
  coden =        "PLEEE8",
  doi =          "http://dx.doi.org/10.1103/PhysRevE.59.4945",
  issn =         "1539-3755 (print), 1550-2376 (electronic)",
  issn-l =       "1539-3755",
  bibdate =      "Tue Feb 26 06:25:24 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  url =          "http://link.aps.org/doi/10.1103/PhysRevE.59.4945",
  acknowledgement = ack-nhfb,
  fjournal =     "Physical Review E (Statistical physics, plasmas,
                 fluids, and related interdisciplinary topics)",
  issue =        "5",
  keywords =     "Zipf's law",
}

@Article{Manrubia:1999:TDS,
  author =       "Susanna C. Manrubia and Dami{\'a}n H. Zanette and
                 Ricard V. Sol{\'e}",
  title =        "Transient Dynamics and Scaling Phenomena in Urban
                 Growth",
  journal =      j-FRACTALS,
  volume =       "7",
  number =       "1",
  pages =        "1--8",
  month =        mar,
  year =         "1999",
  coden =        "FRACEG",
  doi =          "http://dx.doi.org/10.1142/S0218348X99000025",
  issn =         "0218-348X",
  issn-l =       "0218-348X",
  bibdate =      "Wed Feb 27 07:11:42 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  url =          "http://www.worldscientific.com/doi/abs/10.1142/S0218348X99000025",
  acknowledgement = ack-nhfb,
  fjournal =     "Fractals",
  keywords =     "Zipf's Law",
}

@Article{Matthews:1999:PO,
  author =       "Robert Matthews",
  title =        "The Power of One",
  journal =      j-NEW-SCIENTIST,
  volume =       "163",
  number =       "2194",
  pages =        "27--30",
  day =          "10",
  month =        jul,
  year =         "1999",
  coden =        "NWSCAL",
  issn =         "0262-4079 (print), 1364-8500 (electronic)",
  issn-l =       "0262-4079",
  bibdate =      "Mon Nov 14 16:04:36 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  url =          "http://www.fortunecity.com/emachines/e11/86/one.html;
                 http://www.newscientist.com/article/mg16321944.600-the-power-of-one.html",
  acknowledgement = ack-nhfb,
  fjournal =     "New Scientist",
  xxissn =       "0262-4079, 0028-6664",
}

@Article{Mercik:1999:SAI,
  author =       "Szymon Mercik and Karina Weron and Zuzanna Siwy",
  title =        "Statistical analysis of ionic current fluctuations in
                 membrane channels",
  journal =      j-PHYS-REV-E,
  volume =       "60",
  number =       "6",
  pages =        "7343--7348",
  day =          "1",
  month =        dec,
  year =         "1999",
  coden =        "PLEEE8",
  doi =          "http://dx.doi.org/10.1103/PhysRevE.60.7343",
  issn =         "1539-3755 (print), 1550-2376 (electronic)",
  issn-l =       "1539-3755",
  bibdate =      "Tue Feb 26 06:40:57 MST 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  url =          "http://link.aps.org/doi/10.1103/PhysRevE.60.7343",
  acknowledgement = ack-nhfb,
  fjournal =     "Physical Review E (Statistical physics, plasmas,
                 fluids, and related interdisciplinary topics)",
  keywords =     "Zipf's Law",
}

@Article{Nigrini:1999:AVD,
  author =       "Mark J. Nigrini",
  title =        "Adding value with digital analysis",
  journal =      "The Internal Auditor: Journal of the {Institute of
                 Internal Auditors}",
  volume =       "56",
  number =       "1",
  pages =        "21--23",
  month =        "????",
  year =         "1999",
  coden =        "ITAUAB",
  issn =         "0020-5745",
  issn-l =       "0020-5745",
  bibdate =      "Sat Feb 16 18:56:27 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
}

@Article{Nigrini:1999:IGY,
  author =       "M. Nigrini",
  title =        "{I}'ve Got Your Number",
  journal =      j-J-ACCOUNTANCY,
  volume =       "187",
  number =       "??",
  pages =        "79--83",
  month =        may,
  year =         "1999",
  coden =        "JACYAD",
  issn =         "0021-8448 (print), 1945-0729 (electronic)",
  issn-l =       "0021-8448",
  bibdate =      "Mon Nov 14 16:31:40 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  url =          "http://www.aicpa.org/pubs/jofa/may1999/nigrini.htm",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Accountancy",
}

@Article{Nigrini:1999:PPF,
  author =       "Mark J. Nigrini",
  title =        "Peculiar patterns of first digits",
  journal =      j-IEEE-POT,
  volume =       "18",
  number =       "2",
  pages =        "24--27",
  month =        apr # "\slash " # may,
  year =         "1999",
  coden =        "IEPTDF",
  doi =          "http://dx.doi.org/10.1109/45.755849",
  issn =         "0278-6648 (print), 1558-1772 (electronic)",
  issn-l =       "0278-6648",
  bibdate =      "Mon Nov 21 22:18:30 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  abstract =     "Despite seeing numbers all the time only occasionally
                 would one say that a list of numbers seems odd. For
                 this to occur, the numbers are typically highly rounded
                 or implausible (too much of a coincidence). However
                 digit pattern analysis, using a computer, can produce
                 valuable findings not revealed at a mere glance. The
                 most widely cited paper on digit frequencies was
                 published by Frank Benford in 1938. With powerful,
                 low-cost personal computers, Benford's law can help us
                 to efficiently test the integrity of data. The first
                 step is to assess whether Benford's law should apply to
                 the data. If the data is expected to conform, then
                 Benford's law becomes the expected distribution.
                 Conformity means that the actual distribution closely
                 approximates the expected distribution",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Potentials",
}

@Article{Okuyama:1999:ZLI,
  author =       "K. Okuyama and M. Takayasu and H. Takayasu",
  title =        "{Zipf}'s law in income distribution of companies",
  journal =      j-PHYSICA-A,
  volume =       "269",
  number =       "1",
  pages =        "125--131",
  day =          "1",
  month =        jul,
  year =         "1999",
  coden =        "PHYADX",
  doi =          "http://dx.doi.org/10.1016/S0378-4371(99)00086-2",
  issn =         "0378-4371 (print), 1873-2119 (electronic)",
  issn-l =       "0378-4371",
  bibdate =      "Wed Feb 27 07:32:55 MST 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  url =          "http://www.sciencedirect.com/science/article/pii/S0378437199000862",
  acknowledgement = ack-nhfb,
  fjournal =     "Physica A. Statistical Mechanics and its
                 Applications",
  keywords =     "Growth rate of assets; Income distribution; Zipf's
                 Law",
}

@Article{Piqueira:1999:ZLO,
  author =       "J. R. C. Piqueira and L. H. A. Monteiro and T. M. C.
                 de Magalh{\~a}es and R. T. Ramos and R. B. Sassi and E.
                 G. Cruz",
  title =        "{Zipf's Law} Organizes a Psychiatric Ward",
  journal =      j-J-THEOR-BIOL,
  volume =       "198",
  number =       "3",
  pages =        "439--443",
  day =          "7",
  month =        jun,
  year =         "1999",
  coden =        "JTBIAP",
  doi =          "http://dx.doi.org/10.1006/jtbi.1999.0923",
  issn =         "0022-5193 (print), 1095-8541 (electronic)",
  issn-l =       "0022-5193",
  bibdate =      "Wed Feb 27 07:32:55 MST 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  url =          "http://www.sciencedirect.com/science/article/pii/S0022519399909232",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Theoretical Biology",
  keywords =     "Zipf's Law",
}

@Article{Stanley:1999:SUR,
  author =       "H. Eugene Stanley",
  title =        "Scaling, universality, and renormalization: Three
                 pillars of modern critical phenomena",
  journal =      j-REV-MOD-PHYS,
  volume =       "71",
  number =       "2",
  pages =        "S358--S366",
  month =        mar,
  year =         "1999",
  coden =        "RMPHAT",
  doi =          "http://dx.doi.org/10.1103/RevModPhys.71.S358",
  issn =         "0034-6861 (print), 1538-4527 (electronic), 1539-0756",
  issn-l =       "0034-6861",
  bibdate =      "Wed May 23 10:16:18 MDT 2012",
  bibsource =    "http://rmp.aps.org/toc/RMP/v71/i2;
                 http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 http://www.math.utah.edu/pub/tex/bib/revmodphys1990.bib",
  url =          "http://link.aps.org/doi/10.1103/RevModPhys.71.S358;
                 http://rmp.aps.org/abstract/RMP/v71/i2/pS358_1",
  acknowledgement = ack-nhfb,
  fjournal =     "Reviews of Modern Physics",
}

@Article{Vandewalle:1999:ZAF,
  author =       "N. Vandewalle and M. Ausloos",
  title =        "The $n$-{Zipf} analysis of financial data series and
                 biased data series",
  journal =      j-PHYSICA-A,
  volume =       "268",
  number =       "1--2",
  pages =        "240--249",
  day =          "1",
  month =        jun,
  year =         "1999",
  coden =        "PHYADX",
  doi =          "http://dx.doi.org/10.1016/S0378-4371(99)00031-X",
  issn =         "0378-4371 (print), 1873-2119 (electronic)",
  issn-l =       "0378-4371",
  bibdate =      "Wed Feb 27 07:32:55 MST 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  url =          "http://www.sciencedirect.com/science/article/pii/S037843719900031X",
  acknowledgement = ack-nhfb,
  fjournal =     "Physica A. Statistical Mechanics and its
                 Applications",
  keywords =     "Zipf's Law",
}

@Article{Vardi:1999:PCS,
  author =       "Ilan Vardi",
  title =        "Premiers chiffres significatifs et nombres
                 alg{\'e}briques. ({French}) [Significant leading digits
                 and algebraic numbers]",
  journal =      j-C-R-ACAD-SCI-I,
  volume =       "328",
  number =       "9",
  pages =        "749--754",
  month =        may,
  year =         "1999",
  coden =        "CASMEI",
  doi =          "http://dx.doi.org/10.1016/S0764-4442(99)80265-1",
  issn =         "0764-4442 (print), 1778-3577 (electronic)",
  issn-l =       "0764-4442",
  bibdate =      "Tue Nov 22 11:28:19 MST 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 http://www.sciencedirect.com/",
  url =          "http://www.sciencedirect.com/science/article/pii/S0764444299802651",
  acknowledgement = ack-nhfb,
  fjournal =     "Comptes rendus de l'Acad{\'e}mie des sciences.
                 S{\'e}rie I, Math{'e}matique",
  keywords =     "Benford's Law",
  language =     "French",
}

@Article{Walthoe:1999:LNO,
  author =       "Jon Walthoe and Robert Hunt and Mike Pearson",
  title =        "Looking out for number one",
  journal =      "Plus Magazine",
  volume =       "??",
  number =       "??",
  pages =        "1--9",
  month =        sep,
  year =         "1999",
  doi =          "????",
  bibdate =      "Mon Feb 18 06:59:18 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  note =         "Published by the University of Cambridge Millennium
                 Mathematics Project.",
  url =          "http://plus.maths.org/issue9/features/benford/2pdf/index.html/op.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "Benford's Law",
}

@Article{Blank:2000:PLC,
  author =       "Aharon Blank and Sorin Solomon",
  title =        "Power laws in cities population, financial markets and
                 {Internet} sites (scaling in systems with a variable
                 number of components)",
  journal =      j-PHYSICA-A,
  volume =       "287",
  number =       "1--2",
  pages =        "279--288",
  day =          "15",
  month =        nov,
  year =         "2000",
  coden =        "PHYADX",
  doi =          "http://dx.doi.org/10.1016/S0378-4371(00)00464-7",
  issn =         "0378-4371 (print), 1873-2119 (electronic)",
  issn-l =       "0378-4371",
  bibdate =      "Wed Feb 27 06:24:21 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  url =          "http://www.sciencedirect.com/science/article/pii/S0378437100004647",
  acknowledgement = ack-nhfb,
  fjournal =     "Physica A. Statistical Mechanics and its
                 Applications",
  keywords =     "Zipf's Law",
}

@Article{Drake:2000:CAA,
  author =       "P. D. Drake and M. J. Nigrini",
  title =        "Computer assisted analytical procedures using
                 {Benford}'s law",
  journal =      j-J-ACCOUNT-EDUC,
  volume =       "18",
  number =       "2",
  pages =        "127--146",
  month =        "Spring",
  year =         "2000",
  coden =        "????",
  doi =          "http://dx.doi.org/10.1016/S0748-5751(00)00008-7",
  issn =         "0748-5751 (print), 1873-1996 (electronic)",
  issn-l =       "0748-5751",
  bibdate =      "Tue Nov 22 10:36:47 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  url =          "http://www.sciencedirect.com/science/article/pii/S0748575100000087;
                 http://www.sciencedirect.com/science/journal/07485751",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Accounting Education",
}

@Article{Lanza:2000:UDA,
  author =       "R. B. Lanza",
  title =        "Using digital analysis to detect fraud: Review of the
                 {DATAS\reg} statistical analysis tool",
  journal =      j-J-FORENSIC-ACCOUNT,
  volume =       "1",
  number =       "??",
  pages =        "291--296",
  month =        "????",
  year =         "2000",
  coden =        "????",
  issn =         "1524-5586",
  bibdate =      "Tue Nov 22 10:47:45 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  url =          "http://www.rtedwards.com/journals/JFA/",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Forensic Accounting",
}

@Article{Leemis:2000:SDS,
  author =       "Lawrence M. Leemis and Bruce W. Schmeiser and Diane L.
                 Evans",
  title =        "Survival Distributions Satisfying {Benford's Law}",
  journal =      j-AMER-STAT,
  volume =       "54",
  number =       "4",
  pages =        "236--241",
  month =        nov,
  year =         "2000",
  coden =        "ASTAAJ",
  issn =         "0003-1305 (print), 1537-2731 (electronic)",
  issn-l =       "0003-1305",
  mrclass =      "62E15 (62N05)",
  mrnumber =     "1803620",
  bibdate =      "Fri Jan 27 18:16:34 MST 2012",
  bibsource =    "http://www.amstat.org/publications/tas/;
                 http://www.jstor.org/journals/00031305.html;
                 http://www.jstor.org/stable/i326510;
                 http://www.math.utah.edu/pub/tex/bib/amstat.bib;
                 http://www.math.utah.edu/pub/tex/bib/amstat2000.bib;
                 http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  url =          "http://www.amstat.org/publications/tas/Leemis.htm;
                 http://www.jstor.org/stable/2685773",
  acknowledgement = ack-nhfb,
  fjournal =     "The American Statistician",
}

@InProceedings{Lei:2000:EIN,
  author =       "Skylar Lei and Michael Smith and Giancarlo Succi",
  title =        "Empirical investigation of a novel approach to check
                 the integrity of software engineering measuring
                 processes",
  crossref =     "ACM:2000:PIC",
  pages =        "773--773",
  year =         "2000",
  doi =          "http://dx.doi.org/10.1145/337180.337629",
  bibdate =      "Sat Feb 16 18:28:12 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Benford's Law",
}

@TechReport{Nigrini:2000:CA,
  author =       "Mark J. Nigrini",
  title =        "Continuous Auditing",
  type =         "Preprint",
  institution =  "Ernst \& Young Center for Auditing Research and
                 Advanced Technology, University of Kansas",
  address =      "Lawrence, KS, USA",
  pages =        "23",
  day =          "30",
  month =        aug,
  year =         "2000",
  bibdate =      "Sat Feb 16 18:57:40 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  url =          "https://aaahq.org/audit/midyear/01midyear/papers/nigrini_continuous_audit.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "Benford's Law",
}

@Book{Nigrini:2000:DAU,
  author =       "Mark John Nigrini",
  title =        "Digital analysis using {Benford}'s law: tests and
                 statistics for auditors",
  publisher =    "Global Audit Publications",
  address =      "Vancouver, BC, Canada",
  edition =      "Second",
  pages =        "xvii + 278",
  year =         "2000",
  isbn =         "189449709 (??invalid isbn??)",
  isbn-13 =      "189449709 (??invalid isbn??)",
  lccn =         "????",
  bibdate =      "Tue Nov 22 20:48:29 MST 2011",
  bibsource =    "amicus.nlc-bnc.ca:210/NL;
                 http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  subject =      "Numerical analysis; Data processing; Auditing;
                 Statistical methods; Analyse num{\'e}rique;
                 Informatique; V{\'e}rification comptable; M{\'e}thodes
                 statistiques",
}

@Article{Padmanabhan:2000:CAD,
  author =       "Venkata N. Padmanabhan and Lili Qiu",
  title =        "The content and access dynamics of a busy {Web} server
                 (poster session)",
  journal =      j-SIGMETRICS,
  volume =       "28",
  number =       "1",
  pages =        "122--123",
  month =        jun,
  year =         "2000",
  coden =        "????",
  doi =          "http://doi.acm.org/10.1145/339331.339405",
  issn =         "0163-5999 (print), 1557-9484 (electronic)",
  issn-l =       "0163-5999",
  bibdate =      "Thu Jun 26 11:31:11 MDT 2008",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 http://www.math.utah.edu/pub/tex/bib/sigmetrics.bib",
  abstract =     "We study the MSNBC Web site, one of the busiest in the
                 Internet today. We analyze the dynamics of content
                 creation and modification as well as client accesses.
                 Our key findings are (a) files tend to change little
                 upon modification, (b) a small set of files get
                 modified repeatedly, (c) file popularity follows a
                 Zipf-like distribution with an $\alpha$ much larger
                 than reported in previous, proxy-based studies, and (d)
                 there is significant temporal stability in file
                 popularity but not much stability in the domains from
                 which popular content is accessed. We discuss
                 implications of these findings.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM SIGMETRICS Performance Evaluation Review",
}

@Book{Sole:2000:SLH,
  author =       "Ricard Vicente Sol{\'e} and Brian Goodwin",
  title =        "Signs of Life: How Complexity Pervades Biology",
  publisher =    pub-BASIC-BOOKS,
  address =      pub-BASIC-BOOKS:adr,
  pages =        "xi + 322",
  year =         "2000",
  isbn =         "0-465-01927-7, 0-465-01928-5 (paperback)",
  isbn-13 =      "978-0-465-01927-4, 978-0-465-01928-1 (paperback)",
  lccn =         "QH501 .S65 2000",
  bibdate =      "Thu Feb 28 09:59:50 MST 2013",
  bibsource =    "fsz3950.oclc.org:210/WorldCat;
                 http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Mandelbrot; Zipf's law",
  tableofcontents = "Nonlinearity, chaos, and emergence \\
                 Order, complexity, disorder \\
                 Genetic networks, cell differentiation, and development
                 \\
                 Physiology on the edge of chaos \\
                 Brain dynamics \\
                 Ants, brains, and chaos \\
                 The Baroque of nature \\
                 Life on the edge of catastrophe \\
                 Evolution and extinction \\
                 Fractal cities and market crashes",
}

@Article{Stanley:2000:SIU,
  author =       "H. E. Stanley and L. A. N. Amaral and P. Gopikrishnan
                 and P. Ch. Ivanov and T. H. Keitt and V. Plerou",
  title =        "Scale invariance and universality: organizing
                 principles in complex systems",
  journal =      j-PHYSICA-A,
  volume =       "281",
  number =       "1--4",
  pages =        "60--68",
  day =          "15",
  month =        jun,
  year =         "2000",
  coden =        "PHYADX",
  doi =          "http://dx.doi.org/10.1016/S0378-4371(00)00195-3",
  issn =         "0378-4371 (print), 1873-2119 (electronic)",
  issn-l =       "0378-4371",
  bibdate =      "Thu Feb 28 09:52:12 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  url =          "http://www.sciencedirect.com/science/article/pii/S0378437100001953",
  acknowledgement = ack-nhfb,
  fjournal =     "Physica A",
  keywords =     "power law; scale invariance; Zipf's law",
}

@Article{Tolle:2000:DDS,
  author =       "Charles R. Tolle and Joanne L. Budzien and Randall A.
                 Laviolette",
  title =        "Do dynamical systems follow {Benford}'s law?",
  journal =      j-CHAOS,
  volume =       "10",
  number =       "2",
  pages =        "331--336",
  month =        "????",
  year =         "2000",
  coden =        "CHAOEH",
  doi =          "http://dx.doi.org/10.1063/1.166498",
  issn =         "1054-1500",
  issn-l =       "1054-1500",
  bibdate =      "Mon Nov 14 17:35:25 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  url =          "http://adsabs.harvard.edu/abs/2000Chaos..10..331T;
                 http://link.aip.org/link/chaoeh/v10/i2/p331/s1;
                 http://link.aip.org/link/doi/10.1063/1.166498",
  abstract =     "Data compiled from a variety of sources follow
                 Benford's law, which gives a monotonically decreasing
                 distribution of the first digit (1 through 9). We
                 examine the frequency of the first digit of the
                 coordinates of the trajectories generated by some
                 common dynamical systems. One-dimensional cellular
                 automata fulfill the expectation that the frequency of
                 the first digit is uniform. The molecular dynamics of
                 fluids, on the other hand, provides trajectories that
                 follow Benford's law. Finally, three chaotic systems
                 are considered: Lorenz, H{\'e}non, and R{\"o}ssler. The
                 Lorenz system generates trajectories that follow
                 Benford's law. The H{\'e}non system generates
                 trajectories that resemble neither the uniform
                 distribution nor Benford's law. Finally, the
                 R{\"o}ssler system generates trajectories that follow
                 the uniform distribution for some parameters choices,
                 and Benford's law for others.",
  acknowledgement = ack-nhfb,
  fjournal =     "Chaos (Woodbury, NY)",
  xxpages =      "331--337",
}

@Article{Urzua:2000:SET,
  author =       "Carlos M. Urz{\'u}a",
  title =        "A simple and efficient test for {Zipf}'s law",
  journal =      j-ECONOM-LETT,
  volume =       "66",
  number =       "3",
  pages =        "257--260",
  day =          "1",
  month =        mar,
  year =         "2000",
  coden =        "ECLEDS",
  doi =          "http://dx.doi.org/10.1016/S0165-1765(99)00215-3",
  issn =         "0165-1765 (print), 1873-7374 (electronic)",
  issn-l =       "0165-1765",
  bibdate =      "Wed Feb 27 07:32:55 MST 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  url =          "http://www.sciencedirect.com/science/article/pii/S0165176599002153",
  zmnumber =     "0951.91059",
  abstract =     "This paper presents a simple and locally optimal test
                 for Zipf's law. Its use is illustrated in the case of
                 the largest US metropolitan areas. An objection to the
                 general relevance of that law is also presented.",
  acknowledgement = ack-nhfb,
  classmath =    "91B82 (Statistical methods in economics) 91B74 (Models
                 of real-world systems)",
  fjournal =     "Economics Letters",
  keywords =     "rank-size law; Zipf's law",
}

@Article{Vogt:2000:BGS,
  author =       "W. Vogt",
  title =        "{Benford's Gesetz: Steuer- und Budgets{\"u}ndern auf
                 der Spur --- Zahlen l{\"u}gen nichts}. ({German})
                 [{Benford's Law}: tax and budget sinners lying on the
                 track --- Numbers do not lie]",
  journal =      "Schweizer Versicherung",
  volume =       "9",
  number =       "??",
  pages =        "27--29",
  month =        "????",
  year =         "2000",
  doi =          "????",
  bibdate =      "Mon Feb 18 06:57:07 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  url =          "????",
  acknowledgement = ack-nhfb,
  journal-url =  "http://www.schweizerversicherung.ch/de/archiv_suche",
  language =     "German",
  remark =       "No issn assigned. Not found in journal archive on 18
                 February 2013.",
}

@Article{York:2000:ATB,
  author =       "D. York",
  title =        "Auditing Technique --- {Benford}'s law",
  journal =      j-ACCOUNTANCY,
  volume =       "126",
  number =       "1283",
  pages =        "126--??",
  month =        "????",
  year =         "2000",
  coden =        "ACTYAD",
  issn =         "0001-4664",
  issn-l =       "0001-4664",
  bibdate =      "Wed Nov 23 11:30:54 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Accountancy",
}

@Article{Axtell:2001:ZDU,
  author =       "R. L. Axtell",
  title =        "{Zipf} Distribution of {U.S.} Firm Sizes",
  journal =      j-SCIENCE,
  volume =       "293",
  number =       "5536",
  pages =        "1818--1820",
  day =          "7",
  month =        sep,
  year =         "2001",
  coden =        "SCIEAS",
  doi =          "http://dx.doi.org/10.1126/science.1062081",
  issn =         "0036-8075 (print), 1095-9203 (electronic)",
  issn-l =       "0036-8075",
  bibdate =      "Wed Feb 27 06:38:34 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  url =          "http://www.sciencemag.org/content/293/5536/1818",
  acknowledgement = ack-nhfb,
  fjournal =     "Science",
  keywords =     "Zipf's Law",
}

@Article{Dolgikh:2001:PCS,
  author =       "Dmitry G. Dolgikh and Andrei M. Sukhov",
  title =        "Parameters of cache systems based on a {Zipf}-like
                 distribution",
  journal =      j-COMP-NET-AMSTERDAM,
  volume =       "37",
  number =       "6",
  pages =        "711--716",
  day =          "15",
  month =        dec,
  year =         "2001",
  coden =        "????",
  doi =          "http://dx.doi.org/10.1016/S1389-1286(01)00243-2",
  issn =         "1389-1286 (print), 1872-7069 (electronic)",
  issn-l =       "1389-1286",
  bibdate =      "Wed Feb 27 07:32:55 MST 2013",
  bibsource =    "http://www.elsevier.com/locate/issn/13891286;
                 http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  url =          "http://www.elsevier.nl/gej-ng/10/15/22/67/36/31/abstract.html;
                 http://www.sciencedirect.com/science/article/pii/S1389128601002432",
  acknowledgement = ack-nhfb,
  fjournal =     "Computer Networks (Amsterdam, Netherlands: 1999)",
  keywords =     "Zipf's Law",
}

@Article{Dubinsky:2001:MFF,
  author =       "Bruce G. Dubinsky",
  title =        "Math formula fights fraud",
  journal =      "Legal Times of {Washington}",
  volume =       "XXIV",
  number =       "9",
  pages =        "??--??",
  day =          "26",
  month =        feb,
  year =         "2001",
  issn =         "0732-7536",
  issn-l =       "0732-7536",
  bibdate =      "Sat Feb 16 17:35:39 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Benford's Law",
  xxjournal =    "Legal Times",
}

@Article{Gelbukh:2001:ZHL,
  author =       "Alexander Gelbukh and Grigori Sidorov",
  title =        "{Zipf} and {Heaps Laws}' Coefficients Depend on
                 Language",
  journal =      j-LECT-NOTES-COMP-SCI,
  volume =       "2004",
  pages =        "332--??",
  year =         "2001",
  coden =        "LNCSD9",
  issn =         "0302-9743 (print), 1611-3349 (electronic)",
  issn-l =       "0302-9743",
  bibdate =      "Sat Feb 2 13:03:22 MST 2002",
  bibsource =    "http://link.springer-ny.com/link/service/series/0558/tocs/t2004.htm;
                 http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  url =          "http://link.springer-ny.com/link/service/series/0558/bibs/2004/20040332.htm;
                 http://link.springer-ny.com/link/service/series/0558/papers/2004/20040332.pdf",
  acknowledgement = ack-nhfb,
  fjournal =     "Lecture Notes in Computer Science",
}

@TechReport{Gent:2001:BL,
  author =       "Ian Gent and Toby Walsh",
  title =        "{Benford's Law}",
  type =         "Report",
  institution =  "School of Computer Science, University of St. Andrews,
                 and Department of Computer Science, University of
                 York",
  address =      "St. Andrews, Scotland and York, England",
  pages =        "7",
  day =          "2",
  month =        feb,
  year =         "2001",
  bibdate =      "Fri Nov 18 08:37:38 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  url =          "http://www.dcs.st-and.ac.uk/~apes/reports/apes-25-2001.pdf",
  abstract =     "Benford's Law predicts the frequency of the leading
                 digit in numbers met in a wide range of naturally
                 occurring phenomena. In data following Benford's Law,
                 numbers start with a small leading digit more often
                 those with a large leading digit. Here we demonstrate
                 that Benford's Law also describes a wide range of
                 computational phenomena. In particular, we show that a
                 number of different statistics associated with
                 computation like space and runtime often follow
                 Benford's Law. We also show that search cost on input
                 data that follows Benford's Law is often very different
                 to that on more uniform data. These results could be
                 used to improve algorithm performance (for example, for
                 load balancing or disk de-fragmentation), as well as to
                 help model algorithm performance. Benford's Law can
                 also be used to generate data for benchmarking
                 algorithms that may be more realistic than purely
                 random data.",
  acknowledgement = ack-nhfb,
  remark =       "PDF file no longer at the St. Andrews url on 18
                 November 2011, but recovered from
                 http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.3.3357.",
}

@Article{Harremoes:2001:MEF,
  author =       "Peter Harremo{\"e}s and Flemming Tops{\o}e",
  title =        "Maximum Entropy Fundamentals",
  journal =      j-ENTROPY,
  volume =       "3",
  number =       "3",
  pages =        "191--226",
  month =        sep,
  year =         "2001",
  coden =        "ENTRFG",
  doi =          "http://dx.doi.org/10.3390/e3030191",
  issn =         "1099-4300",
  issn-l =       "1099-4300",
  bibdate =      "Thu Feb 28 10:55:45 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  url =          "http://www.mdpi.com/1099-4300/3/3/191",
  acknowledgement = ack-nhfb,
  fjournal =     "Entropy",
  keywords =     "continuity of entropy; entropy loss; exponential
                 family; game theoretical equilibrium; hyperbolic
                 distributions; information topology; maximum entropy;
                 minimum risk; Nash equilibrium code; partition
                 function; Zipf's law",
  remark =       "Open access journal.",
}

@Article{Hobza:2001:NBL,
  author =       "Tom{\'a}{\v{s}} Hobza and Igor Vajda",
  title =        "On the {Newcomb--Benford} law in models of statistical
                 data",
  journal =      "Revista Matem{\'a}tica Complutense",
  volume =       "14",
  number =       "2",
  pages =        "407--420",
  year =         "2001",
  coden =        "????",
  issn =         "1139-1138, 1696-8220, 1988-2807",
  issn-l =       "1139-1138",
  mrclass =      "62E10",
  mrnumber =     "1871305 (2002j:62015)",
  bibdate =      "Sat Nov 12 09:13:23 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  ajournal =     "Rev. Mat. Complut.",
  fjournal =     "Revista Matem{\'a}tica Complutense",
}

@Article{Huang:2001:PLE,
  author =       "Z. F. Huang and S. Solomon",
  title =        "Power, {L{\'e}vy}, exponential and {Gaussian}-like
                 regimes in autocatalytic financial systems",
  journal =      j-EUR-PHYS-J-B,
  volume =       "20",
  number =       "4",
  pages =        "601--607",
  month =        apr,
  year =         "2001",
  coden =        "EPJBFY",
  doi =          "http://dx.doi.org/10.1007/PL00011114",
  issn =         "1434-6028 (print), 1434-6036 (electronic)",
  issn-l =       "1434-6028",
  bibdate =      "Thu Feb 28 10:26:53 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  url =          "http://link.springer.com/article/10.1007/PL00011114",
  acknowledgement = ack-nhfb,
  fjournal =     "European Physical Journal B: Condensed Matter and
                 Complex Systems",
  keywords =     "power law; scale invariance; Zipf's law",
}

@MastersThesis{Jamain:2001:BL,
  author =       "Adrien Jamain",
  title =        "{Benford's Law}",
  type =         "{Master}'s thesis",
  school =       "Department of Mathematics, Imperial College of London
                 and ENSIMAG",
  address =      "London, UK",
  pages =        "????",
  year =         "2001",
  bibdate =      "Sat Feb 16 18:06:41 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  note =         "Not found in Imperial College Library or COPAC
                 catalogs on 16 February 2013. url link is broken too.",
  url =          "http://www.math.ualberta.ca/~aberger/benford_bibliography/jamain_thesis01.pdf",
  acknowledgement = ack-nhfb,
}

@Article{Jansen:2001:RNP,
  author =       "C. J. M. Jansen and M. M. W. Pollmann",
  title =        "On Round Numbers: Pragmatic Aspects of Numerical
                 Expressions",
  journal =      j-J-QUANT-LINGUISTICS,
  volume =       "8",
  number =       "3",
  pages =        "187--201",
  month =        "????",
  year =         "2001",
  doi =          "http://dx.doi.org/10.1076/jqul.8.3.187.4095",
  issn =         "0929-6174 (print), 1744-5035 (electronic)",
  issn-l =       "0929-6174",
  bibdate =      "Sat Jan 07 09:51:05 2012",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  url =          "http://www.tandfonline.com/doi/abs/10.1076/jqul.8.3.187.4095",
  abstract =     "This paper describes and explains some regularities in
                 the frequency of numbers in text. An analysis of number
                 frequencies in text corpora in Dutch, English, German,
                 and French confirms the expectation that frequency is
                 highly dependent on two factors: magnitude and
                 roundness. Roundness (defined as number frequency in an
                 approximation context) proves to be related to three
                 arithmetical properties: `10-ness', `2-ness', and
                 `5-ness'. In predicting the frequency of numbers
                 irrespective of their context `$2 1/2$-ness' should be
                 added to these factors, as is suggested in the work of
                 Sigurd (1988). The role of the four number
                 characteristics found in this study can be explained by
                 the preference of the language user for using base
                 numbers, and for doubling and halving quantities.",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Quantitative Linguistics",
  onlinedate =   "09 Aug 2010",
}

@Article{Jolion:2001:IBL,
  author =       "Jean-Michel Jolion",
  title =        "Images and {Benford}'s law",
  journal =      j-J-MATH-IMAG-VIS,
  volume =       "14",
  number =       "1",
  pages =        "73--81",
  year =         "2001",
  coden =        "JMIVEK",
  doi =          "http://dx.doi.org/10.1023/A:1008363415314",
  issn =         "0924-9907 (print), 1573-7683 (electronic)",
  issn-l =       "0924-9907",
  mrclass =      "94A08 (68U10)",
  mrnumber =     "1818436 (2001m:94007)",
  bibdate =      "Sat Nov 12 09:13:23 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Mathematical Imaging and Vision: JMIV",
}

@Article{Knudsen:2001:ZLC,
  author =       "Thorbj{\o}rn Knudsen",
  title =        "{Zipf}'s law for cities and beyond: the case of
                 {Denmark}",
  journal =      j-AM-J-ECON-SOCIOL,
  volume =       "60",
  number =       "1",
  pages =        "123--146",
  month =        jan,
  year =         "2001",
  coden =        "AJESA3",
  doi =          "http://dx.doi.org/10.1111/1536-7150.00057",
  issn =         "0002-9246 (print), 1536-7150 (electronic)",
  issn-l =       "0002-9246",
  bibdate =      "Sat Feb 16 18:14:02 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  url =          "http://www.jstor.org/stable/3487947",
  acknowledgement = ack-nhfb,
  fjournal =     "The American Journal of Economics and Sociology",
}

@Article{Levene:2001:ZLW,
  author =       "Mark Levene and Jos{\'e} Borges and George Loizou",
  title =        "{Zipf}'s law for {Web} surfers",
  journal =      j-KNOWL-INFO-SYS,
  volume =       "3",
  number =       "1",
  pages =        "120--129",
  year =         "2001",
  coden =        "KISNCR",
  doi =          "http://dx.doi.org/10.1007/PL00011657",
  issn =         "0219-1377",
  bibdate =      "Sat Nov 12 11:00:30 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  zmnumber =     "0991.68622",
  abstract =     "One of the main activities of Web users, known as
                 `surfing', is to follow links. Lengthy navigation often
                 leads to disorientation when users lose track of the
                 context in which they are navigating and are unsure how
                 to proceed in terms of the goal of their original
                 query. Studying navigation patterns of Web users is
                 thus important, since it can lead us to a better
                 understanding of the problems users face when they are
                 surfing. We derive Zipf's rank frequency law (i.e., an
                 inverse power law) from an absorbing Markov chain model
                 of surfers' behavior assuming that less probable
                 navigation trails are, on average, longer than more
                 probable ones. In our model the probability of a trail
                 is interpreted as the relevance (or `value') of the
                 trail. We apply our model to two scenarios: in the
                 first the probability of a user terminating the
                 navigation session is independent of the number of
                 links he has followed so far, and in the second the
                 probability of a user terminating the navigation
                 session increases by a constant each time the user
                 follows a link. We analyze these scenarios using two
                 sets of experimental data sets showing that, although
                 the first scenario is only a rough approximation of
                 surfers' behavior, the data is consistent with the
                 second scenario and can thus provide an explanation of
                 surfers' behavior.",
  acknowledgement = ack-nhfb,
  classmath =    "68U99 (Computing methodologies) 68P15 (Database
                 theory) 68P20 (Information storage and retrieval)",
  fjournal =     "Knowledge and Information Systems",
  keywords =     "Markov chain; Web navigation; Zipf's law",
}

@Article{Losee:2001:TDB,
  author =       "Robert M. Losee",
  title =        "Term dependence: a basis for {Luhn} and {Zipf}
                 models",
  journal =      j-J-AM-SOC-INF-SCI-TECHNOL,
  volume =       "52",
  number =       "12",
  pages =        "1019--1025",
  year =         "2001",
  coden =        "JASIEF",
  doi =          "http://dx.doi.org/10.1002/asi.1155",
  issn =         "1532-2882 (print), 1532-2890 (electronic)",
  issn-l =       "1532-2882",
  bibdate =      "Mon Feb 25 06:13:56 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of the American Society for Information
                 Science and Technology",
}

@Article{Malacarne:2001:QED,
  author =       "L. C. Malacarne and R. S. Mendes and E. K. Lenzi",
  title =        "$q$-exponential distribution in urban agglomeration",
  journal =      j-PHYS-REV-E,
  volume =       "65",
  number =       "??",
  pages =        "017106",
  day =          "21",
  month =        dec,
  year =         "2001",
  coden =        "PLEEE8",
  doi =          "http://dx.doi.org/10.1103/PhysRevE.65.017106",
  issn =         "1539-3755 (print), 1550-2376 (electronic)",
  issn-l =       "1539-3755",
  bibdate =      "Tue Feb 26 06:40:57 MST 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  url =          "http://link.aps.org/doi/10.1103/PhysRevE.65.017106",
  acknowledgement = ack-nhfb,
  fjournal =     "Physical Review E (Statistical physics, plasmas,
                 fluids, and related interdisciplinary topics)",
  keywords =     "Zipf--Mandelbrot law",
}

@Article{Montemurro:2001:BZM,
  author =       "Marcelo A. Montemurro",
  title =        "Beyond the {Zipf--Mandelbrot} law in quantitative
                 linguistics",
  journal =      j-PHYSICA-A,
  volume =       "300",
  number =       "3--4",
  pages =        "567--578",
  day =          "15",
  month =        nov,
  year =         "2001",
  coden =        "PHYADX",
  doi =          "http://dx.doi.org/10.1016/S0378-4371(01)00355-7",
  issn =         "0378-4371 (print), 1873-2119 (electronic)",
  issn-l =       "0378-4371",
  bibdate =      "Wed Feb 27 07:32:55 MST 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  url =          "http://www.sciencedirect.com/science/article/pii/S0378437101003557",
  acknowledgement = ack-nhfb,
  fjournal =     "Physica A. Statistical Mechanics and its
                 Applications",
  keywords =     "Zipf's Law",
}

@PhdThesis{Morters:2001:BGV,
  author =       "Peter M{\"o}rters",
  title =        "{Benford's Gesetz {\"u}ber die Verteilung der
                 Ziffern}. (German) [{Benford}'s law on the distribution
                 of digits]",
  type =         "{Habilitationsvorlesung}",
  school =       "????",
  address =      "Kaiserslauten, Germany, and Bath, UK",
  pages =        "4",
  month =        "????",
  year =         "2001",
  bibdate =      "Sat Feb 16 18:47:15 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  url =          "http://people.bath.ac.uk/maspm/benford.ps",
  acknowledgement = ack-nhfb,
  language =     "German",
}

@Article{Nigrini:2001:DAU,
  author =       "Mark Nigrini",
  title =        "Digital Analysis Using {Benford's} Law: Tests and
                 Statistics for Auditors",
  journal =      j-EDPACS,
  volume =       "28",
  number =       "9",
  pages =        "1--2",
  month =        "????",
  year =         "2001",
  coden =        "EDPCDF",
  doi =          "http://dx.doi.org/10.1201/1079/43266.28.9.20010301/30389.4",
  issn =         "0736-6981 (print), 1936-1009 (electronic)",
  issn-l =       "0736-6981",
  bibdate =      "Sat Jan 07 09:08:09 2012",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  url =          "http://www.tandfonline.com/doi/abs/10.1201/1079/43266.28.9.20010301/30389.4",
  acknowledgement = ack-nhfb,
  fjournal =     "EDPACS",
  onlinedate =   "21 Dec 2006",
}

@Article{Pietronero:2001:EUD,
  author =       "L. Pietronero and E. Tosatti and V. Tosatti and A.
                 Vespignani",
  title =        "Explaining the uneven distribution of numbers in
                 nature: the laws of {Benford} and {Zipf}",
  journal =      j-PHYSICA-A,
  volume =       "293",
  number =       "1--2",
  pages =        "297--304",
  day =          "1",
  month =        apr,
  year =         "2001",
  coden =        "PHYADX",
  doi =          "http://dx.doi.org/10.1016/S0378-4371(00)00633-6",
  issn =         "0378-4371 (print), 1873-2119 (electronic)",
  issn-l =       "0378-4371",
  bibdate =      "Wed Feb 27 07:32:55 MST 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  url =          "http://adsabs.harvard.edu/abs/2001PhyA..293..297P;
                 http://www.sciencedirect.com/science/article/pii/S0378437100006336",
  abstract =     "The distribution of first digits in numbers series
                 obtained from very different origins shows a marked
                 asymmetry in favor of small digits that goes under the
                 name of Benford's law. We analyze in detail this
                 property for different data sets and give a general
                 explanation for the origin of the Benford's law in
                 terms of multiplicative processes. We show that this
                 law can be also generalized to series of numbers
                 generated from more complex systems like the catalogs
                 of seismic activity. Finally, we derive a relation
                 between the generalized Benford's law and the popular
                 Zipf's law which characterize the rank order statistics
                 and has been extensively applied to many problems
                 ranging from city population to linguistics.",
  acknowledgement = ack-nhfb,
  fjournal =     "Physica A: Statistical Mechanics and its
                 Applications",
  keywords =     "Benford's Law; Law of Anomalous Numbers; Zipf's Law",
}

@Article{Reed:2001:PZO,
  author =       "William J. Reed",
  title =        "The {Pareto}, {Zipf} and other power laws",
  journal =      j-ECONOM-LETT,
  volume =       "74",
  number =       "1",
  pages =        "15--19",
  day =          "20",
  month =        dec,
  year =         "2001",
  coden =        "ECLEDS",
  doi =          "http://dx.doi.org/10.1016/S0165-1765(01)00524-9",
  issn =         "0165-1765 (print), 1873-7374 (electronic)",
  issn-l =       "0165-1765",
  bibdate =      "Wed Feb 27 07:32:55 MST 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  url =          "http://www.sciencedirect.com/science/article/pii/S0165176501005249",
  acknowledgement = ack-nhfb,
  fjournal =     "Economics Letters",
  keywords =     "Zipf's Law",
}

@TechReport{Scott:2001:BLE,
  author =       "P. D. Scott and M. Fasli",
  title =        "{Benford's Law}: An Empirical Investigation and a
                 Novel Explanation",
  type =         "CSM Technical Report",
  number =       "349",
  institution =  "Department of Computer Science, University Essex",
  address =      "Colchester, UK",
  day =          "26",
  month =        oct,
  year =         "2001",
  bibdate =      "Tue Nov 22 21:05:22 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  url =          "http://www.essex.ac.uk/csee/research/publications/technicalreports/2001/CSM-349.pdf",
  acknowledgement = ack-nhfb,
}

@Article{Sellke:2001:CVT,
  author =       "Thomas Sellke and M. J. Bayarri and James O. Berger",
  title =        "Calibration of $p$ Values for Testing Precise Null
                 Hypotheses",
  journal =      j-AMER-STAT,
  volume =       "55",
  number =       "1",
  pages =        "62--71",
  month =        feb,
  year =         "2001",
  coden =        "ASTAAJ",
  doi =          "http://dx.doi.org/10.1198/000313001300339950",
  issn =         "0003-1305 (print), 1537-2731 (electronic)",
  issn-l =       "0003-1305",
  bibdate =      "Fri Jan 27 18:16:34 MST 2012",
  bibsource =    "http://www.amstat.org/publications/tas/;
                 http://www.jstor.org/journals/00031305.html;
                 http://www.jstor.org/stable/i326511;
                 http://www.math.utah.edu/pub/tex/bib/amstat2000.bib;
                 http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  url =          "http://www.amstat.org/publications/tas/Sellke.htm;
                 http://www.jstor.org/stable/2685531;
                 http://www.tandfonline.com/doi/abs/10.1198/000313001300339950",
  acknowledgement = ack-nhfb,
  fjournal =     "The American Statistician",
}

@Article{Snyder:2001:SAO,
  author =       "Mark A. Snyder and James H. Curry and Anne M.
                 Dougherty",
  title =        "Stochastic aspects of one-dimensional discrete
                 dynamical systems: {Benford}'s law",
  journal =      j-PHYS-REV-E,
  volume =       "64",
  number =       "2",
  pages =        "026222",
  month =        aug,
  year =         "2001",
  coden =        "PLEEE8",
  doi =          "http://dx.doi.org/10.1103/PhysRevE.64.026222",
  issn =         "1539-3755 (print), 1550-2376 (electronic)",
  issn-l =       "1539-3755",
  bibdate =      "Mon Nov 14 17:44:15 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  url =          "http://adsabs.harvard.edu/abs/2001PhRvE..64b6222S;
                 http://pre.aps.org/abstract/PRE/v64/i2/e026222",
  abstract =     "Benford's law owes its discovery to the ``Grubby Pages
                 Hypothesis,'' a 19th century observation made by Simon
                 Newcomb that the beginning pages of logarithm books
                 were grubbier than the last few pages, implying that
                 scientists referenced the values toward the front of
                 the books more frequently. If a data set satisfies
                 Benford's law, then its significant digits will have a
                 logarithmic distribution, which favors smaller
                 significant digits. In this article we demonstrate two
                 ways of creating discrete one-dimensional dynamical
                 systems that satisfy Benford's law. We also develop a
                 numerical simulation methodology that we use to study
                 dynamical systems when analytical results are not
                 readily available.",
  acknowledgement = ack-nhfb,
  fjournal =     "Physical Review E (Statistical physics, plasmas,
                 fluids, and related interdisciplinary topics)",
  pagecount =    "5",
}

@InCollection{Solomon:2001:SPZ,
  author =       "Sorin Solomon and Peter Richmond",
  booktitle =    "Economics with heterogeneous interacting agents
                 ({Marseille}, 2000)",
  title =        "Stability of {Pareto--Zipf} law in non-stationary
                 economies",
  volume =       "503",
  publisher =    pub-SV,
  address =      pub-SV:adr,
  pages =        "141--159",
  year =         "2001",
  mrclass =      "91B28 (91B62)",
  mrnumber =     "1838925",
  bibdate =      "Sat Nov 12 09:13:23 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  series =       "Lecture Notes in Econom. and Math. Systems",
  acknowledgement = ack-nhfb,
}

@Article{Zanette:2001:VTC,
  author =       "Dami{\'a}n H. Zanette and Susanna C. Manrubia",
  title =        "Vertical transmission of culture and the distribution
                 of family names",
  journal =      j-PHYSICA-A,
  volume =       "295",
  number =       "1--2",
  pages =        "1--8",
  day =          "1",
  month =        jun,
  year =         "2001",
  coden =        "PHYADX",
  doi =          "http://dx.doi.org/10.1016/S0378-4371(01)00046-2",
  issn =         "0378-4371 (print), 1873-2119 (electronic)",
  issn-l =       "0378-4371",
  bibdate =      "Wed Feb 27 07:03:20 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  url =          "http://www.sciencedirect.com/science/article/pii/S0378437101000462",
  acknowledgement = ack-nhfb,
  fjournal =     "Physica A. Statistical Mechanics and its
                 Applications",
  keywords =     "Zipf's Law",
}

@Article{Abe:2002:STE,
  author =       "Sumiyoshi Abe",
  title =        "Stability of {Tsallis} entropy and instabilities of
                 {R{\'e}nyi} and normalized {Tsallis} entropies: a basis
                 for $q$-exponential distributions",
  journal =      j-PHYS-REV-E,
  volume =       "66",
  number =       "??",
  pages =        "046134",
  day =          "24",
  month =        oct,
  year =         "2002",
  coden =        "PLEEE8",
  doi =          "http://dx.doi.org/10.1103/PhysRevE.66.046134",
  issn =         "1539-3755 (print), 1550-2376 (electronic)",
  issn-l =       "1539-3755",
  bibdate =      "Tue Feb 26 06:40:57 MST 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  url =          "http://link.aps.org/doi/10.1103/PhysRevE.66.046134",
  acknowledgement = ack-nhfb,
  fjournal =     "Physical Review E (Statistical physics, plasmas,
                 fluids, and related interdisciplinary topics)",
  keywords =     "Zipf's Law",
}

@Article{Anonymous:2002:ZLM,
  author =       "Anonymous",
  title =        "{Zipf}'s law and maximum sustainable growth",
  journal =      j-STAT-PROB-LETT,
  volume =       "56",
  number =       "2",
  pages =        "??--??",
  day =          "15",
  month =        jan,
  year =         "2002",
  coden =        "SPLTDC",
  doi =          "http://dx.doi.org/10.1016/j.jedc.2013.02.004",
  issn =         "0167-7152 (print), 1879-2103 (electronic)",
  issn-l =       "0167-7152",
  bibdate =      "Wed Feb 27 07:32:55 MST 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  url =          "http://www.sciencedirect.com/science/article/pii/S0165188913000341",
  acknowledgement = ack-nhfb,
  fjournal =     "Statistics \& Probability Letters",
  keywords =     "Zipf's Law",
  onlinedate =   "19 February 2013",
}

@InProceedings{Bhattacharya:2002:KBT,
  author =       "S. Bhattacharya",
  editor =       "????",
  booktitle =    "9th World Congress of Accounting Historians, Deakin
                 University, Melbourne, Australia July 30--August 3,
                 2002",
  title =        "From {Kautilya} to {Benford} --- Trends in Forensic
                 and Investigative Accounting",
  publisher =    "Accounting Association of Australia and New Zealand",
  address =      "????",
  pages =        "??--??",
  year =         "2002",
  isbn =         "????",
  isbn-13 =      "????",
  lccn =         "????",
  bibdate =      "Sat Feb 16 17:22:29 2013",
  bibsource =    "fsz3950.oclc.org:210/WorldCat;
                 http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  journal-url =  "http://ach.sagepub.com/",
  remark =       "I cannot find the published proceedings in online
                 catalogs or bookstores, or in the Deakin University
                 library catalogs. Where only selected papers published
                 from the conference in the journal Accounting
                 History??",
  review-doi =   "http://dx.doi.org/10.1177/103237320200700207",
  review-url =   "http://dro.deakin.edu.au/view/DU:30012663;
                 http://www.highbeam.com/doc/1G1-97484707.html",
}

@TechReport{Diekmann:2002:DFM,
  author =       "Andreas Diekmann",
  title =        "{Diagnose von Fehlerquellen und methodische
                 Qualit{\"a}t in der sozialwissenschaftlichen
                 Forschung}. ({German}) [{Diagnosis} of errors and
                 methodological quality in social science research]",
  type =         "Report",
  number =       "ITA-02-04",
  institution =  "Institut f{\"u}r Technikfolgen-Absch{\"a}tzung",
  address =      "Vienna, Austria",
  pages =        "????",
  year =         "2002",
  bibdate =      "Thu Nov 17 19:11:00 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  language =     "German",
}

@Article{FerreriCancho:2002:ZLR,
  author =       "Ramon {Ferrer i Cancho} and Ricard V. Sol{\'e}",
  title =        "{Zipf}'s law and random texts",
  journal =      j-ADV-COMPLEX-SYST,
  volume =       "5",
  number =       "1",
  pages =        "1--6",
  year =         "2002",
  coden =        "????",
  doi =          "http://dx.doi.org/10.1142/S0219525902000468",
  issn =         "0219-5259",
  bibdate =      "Sat Nov 12 11:00:23 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  zmnumber =     "1090.91595",
  abstract =     "Random-text models have been proposed as an
                 explanation for the power law relationship between word
                 frequency and rank, the so-called Zipf's law. They are
                 generally regarded as null hypotheses rather than
                 models in the strict sense. In this context, recent
                 theories of language emergence and evolution assume
                 this law as a priori information with no need of
                 explanation. Here, random texts and real texts are
                 compared through (a) the so-called lexical spectrum and
                 (b) the distribution of words having the same length.
                 It is shown that real texts fill the lexical spectrum
                 much more efficiently and regardless of the word
                 length, suggesting that the meaningfulness of Zipf's
                 law is high.",
  acknowledgement = ack-nhfb,
  classmath =    "91F20 (Linguistics)",
  fjournal =     "Advances in Complex Systems",
  journal-url =   "http://www.worldscinet.com/acs/acs.shtml",
  keywords =     "Human language; monkey languages; random texts;
                 scaling; Zipf's law",
}

@Article{Gottwald:2002:NBL,
  author =       "Georg A. Gottwald and Matthew Nicol",
  title =        "On the nature of {Benford's Law}",
  journal =      j-PHYSICA-A,
  volume =       "303",
  number =       "3--4",
  pages =        "387--396",
  day =          "15",
  month =        jan,
  year =         "2002",
  coden =        "PHYADX",
  doi =          "http://dx.doi.org/10.1016/S0378-4371(01)00497-6",
  issn =         "0378-4371 (print), 1873-2119 (electronic)",
  issn-l =       "0378-4371",
  mrclass =      "60C05 (28D05 60E05 82B05)",
  mrnumber =     "1917635 (2003d:60015)",
  bibdate =      "Tue Nov 22 11:28:19 MST 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 http://www.sciencedirect.com/",
  url =          "http://adsabs.harvard.edu/abs/2002PhyA..303..387G;
                 http://www.sciencedirect.com/science/article/pii/S0378437101004976",
  acknowledgement = ack-nhfb,
  fjournal =     "Physica A. Statistical Mechanics and its
                 Applications",
  keywords =     "Benford's Law; Law of Anomalous Numbers; Zipf's Law",
}

@Article{Hasan:2002:ADA,
  author =       "Bassam Hasan",
  title =        "Assessing data authenticity with {Benford}'s law",
  journal =      "Information Systems Control Journal",
  volume =       "6",
  pages =        "??--??",
  year =         "2002",
  coden =        "ISYJFS",
  issn =         "1526-7407",
  bibdate =      "Sat Feb 16 17:45:21 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  url =          "http://www.isaca.org/Journal/Past-Issues/2002/Volume-6/Pages/Assessing-Data-Authenticity-With-Benfords-Law.aspx",
  acknowledgement = ack-nhfb,
  journal-url =  "http://www.isaca.org/",
  remark =       "Journal publication ceased at volume 6 in 2008,
                 according to one library catalog, but volumes up to
                 2013 are available at journal Web site.",
}

@InProceedings{Hill:2002:RAB,
  author =       "T. P. Hill",
  editor =       "????",
  booktitle =    "Conference, Leiden University",
  title =        "Recent applications of {Benford}'s law",
  publisher =    "????",
  address =      "????",
  pages =        "??--??",
  year =         "2002",
  isbn =         "????",
  isbn-13 =      "????",
  lccn =         "????",
  bibdate =      "Sat Feb 16 17:55:46 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
}

@Article{Hoyle:2002:MSM,
  author =       "David C. Hoyle and Magnus Rattray and Ray Jupp and
                 Andrew Brass",
  title =        "Making sense of microarray data distributions",
  journal =      j-BIOINFORMATICS,
  volume =       "18",
  number =       "4",
  pages =        "576--584",
  month =        apr,
  year =         "2002",
  issn =         "1367-4803 (print), 1367-4811 (electronic)",
  issn-l =       "1367-4803",
  bibdate =      "Fri Nov 25 11:16:37 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Bioinformatics",
  keywords =     "Benford's Law; mRNA transcription data",
}

@Article{Jones:2002:LDR,
  author =       "B. K. Jones",
  title =        "Logarithmic distributions in reliability analysis",
  journal =      j-MICROELECT-RELIABILITY,
  volume =       "42",
  number =       "4--5",
  pages =        "779--786",
  month =        apr # "\slash " # may,
  year =         "2002",
  coden =        "MCRLAS",
  doi =          "http://dx.doi.org/10.1016/S0026-2714(02)00031-8",
  issn =         "0026-2714 (print), 1872-941X (electronic)",
  issn-l =       "0026-2714",
  bibdate =      "Tue Nov 22 11:28:19 MST 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 http://www.sciencedirect.com/",
  url =          "http://www.sciencedirect.com/science/article/pii/S0026271402000318",
  acknowledgement = ack-nhfb,
  fjournal =     "Microelectronics and Reliability",
  keywords =     "Benford's Law; Pareto distribution; Zipf's Law",
}

@Article{Kawamura:2002:UZL,
  author =       "Kenji Kawamura and Naomichi Hatano",
  title =        "Universality of {Zipf}'s law",
  journal =      j-J-PHYS-SOC-JAP,
  volume =       "71",
  number =       "5",
  pages =        "1211--1213",
  year =         "2002",
  coden =        "JUPSAU",
  doi =          "http://dx.doi.org/10.1143/JPSJ.71.1211",
  issn =         "0031-9015 (print), 1347-4073 (electronic)",
  issn-l =       "0031-9015",
  bibdate =      "Sat Nov 12 11:00:54 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  url =          "http://jpsj.ipap.jp/",
  zmnumber =     "1063.60114",
  abstract =     "The aim of the present paper is to propose and
                 simulate a simple and generic model that reproduces
                 Zipf's law. In the proposed model, the time evolution
                 is considered to be a random walk in the logarithmic
                 scale reflecting the company asset distribution and/or
                 the evolution of city populations (e.g. Zipf's law for
                 income distribution asserts that the size and number of
                 companies are in inverse proportional relationship).
                 The paper explains theoretically and shows by numerical
                 simulation that the introduced model of Zipf's law has
                 a very robust behaviour when applied to various natural
                 and social phenomena. The authors do not investigate
                 the famous case of Zipf's law application to the
                 frequency of English words, but they speculate that
                 this case might be also explained within the same time
                 development of the proposed model.",
  acknowledgement = ack-nhfb,
  classmath =    "60J60 (Diffusion processes) 60J70 (Appl. of diffusion
                 theory) 76R50 (Diffusion) 82C24 (Interface problems
                 (dynamic and non-equilibrium))",
  fjournal =     "Journal of the Physical Society of Japan",
  keywords =     "city population evolution; company asset distribution;
                 diffusion; generic model of Zipf's law; natural and
                 social phenomena; random walk in logarithmic scale",
  ZMreviewer =   "Neculai Curteanu (Ia\c si)",
}

@TechReport{Kreiner:2002:FDL,
  author =       "W. A. Kreiner",
  title =        "First digit law",
  type =         "Preprint",
  institution =  "Abteilung Chemische Physik, Arbeitsgruppe
                 Laseranwendungen, Universit{\"a}t Ulm",
  address =      "Ulm, Germany",
  pages =        "7",
  day =          "3",
  month =        may,
  year =         "2002",
  bibdate =      "Sat Feb 16 18:18:49 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  url =          "http://vts.uni-ulm.de/docs/2002/1441/vts_1441.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "Benford's Law; First Digit Law; Newcomb; Statistisches
                 Fraktal",
  language =     "German",
}

@Article{Li:2002:ZLI,
  author =       "Wentian Li and Yaning Yang",
  title =        "{Zipf's Law} in Importance of Genes for Cancer
                 Classification Using Microarray Data",
  journal =      j-J-THEOR-BIOL,
  volume =       "219",
  number =       "4",
  pages =        "539--551",
  day =          "21",
  month =        dec,
  year =         "2002",
  coden =        "JTBIAP",
  doi =          "http://dx.doi.org/10.1006/jtbi.2002.3145",
  issn =         "0022-5193 (print), 1095-8541 (electronic)",
  issn-l =       "0022-5193",
  mrclass =      "92C40 (92D10)",
  mrnumber =     "2044066",
  bibdate =      "Wed Feb 27 07:32:55 MST 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  url =          "http://www.sciencedirect.com/science/article/pii/S0022519302931450",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Theoretical Biology",
  keywords =     "Zipf's Law",
}

@Book{Livio:2002:GRS,
  author =       "Mario Livio",
  title =        "The golden ratio: the story of phi, the world's most
                 astonishing number",
  publisher =    "Broadway Books",
  address =      "New York, NY, USA",
  pages =        "viii + 294",
  year =         "2002",
  isbn =         "0-7679-0815-5",
  isbn-13 =      "978-0-7679-0815-3",
  lccn =         "QA466 .L58 2002",
  bibdate =      "Tue Jul 08 12:29:44 2003",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 http://www.math.utah.edu/pub/tex/bib/master.bib",
  note =         "Benford's Law is treated on pages 231--237.",
  price =        "US\$24.95, CAN\$37.95",
  acknowledgement = ack-nhfb,
}

@InProceedings{Manaris:2002:PTR,
  author =       "B. Manaris and T. Purewal and C. McCormick",
  editor =       "{IEEE}",
  booktitle =    "Proceedings: IEEE SoutheastCon 2002: April 5--7, 2002,
                 Embassy Suites Hotel, Columbia, South Carolina, USA",
  title =        "Progress Towards Recognizing and Classifying Beautiful
                 Music with Computers: {MIDI}-Encoded Music and the
                 {Zipf-Mandelbrot Law}",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "52--57",
  year =         "2002",
  doi =          "http://dx.doi.org/10.1109/.2002.995557",
  isbn =         "0-7803-7252-2",
  isbn-13 =      "978-0-7803-7252-8",
  lccn =         "TK7801 .I56 2002",
  bibdate =      "Mon Feb 18 10:40:27 2013",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/m/mandelbrot-benoit.bib;
                 http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  url =          "http://ieeexplore.ieee.org/servlet/opac?punumber=7814",
  acknowledgement = ack-nhfb,
  bookpages =    "xviii + 482",
}

@Article{Mochty:2002:AMI,
  author =       "L. Mochty",
  title =        "{Die Aufdeckung von Manipulationen im Rechnungswesen
                 --- Was leistet das Benford's Law?}. ({German}) [{The}
                 disclosure of accounting manipulations --- what does
                 {Benford's Law} mean?]",
  journal =      "Die Wirtschaftspr{\"u}fung",
  volume =       "14",
  number =       "??",
  pages =        "725--736",
  month =        "????",
  year =         "2002",
  coden =        "????",
  issn =         "0043-6313",
  issn-l =       "0043-6313",
  bibdate =      "Thu Nov 17 19:20:24 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  language =     "German",
}

@Book{Newman:2002:ME,
  author =       "M. E. J. (Mark E. J.) Newman and Richard G. Palmer",
  title =        "Modeling extinction",
  publisher =    pub-OXFORD,
  address =      pub-OXFORD:adr,
  pages =        "xii + 102",
  year =         "2002",
  isbn =         "0-19-515946-2 (paperback), 0-19-515945-4 (hardcover)",
  isbn-13 =      "978-0-19-515946-2 (paperback), 978-0-19-515945-5 (hardcover)",
  lccn =         "QH78 .N48 2002",
  bibdate =      "Thu Feb 28 10:36:25 MST 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 library.ox.ac.uk:210/ADVANCE",
  series =       "Santa Fe Institute studies in the sciences of
                 complexity",
  acknowledgement = ack-nhfb,
  subject =      "Extinction (Biology); Statistical methods;
                 Mathematical models",
  keywords =     "power law; Zipf's law",
}

@Misc{Popescu:2002:LNZ,
  author =       "Ioan-Iovitz Popescu",
  title =        "On the {Lavelette}'s nonlinear {Zipf}'s law",
  howpublished = "Web preprint.",
  month =        feb,
  year =         "2002",
  bibdate =      "Sat Feb 16 19:02:15 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  url =          "http://alpha2.infim.ro/~ltpd/Zipf's_Law.html",
  acknowledgement = ack-nhfb,
}

@Article{Reed:2002:GFG,
  author =       "William J. Reed and Barry D. Hughes",
  title =        "From gene families and genera to incomes and
                 {Internet} file sizes: Why power laws are so common in
                 nature",
  journal =      j-PHYS-REV-E,
  volume =       "66",
  number =       "6",
  pages =        "067103",
  month =        dec,
  year =         "2002",
  coden =        "PLEEE8",
  doi =          "http://dx.doi.org/10.1103/PhysRevE.66.067103",
  issn =         "1539-3755 (print), 1550-2376 (electronic)",
  issn-l =       "1539-3755",
  bibdate =      "Wed Feb 27 06:58:05 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  url =          "http://link.aps.org/doi/10.1103/PhysRevE.66.067103",
  acknowledgement = ack-nhfb,
  fjournal =     "Physical Review E (Statistical physics, plasmas,
                 fluids, and related interdisciplinary topics)",
  keywords =     "Pareto's Law; Zipf's Law; rank-size property",
  pagecount =    "4",
}

@Article{Sandron:2002:DPC,
  author =       "Fr{\'e}d{\'e}ric Sandron",
  title =        "Do populations conform to the {Law of Anomalous
                 Numbers}?",
  journal =      "Population",
  volume =       "57",
  number =       "4--5",
  pages =        "755--761",
  month =        "????",
  year =         "2002",
  coden =        "????",
  doi =          "????",
  issn =         "1169-1018",
  issn-l =       "1169-1018",
  bibdate =      "Sat Feb 16 19:08:50 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  note =         "Translation from French by S. R. Hayford.",
  url =          "http://www.cairn.info/article_p.php?ID_ARTICLE=POPE_204_0753",
  acknowledgement = ack-nhfb,
  journal-url =  "http://www.jstor.org/journals/11691018.html",
}

@Article{Sandron:2002:PSE,
  author =       "Fr{\'e}d{\'e}ric Sandron",
  title =        "Les populations suivent-elles la loi des nombres
                 anomaux? ({French}). [{Do} populations conform to the
                 {Law of Anomalous Numbers}?]",
  journal =      "Population ({French} edition)",
  volume =       "57",
  number =       "4--5",
  pages =        "761--768",
  month =        "????",
  year =         "2002",
  coden =        "POPUAQ",
  doi =          "????",
  issn =         "0032-4663 (print), 1957-7966 (electronic)",
  issn-l =       "0032-4663",
  bibdate =      "Sat Feb 16 19:08:50 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  url =          "http://www.persee.fr/web/revues/home/prescript/article/pop_0032-4663_2002_num_57_4_16873",
  acknowledgement = ack-nhfb,
}

@TechReport{Seaman:2002:BLB,
  author =       "R. S. Seaman",
  title =        "{Benford}'s law and and background field errors in
                 data assimilation",
  type =         "Preprint",
  institution =  "Bureau of Meteorology Research Centre",
  address =      "Melbourne, Australia",
  month =        "????",
  year =         "2002",
  bibdate =      "Sun Feb 17 14:01:22 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  url =          "http://amm.bom.gov.au/amoj/docs/2002/seaman.pdf",
  acknowledgement = ack-nhfb,
}

@Article{Seaman:2002:RBL,
  author =       "R. S. Seaman",
  title =        "The relevance of {Benford's Law} to background field
                 errors in data assimilation",
  journal =      "Australian Meteorological Magazine",
  volume =       "51",
  number =       "1",
  pages =        "25--33",
  month =        "????",
  year =         "2002",
  coden =        "AMMGAS",
  issn =         "0004-9743",
  issn-l =       "0004-9743",
  bibdate =      "Mon Nov 14 16:08:25 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  url =          "http://www.bom.gov.au/amm/docs/2002/seaman.pdf;
                 http://www.bom.gov.au/amm/docs/2002/seaman_hres.pdf",
  acknowledgement = ack-nhfb,
  ajournal =     "Aust. Met. Mag.",
  ajournal-2 =   "Aust. Meteorol. Mag.",
  fjournal =     "Australian Meteorological Magazine",
  journal-url =  "http://www.bom.gov.au/amm/",
}

@Article{Taylor:2002:STD,
  author =       "Rosemary N. Taylor and Damian J. McEntegart and
                 Eleanor C. Stillman",
  title =        "Statistical techniques to detect fraud and other data
                 irregularities in clinical questionnaire data",
  journal =      "Drug Information Journal",
  volume =       "36",
  number =       "1",
  pages =        "115--125",
  month =        jan,
  year =         "2002",
  doi =          "http://dx.doi.org/10.1177/009286150203600115",
  issn =         "0092-8615",
  issn-l =       "0092-8615",
  bibdate =      "Mon Feb 18 06:42:24 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  url =          "http://www.diahome.org/DIAHome/resources/content.aspx?type=eopdf&file=%2Fproductfiles%2F8357%2Fdiaj_11524.pdf????",
  acknowledgement = ack-nhfb,
  keywords =     "Benford's Law",
}

@Article{Yeh:2002:SMZ,
  author =       "Hsiaw-Chan Yeh",
  title =        "Six multivariate {Zipf} distributions and their
                 related properties",
  journal =      j-STAT-PROB-LETT,
  volume =       "56",
  number =       "2",
  pages =        "131--141",
  day =          "15",
  month =        jan,
  year =         "2002",
  coden =        "SPLTDC",
  doi =          "http://dx.doi.org/10.1016/S0167-7152(01)00149-3",
  issn =         "0167-7152 (print), 1879-2103 (electronic)",
  issn-l =       "0167-7152",
  mrclass =      "62H10",
  mrnumber =     "1881166 (2002m:62084)",
  bibdate =      "Wed Feb 27 07:32:55 MST 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  url =          "http://www.sciencedirect.com/science/article/pii/S0167715201001493",
  acknowledgement = ack-nhfb,
  fjournal =     "Statistics \& Probability Letters",
  keywords =     "Zipf's Law",
}

@Article{Abdel-All:2003:GPP,
  author =       "N. H. Abdel-All and M. A. W. Mahmoud and H. N.
                 Abd-Ellah",
  title =        "Geometrical properties of {Pareto} distribution",
  journal =      j-APPL-MATH-COMP,
  volume =       "145",
  number =       "2--3",
  pages =        "321--339",
  day =          "25",
  month =        dec,
  year =         "2003",
  coden =        "AMHCBQ",
  issn =         "0096-3003 (print), 1873-5649 (electronic)",
  issn-l =       "0096-3003",
  bibdate =      "Fri Jan 9 08:41:12 MST 2004",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/applmathcomput2000.bib;
                 http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Applied Mathematics and Computation",
}

@Article{Alvarez-Ramirez:2003:ZMS,
  author =       "Jose Alvarez-Ramirez and Monica Meraz and Gustavo
                 Gallegos",
  title =        "{Zipf--Mandelbrot} scaling law for world track
                 records",
  journal =      j-PHYSICA-A,
  volume =       "328",
  number =       "3--4",
  pages =        "545--560",
  day =          "15",
  month =        oct,
  year =         "2003",
  coden =        "PHYADX",
  doi =          "http://dx.doi.org/10.1016/S0378-4371(03)00579-X",
  issn =         "0378-4371 (print), 1873-2119 (electronic)",
  issn-l =       "0378-4371",
  bibdate =      "Wed Feb 27 07:32:55 MST 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  url =          "http://www.sciencedirect.com/science/article/pii/S037843710300579X",
  acknowledgement = ack-nhfb,
  fjournal =     "Physica A. Statistical Mechanics and its
                 Applications",
  keywords =     "Zipf's Law",
}

@Book{Anastasi:2003:NFI,
  author =       "Joe Anastasi",
  title =        "The new forensics: investigating corporate fraud and
                 the theft of intellectual property",
  publisher =    pub-WILEY,
  address =      pub-WILEY:adr,
  pages =        "xiv + 270",
  year =         "2003",
  isbn =         "0-471-26994-8 (hardcover)",
  isbn-13 =      "978-0-471-26994-6 (hardcover)",
  lccn =         "HV8079.W47 A5 2003",
  bibdate =      "Tue Nov 22 11:42:36 MST 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 z3950.loc.gov:7090/Voyager",
  url =          "http://www.loc.gov/catdir/bios/wiley044/2003001697.html;
                 http://www.loc.gov/catdir/description/wiley037/2003001697.html;
                 http://www.loc.gov/catdir/toc/wiley031/2003001697.html",
  acknowledgement = ack-nhfb,
  remark =       "Brief mention of Benford's Law on pp. 184--185.",
  subject =      "white collar crime investigation; data processing;
                 case studies; fraud investigation; forensic accounting;
                 computer security",
}

@Article{Ausloos:2003:SIZ,
  author =       "M. Ausloos and Ph. Bronlet",
  title =        "Strategy for investments from {Zipf} law(s)",
  journal =      j-PHYSICA-A,
  volume =       "324",
  number =       "1--2",
  pages =        "30--37",
  day =          "1",
  month =        jun,
  year =         "2003",
  coden =        "PHYADX",
  doi =          "http://dx.doi.org/10.1016/S0378-4371(02)01845-9",
  issn =         "0378-4371 (print), 1873-2119 (electronic)",
  issn-l =       "0378-4371",
  mrclass =      "91B82",
  mrnumber =     "2030919",
  bibdate =      "Wed Feb 27 07:32:55 MST 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  note =         "International Econophysics Conference IEC2002 (Bali)",
  url =          "http://www.sciencedirect.com/science/article/pii/S0378437102018459",
  acknowledgement = ack-nhfb,
  fjournal =     "Physica A. Statistical Mechanics and its
                 Applications",
  keywords =     "Zipf's Law",
}

@Book{Baldi:2003:MIW,
  author =       "Pierre Baldi and Paolo Frasconi and Padhraic Smyth",
  title =        "Modeling the {Internet} and the {Web}: probabilistic
                 methods and algorithms",
  publisher =    pub-WILEY,
  address =      pub-WILEY:adr,
  pages =        "xix + 285",
  year =         "2003",
  isbn =         "0-470-86492-3 (e-book), 0-470-84906-1",
  isbn-13 =      "978-0-470-86492-0 (e-book), 978-0-470-84906-4",
  lccn =         "TK5105.875.I57 B35 2003eb",
  bibdate =      "Fri Jun 3 10:03:23 MDT 2011",
  bibsource =    "fsz3950.oclc.org:210/WorldCat;
                 http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 http://www.math.utah.edu/pub/tex/bib/pagerank.bib",
  acknowledgement = ack-nhfb,
  subject =      "Internet; Mathematical models; Telecommunication;
                 Traffic; World Wide Web; Cyberspace; Probabilities;
                 Computers; Web; General; Networking; Intranets and
                 Extranets",
  tableofcontents = "Mathematical Background \\
                 Probability and Learning from a Bayesian Perspective
                 \\
                 Parameter Estimation from Data \\
                 Basic principles \\
                 A simple die example \\
                 Mixture Models and the Expectation Maximization
                 Algorithm \\
                 Graphical Models \\
                 Bayesian networks \\
                 Belief propagation \\
                 Learning directed graphical models from data \\
                 Classification \\
                 Clustering \\
                 Power-Law Distributions \\
                 Scale-free properties (80/20 rule) \\
                 Applications to Languages: Zipf's and Heaps' Laws \\
                 Origin of power-law distributions and Fermi's model \\
                 Basic WWW Technologies \\
                 Web Documents \\
                 SGML and HTML \\
                 General structure of an HTML document \\
                 Links \\
                 Resource Identifiers: URI, url, and URN \\
                 Protocols \\
                 Reference models and TCP/IP \\
                 The domain name system \\
                 The Hypertext Transfer Protocol \\
                 Programming examples \\
                 Log Files \\
                 Search Engines \\
                 Coverage \\
                 Basic crawling \\
                 Web Graphs \\
                 Internet and Web Graphs \\
                 Power-law size \\
                 Power-law connectivity \\
                 Small-world networks \\
                 Power law of PageRank \\
                 The bow-tie structure \\
                 Generative Models for the Web Graph and Other Networks
                 \\
                 Web page growth \\
                 Lattice perturbation models: between order and disorder
                 \\
                 Preferential attachment models, or the rich get richer
                 \\
                 Copy models \\
                 PageRank models \\
                 Applications \\
                 Distributed search algorithms \\
                 Subgraph patterns and communities \\
                 Robustness and vulnerability \\
                 Notes and Additional Technical References \\
                 Text Analysis \\
                 Indexing \\
                 Compression techniques \\
                 Lexical Processing \\
                 Tokenization",
}

@TechReport{Berger:2003:BLP,
  author =       "Arno Berger",
  title =        "{Benford}'s law in power-like nonautonomous dynamical
                 systems",
  type =         "Preprint",
  institution =  "Vienna University of Technology",
  address =      "Vienna, Austria",
  year =         "2003",
  bibdate =      "Sat Feb 16 17:18:18 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
}

@Article{Canessa:2003:TAFa,
  author =       "Enrique Canessa",
  title =        "Theory of Analogous Force on Number Sets",
  journal =      "ArXiv e-prints",
  year =         "2003",
  bibdate =      "Mon Nov 21 06:56:01 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  url =          "http://arxiv.org/abs/cond-mat/0307703",
  abstract =     "A general statistical thermodynamic theory that
                 considers given sequences of $x$-integers to play the
                 role of particles of known type in an isolated elastic
                 system is proposed. By also considering some explicit
                 discrete probability distributions $p_x$ for natural
                 numbers, we claim that they lead to a better
                 understanding of probabilistic laws associated with
                 number theory. Sequences of numbers are treated as the
                 size measure of finite sets. By considering $p_x$ to
                 describe complex phenomena, the theory leads to derive
                 a distinct analogous force $f_x$ on number sets
                 proportional to $(\frac{\partial p_{x}}{\partial x}
                 )_{T}$ at an analogous system temperature $T$. In
                 particular, this yields to an understanding of the
                 uneven distribution of integers of random sets in terms
                 of analogous scale invariance and a screened inverse
                 square force acting on the significant digits. The
                 theory also allows to establish recursion relations to
                 predict sequences of Fibonacci numbers and to give an
                 answer to the interesting theoretical question of the
                 appearance of the Benford's law in Fibonacci numbers. A
                 possible relevance to prime numbers is also analyzed.",
  acknowledgement = ack-nhfb,
  remark =       "To appear in Phys. A.",
}

@Article{Canessa:2003:TAFb,
  author =       "Enrique Canessa",
  title =        "Theory of analogous force on number sets",
  journal =      j-PHYSICA-A,
  volume =       "328",
  number =       "1--2",
  pages =        "44--52",
  month =        oct,
  year =         "2003",
  coden =        "PHYADX",
  doi =          "http://dx.doi.org/10.1016/S0378-4371(03)00526-0",
  issn =         "0378-4371 (print), 1873-2119 (electronic)",
  issn-l =       "0378-4371",
  bibdate =      "Tue Nov 22 11:28:19 MST 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 http://www.sciencedirect.com/",
  url =          "http://www.sciencedirect.com/science/article/pii/S0378437103005260",
  abstract =     "A general statistical thermodynamic theory that
                 considers given sequences of $x$-integers to play the
                 role of particles of known type in an isolated elastic
                 system is proposed. By also considering some explicit
                 discrete probability distributions $p_x$ for natural
                 numbers, we claim that they lead to a better
                 understanding of probabilistic laws associated with
                 number theory. Sequences of numbers are treated as the
                 size measure of finite sets. By considering $p_x$ to
                 describe complex phenomena, the theory leads to derive
                 a distinct analogous force $f_x$ on number sets
                 proportional to $(\partial p_x/\partial x)T$ at an
                 analogous system temperature $T$. In particular, this
                 leads to an understanding of the uneven distribution of
                 integers of random sets in terms of analogous scale
                 invariance and a screened inverse square force acting
                 on the significant digits. The theory also allows to
                 establish recursion relations to predict sequences of
                 Fibonacci numbers and to give an answer to the
                 interesting theoretical question of the appearance of
                 the Benford's law in Fibonacci numbers. A possible
                 relevance to prime numbers is also analyzed.",
  acknowledgement = ack-nhfb,
  fjournal =     "Physica A: Statistical Mechanics and its
                 Applications",
  keywords =     "Benford's Law; Fibonacci numbers; prime numbers",
}

@Article{Engel:2003:BLE,
  author =       "Hans-Andreas Engel and Christoph Leuenberger",
  title =        "{Benford}'s law for exponential random variables",
  journal =      j-STAT-PROB-LETT,
  volume =       "63",
  number =       "4",
  pages =        "361--365",
  day =          "15",
  month =        jul,
  year =         "2003",
  coden =        "SPLTDC",
  doi =          "http://dx.doi.org/10.1016/S0167-7152(03)00101-9",
  issn =         "0167-7152 (print), 1879-2103 (electronic)",
  issn-l =       "0167-7152",
  mrclass =      "60E99 (60C05)",
  mrnumber =     "1996184 (2004d:60050)",
  mrreviewer =   "Ulrich M. Hirth",
  bibdate =      "Tue Nov 22 11:28:19 MST 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 http://www.sciencedirect.com/",
  url =          "http://www.sciencedirect.com/science/article/pii/S0167715203001019",
  acknowledgement = ack-nhfb,
  fjournal =     "Statistics \& Probability Letters",
  keywords =     "Benford's Law",
}

@Article{FerreriCancho:2003:LEO,
  author =       "Ramon {Ferrer i Cancho} and Ricard V. Sol{\'e}",
  title =        "Least effort and the origins of scaling in human
                 language",
  journal =      j-PROC-NATL-ACAD-SCI-USA,
  volume =       "100",
  number =       "3",
  pages =        "788--791",
  day =          "4",
  month =        feb,
  year =         "2003",
  coden =        "PNASA6",
  doi =          "http://dx.doi.org/10.1073/pnas.0335980100",
  issn =         "0027-8424 (print), 1091-6490 (electronic)",
  issn-l =       "0027-8424",
  bibdate =      "Tue Nov 15 09:44:47 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Proceedings of the National Academy of Sciences of the
                 United States of America",
  keywords =     "Zipf's Law",
  onlinedate =   "January 22, 2003",
}

@Article{Furusawa:2003:ZLG,
  author =       "Chikara Furusawa and Kunihiko Kaneko",
  title =        "{Zipf's Law} in Gene Expression",
  journal =      j-PHYS-REV-LET,
  volume =       "90",
  number =       "??",
  pages =        "088102",
  day =          "26",
  month =        feb,
  year =         "2003",
  coden =        "PRLTAO",
  doi =          "http://dx.doi.org/10.1103/PhysRevLett.90.088102",
  issn =         "0031-9007 (print), 1079-7114 (electronic), 1092-0145",
  issn-l =       "0031-9007",
  bibdate =      "Tue Feb 26 06:40:57 MST 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  url =          "http://link.aps.org/doi/10.1103/PhysRevLett.90.088102",
  acknowledgement = ack-nhfb,
  fjournal =     "Physical Review Letters",
  keywords =     "Zipf's Law",
}

@Article{Gabaix:2003:TPL,
  author =       "Xavier Gabaix and Parameswaran Gopikrishnan and
                 Vasiliki Plerou and H. Eugene Stanley",
  title =        "A theory of power-law distributions in financial
                 market fluctuations",
  journal =      j-NATURE,
  volume =       "423",
  number =       "6937",
  pages =        "267--270",
  day =          "15",
  month =        may,
  year =         "2003",
  coden =        "NATUAS",
  doi =          "http://dx.doi.org/10.1038/nature01624",
  issn =         "0028-0836 (print), 1476-4687 (electronic)",
  issn-l =       "0028-0836",
  bibdate =      "Wed Feb 27 06:45:03 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  url =          "http://www.nature.com/nature/journal/v423/n6937/full/nature01624.html",
  acknowledgement = ack-nhfb,
  fjournal =     "Nature",
  keywords =     "Zipf's Law",
}

@InProceedings{Grekos:2003:RSC,
  author =       "G. Grekos and R. Giuliano-Antonini",
  editor =       "????",
  booktitle =    "{Journ{\'e}es Arithm{\'e}tiques XXIII, Graz, July
                 6--12, 2003}",
  title =        "Regular sets and conditional density: an extension of
                 {Benford}'s law",
  publisher =    "????",
  address =      "????",
  pages =        "??--??",
  year =         "2003",
  isbn =         "????",
  isbn-13 =      "????",
  lccn =         "????",
  bibdate =      "Sat Feb 16 17:43:43 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
}

@Article{Hassan:2003:EDA,
  author =       "Bassam Hassan",
  title =        "Examining data accuracy and authenticity with leading
                 digit frequency analysis",
  journal =      "Industrial Management + Data Systems",
  volume =       "103",
  number =       "2",
  pages =        "121--125",
  month =        "????",
  year =         "2003",
  coden =        "MDSD8F",
  issn =         "0263-5577 (print), 1758-5783 (electronic)",
  issn-l =       "0263-5577",
  bibdate =      "Fri Nov 25 11:07:59 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
}

@Book{Havil:2003:GEE,
  author =       "Julian Havil",
  title =        "{Gamma}: Exploring {Euler}'s Constant",
  publisher =    pub-PRINCETON,
  address =      pub-PRINCETON:adr,
  pages =        "xxiii + 266",
  year =         "2003",
  isbn =         "0-691-09983-9",
  isbn-13 =      "978-0-691-09983-5",
  lccn =         "QA41 .H23 2003",
  bibdate =      "Thu Sep 25 16:52:46 2003",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 http://www.math.utah.edu/pub/tex/bib/master.bib",
  note =         "Benford's Law is the subject of Section 14.2, pages
                 145--155.",
  price =        "US\$29.95",
  url =          "http://www.loc.gov/catdir/description/prin031/2002192453.html",
  acknowledgement = ack-nhfb,
}

@Article{Hurlimann:2003:GBL,
  author =       "Werner H{\"u}rlimann",
  title =        "A generalized {Benford} law and its application",
  journal =      j-ADV-APPL-STAT,
  volume =       "3",
  number =       "3",
  pages =        "217--228",
  year =         "2003",
  coden =        "????",
  issn =         "0972-3617",
  issn-l =       "0972-3617",
  mrclass =      "11K31 (11B73)",
  mrnumber =     "2034405 (2004k:11125)",
  mrreviewer =   "Vydas {\v{C}}ekanavi{\v{c}}ius",
  bibdate =      "Sat Nov 12 09:13:23 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Advances and Applications in Statistics",
}

@Article{Ioannides:2003:ZLC,
  author =       "Yannis M. Ioannides and Henry G. Overman",
  title =        "{Zipf}'s law for cities: an empirical examination",
  journal =      j-REG-SCI-URBAN-ECON,
  volume =       "33",
  number =       "2",
  pages =        "127--137",
  day =          "1",
  month =        mar,
  year =         "2003",
  coden =        "RSUEDM",
  doi =          "http://dx.doi.org/10.1016/S0166-0462(02)00006-6",
  issn =         "0166-0462 (print), 1879-2308 (electronic)",
  issn-l =       "0166-0462",
  bibdate =      "Wed Feb 27 07:32:55 MST 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  url =          "http://www.sciencedirect.com/science/article/pii/S0166046202000066",
  acknowledgement = ack-nhfb,
  fjournal =     "Regional Science and Urban Economics",
  keywords =     "Zipf's Law",
}

@Article{Kreiner:2003:NBL,
  author =       "W. A. Kreiner",
  title =        "On the {Newcomb--Benford} law",
  journal =      j-Z-NATURFORSCH,
  volume =       "58a",
  number =       "11",
  pages =        "618--622",
  month =        "????",
  year =         "2003",
  coden =        "ZNTFA2",
  issn =         "0372-9516",
  issn-l =       "0372-9516",
  bibdate =      "Sat Feb 16 18:19:41 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  url =          "http://www.znaturforsch.com/aa/v58a/s58a0618.pdf",
  acknowledgement = ack-nhfb,
  fjournal =     "{Zeitschrift f{\"u}r Naturforschung}",
}

@InCollection{Kumar:2003:BLA,
  author =       "Kuldeep Kumar and Sukanto Bhattacharya",
  editor =       "Cheng-Few Lee",
  booktitle =    "Advances in Financial Planning and Forecasting",
  title =        "{Benford}'s law and its application in financial fraud
                 detection",
  volume =       "11",
  publisher =    pub-ELSEVIER,
  address =      pub-ELSEVIER:adr,
  pages =        "57--70",
  year =         "2003",
  isbn =         "0-7623-1016-2",
  isbn-13 =      "978-0-7623-1016-6",
  issn =         "1046-5847",
  lccn =         "????",
  bibdate =      "Wed Nov 23 16:45:49 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  bookpages =    "ix + 177",
}

@Article{Lanza:2003:FSP,
  author =       "Richard B. Lanza",
  title =        "Fear Not the Software: Proactively Detecting
                 Occupational Fraud Using Computer Audit Reports",
  journal =      "Fraud Magazine",
  volume =       "??",
  number =       "??",
  pages =        "??--??",
  month =        sep # "\slash " # feb,
  year =         "2003",
  issn =         "1553-6645",
  issn-l =       "1553-6645",
  bibdate =      "Sun Feb 17 08:14:47 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  url =          "http://www.fraud-magazine.com/article.aspx?id=4294967868",
  acknowledgement = ack-nhfb,
  fjournal =     "Fraud Magazine. {A} Publication of the Association of
                 Certified Fraud Examiners",
  keywords =     "Benford's Law",
}

@InProceedings{Manaris:2003:EMZ,
  author =       "Bill Manaris and Dallas Vaughan and Christopher Wagner
                 and Juan Romero and Robert B. Davis",
  title =        "Evolutionary Music and the {Zipf--Mandelbrot Law}:
                 Developing Fitness Functions for Pleasant Music",
  crossref =     "Raidl:2003:AEC",
  pages =        "522--534",
  year =         "2003",
  bibdate =      "Mon Feb 18 10:49:54 2013",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/m/mandelbrot-benoit.bib;
                 http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
}

@Article{McAllister:2003:ARE,
  author =       "James W. McAllister",
  title =        "Algorithmic randomness in empirical data",
  journal =      j-STUD-HIST-PHILOS-SCI,
  volume =       "34",
  number =       "3",
  pages =        "633--646",
  month =        sep,
  year =         "2003",
  coden =        "SHPSB5",
  doi =          "http://dx.doi.org/10.1016/S0039-3681(03)00047-5",
  issn =         "0039-3681 (print), 1879-2510 (electronic)",
  issn-l =       "0039-3681",
  bibdate =      "Mon Nov 7 12:11:57 MST 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 http://www.math.utah.edu/pub/tex/bib/shps-a.bib;
                 http://www.sciencedirect.com/science/journal/00393681",
  note =         "See replies
                 \cite{Twardy:2005:EDS,McAllister:2005:ACE}.",
  url =          "http://www.sciencedirect.com/science/article/pii/S0039368103000475",
  acknowledgement = ack-nhfb,
  fjournal =     "Studies in History and Philosophy of Science Part A",
}

@Article{Mitzenmacher:2003:BHG,
  author =       "Michael Mitzenmacher",
  title =        "A Brief History of Generative Models for Power Law and
                 Lognormal Distributions",
  journal =      j-INTERNET-MATH,
  volume =       "1",
  number =       "2",
  pages =        "226--251",
  month =        dec,
  year =         "2003",
  coden =        "????",
  doi =          "http://dx.doi.org/10.1080/15427951.2004.10129088",
  issn =         "1542-7951 (print), 1944-9488 (electronic)",
  issn-l =       "1542-7951",
  bibdate =      "Thu Nov 24 13:38:13 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  url =          "http://projecteuclid.org/euclid.im/1089229510;
                 http://www.eecs.harvard.edu/~michaelm/CS223/powerlaw.pdf;
                 http://www.tandfonline.com/toc/uinm20/1/2",
  acknowledgement = ack-nhfb,
  ajournal =     "Internet Math.",
  fjournal =     "Internet Mathematics",
  keywords =     "Fibonacci sequence; lognormal distribution; monkeys
                 typing randomly; Pareto distribution; power-law
                 distribution; Yule distribution; Zipf's Law",
  remark =       "This is a survey article with a six-page bibliography
                 of earlier work, and a clear description of the
                 differences between lognormal and power-law
                 distributions, which otherwise look similar on log-log
                 plots. Lognormal distributions have finite means and
                 moments, while power-law distributions may have
                 infinite means and/or moments, depending on the
                 exponent. The preprint at author's Web site (last url)
                 contains additional material on the acrimonious debate
                 between Beno{\^\i}t Mandelbrot and Herbert A. Simon
                 (see \cite{Mandelbrot:1959:NCS,Simon:1955:CSD}, and
                 other references in Mitzenmacher's paper) on the
                 derivation and modeling of Zipf's Law distributions.",
}

@PhdThesis{Muller:2003:AZP,
  author =       "Mathias M{\"u}ller",
  title =        "{Anwendungsm{\"o}glichkeiten der Ziffernanalyse in der
                 Pr{\"u}fungspraxis mit Schwerpunkt auf Benford's Law}.
                 ({German}) [Applications of the digit analysis in the
                 audit practice with a focus on {Benford's Law}]",
  type =         "{Diplomarbeit}",
  school =       "Wirtschaftsuniversit{\"a}t Wien",
  address =      "Wien, Austria",
  pages =        "v + 75",
  month =        "????",
  year =         "2003",
  bibdate =      "Sat Feb 16 18:44:50 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  url =          "http://permalink.obvsg.at/wuw/AC03895842",
  acknowledgement = ack-nhfb,
}

@Article{Naldi:2003:CIZ,
  author =       "M. Naldi",
  title =        "Concentration indices and {Zipf}'s law",
  journal =      j-ECONOM-LETT,
  volume =       "78",
  number =       "3",
  pages =        "329--334",
  month =        mar,
  year =         "2003",
  coden =        "ECLEDS",
  doi =          "http://dx.doi.org/10.1016/S0165-1765(02)00251-3",
  issn =         "0165-1765 (print), 1873-7374 (electronic)",
  issn-l =       "0165-1765",
  mrclass =      "91B82",
  mrnumber =     "1959355",
  bibdate =      "Wed Feb 27 07:32:55 MST 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  url =          "http://www.sciencedirect.com/science/article/pii/S0165176502002513",
  acknowledgement = ack-nhfb,
  fjournal =     "Economics Letters",
  keywords =     "Zipf's Law",
}

@Article{Nguyen:2003:DPL,
  author =       "H. T. Nguyen and V. Kreinovich and L. Longpre",
  title =        "Dirty pages of logarithm tables, lifetime of the
                 universe, and subjective (fuzzy) probabilities on
                 finite and infinite intervals",
  journal =      j-IEEE-TRANS-FUZZY-SYSTEMS,
  volume =       "1",
  pages =        "67--73",
  year =         "2003",
  coden =        "IEFSEV",
  doi =          "http://dx.doi.org/10.1109/FUZZ.2003.1209339",
  issn =         "1063-6706 (print), 1941-0034 (electronic)",
  issn-l =       "1063-6706",
  bibdate =      "Sat Feb 16 18:51:15 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  note =         "The 12th IEE International Conference on Fuzzy
                 Systems. FUZZ'03",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Fuzzy Systems",
  xxnote =       "Is this the listed journal, or a conference paper??",
}

@Article{Quick:2003:BLD,
  author =       "Reiner Quick and Matthias Wolz",
  title =        "{Benford's Law in deutschen Rechnungslegungsdaten}.
                 ({German}) [{Benford's Law} in {German} accounting
                 data]",
  journal =      "Betriebswirtschaftliche Forschung und Praxis",
  volume =       "55",
  number =       "2",
  pages =        "208--224",
  month =        "????",
  year =         "2003",
  coden =        "????",
  issn =         "0340-5370",
  issn-l =       "0340-5370",
  bibdate =      "Sat Dec 10 12:01:20 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  remark =       "Betriebswirtschaftliche Forschung und Praxis ==
                 Business Research and Practice.",
}

@Article{Reed:2003:PLI,
  author =       "William J. Reed",
  title =        "The {Pareto} law of incomes---an explanation and an
                 extension",
  journal =      j-PHYSICA-A,
  volume =       "319",
  number =       "1--4",
  pages =        "469--486",
  year =         "2003",
  coden =        "PHYADX",
  doi =          "http://dx.doi.org/10.1016/S0378-4371(02)01507-8",
  issn =         "0378-4371 (print), 1873-2119 (electronic)",
  issn-l =       "0378-4371",
  mrclass =      "91B70",
  mrnumber =     "1965596",
  bibdate =      "Mon Feb 18 17:05:26 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Physica A. Statistical Mechanics and its
                 Applications",
}

@Article{Rose:2003:TEF,
  author =       "Anna M. Rose and Jacob M. Rose",
  title =        "Turn {Excel} into a financial sleuth: an easy-to-use
                 digital analysis tool can red-flag irregularities",
  journal =      j-J-ACCOUNTANCY,
  volume =       "196",
  number =       "2",
  pages =        "58--??",
  month =        aug,
  year =         "2003",
  coden =        "JACYAD",
  issn =         "0021-8448 (print), 1945-0729 (electronic)",
  issn-l =       "0021-8448",
  bibdate =      "Sat Feb 16 19:07:02 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  url =          "http://www.journalofaccountancy.com/Issues/2003/Aug/TurnExcelIntoAFinancialSleuth",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Accountancy",
  journal-url =  "http://www.journalofaccountancy.com/",
}

@Article{Sinai:2003:SP,
  author =       "Ya. G. Sinai",
  title =        "Statistical $(3 x + 1)$ problem",
  journal =      j-COMM-PURE-APPL-MATH,
  volume =       "56",
  number =       "??",
  pages =        "1016--1028",
  month =        "????",
  year =         "2003",
  coden =        "CPAMAT, CPMAMV",
  issn =         "0010-3640 (print), 1097-0312 (electronic)",
  issn-l =       "0010-3640",
  bibdate =      "Mon Nov 21 07:52:19 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  note =         "Dedicated to the memory of J{\"u}rgen K. Moser.",
  acknowledgement = ack-nhfb,
  fjournal =     "Communications on Pure and Applied Mathematics (New
                 York)",
}

@InProceedings{Swanson:2003:DPF,
  author =       "David Swanson and Moon Jung Cho and John Eltinge",
  editor =       "????",
  booktitle =    "Proceedings of the Survey Research Section",
  title =        "Detecting possibly fraudulent or error-prone survey
                 data using {Benford's Law}",
  publisher =    "American Statistical Association",
  address =      "Washington, DC, USA",
  pages =        "4172--4177",
  year =         "2003",
  isbn =         "????",
  isbn-13 =      "????",
  lccn =         "????",
  bibdate =      "Wed Nov 16 10:21:39 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  url =          "http://www.amstat.org/sections/srms/proceedings/y2003/Files/JSM2003-000205.pdf.",
  acknowledgement = ack-nhfb,
}

@InCollection{Warren:2003:DLD,
  author =       "Henry S. Warren",
  title =        "The distribution of leading digits",
  crossref =     "Warren:2003:HD",
  chapter =      "15.3",
  pages =        "264--267",
  year =         "2003",
  bibdate =      "Fri Mar 16 08:02:56 2012",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 http://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@Article{Wu:2003:IPD,
  author =       "Shuo-Jye Wu and Chun-Tao Chang",
  title =        "Inference in the {Pareto} distribution based on
                 progressive {Type II} censoring with random removals",
  journal =      j-J-APPL-STAT,
  volume =       "30",
  number =       "2",
  pages =        "163--172",
  month =        "????",
  year =         "2003",
  coden =        "????",
  issn =         "0266-4763 (print), 1360-0532 (electronic)",
  issn-l =       "0266-4763",
  bibdate =      "Tue Dec 16 15:40:48 MST 2003",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 http://www.tandf.co.uk/journals/routledge/02664763.html",
  acknowledgement = ack-nhfb,
}

@Article{Wu:2003:PDC,
  author =       "Wei Biao Wu and Chinya V. Ravishankar",
  title =        "The performance of difference coding for sets and
                 relational tables",
  journal =      j-J-ACM,
  volume =       "50",
  number =       "5",
  pages =        "665--693",
  month =        sep,
  year =         "2003",
  coden =        "JACOAH",
  doi =          "http://doi.acm.org/10.1145/876638.876641",
  issn =         "0004-5411 (print), 1557-735X (electronic)",
  issn-l =       "0004-5411",
  bibdate =      "Mon Sep 8 17:55:23 MDT 2003",
  bibsource =    "http://portal.acm.org/; http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  abstract =     "We characterize the performance of difference coding
                 for compressing sets and database relations through an
                 analysis of the problem of estimating the number of
                 bits needed for storing the spacings between values in
                 sets of integers. We provide analytical expressions for
                 estimating the effectiveness of difference coding when
                 the elements of the sets or the attribute fields in
                 database tuples are drawn from the uniform and Zipf
                 distributions. We also examine the case where a
                 uniformly distributed domain is combined with a Zipf
                 distribution, and with an arbitrary distribution. We
                 present limit theorems for most cases, and
                 probabilistic convergence results in other cases. We
                 also examine the effects of attribute domain reordering
                 on the compression ratio. Our simulations show
                 excellent agreement with theory.",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of the Association for Computing Machinery",
}

@Article{Aoyama:2004:KDP,
  author =       "Hideaki Aoyama and Yoshi Fujiwara and Wataru Souma",
  title =        "Kinematics and dynamics of {Pareto--Zipf}'s law and
                 {Gibrat}'s law",
  journal =      j-PHYSICA-A,
  volume =       "344",
  number =       "1--2",
  pages =        "117--121",
  day =          "1",
  month =        dec,
  year =         "2004",
  coden =        "PHYADX",
  doi =          "http://dx.doi.org/10.1016/j.physa.2004.06.099",
  issn =         "0378-4371 (print), 1873-2119 (electronic)",
  issn-l =       "0378-4371",
  bibdate =      "Wed Feb 27 07:32:55 MST 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  url =          "http://www.sciencedirect.com/science/article/pii/S0378437104009185",
  acknowledgement = ack-nhfb,
  fjournal =     "Physica A. Statistical Mechanics and its
                 Applications",
  keywords =     "Zipf's Law",
}

@TechReport{Berger:2004:DDU,
  author =       "A. Berger",
  title =        "Dynamics and digits: on the ubiquity of {Benford's
                 Law}",
  type =         "Preprint",
  institution =  "Institute of Mechanics, Vienna University of
                 Technology",
  address =      "Vienna, Austria",
  pages =        "3",
  day =          "19",
  month =        nov,
  year =         "2004",
  bibdate =      "Sat Feb 16 17:20:58 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  url =          "http://www.math.leidenuniv.nl/~verduyn/EQUADIFF03/MS14/berger_eqdiff03.pdf",
  acknowledgement = ack-nhfb,
}

@Article{Challet:2004:BPD,
  author =       "Damien Challet and Andrea Lombardoni",
  title =        "Bug propagation and debugging in asymmetric software
                 structures",
  journal =      j-PHYS-REV-E,
  volume =       "70",
  number =       "4",
  pages =        "046109",
  month =        oct,
  year =         "2004",
  coden =        "PLEEE8",
  doi =          "http://dx.doi.org/10.1103/PhysRevE.70.046109",
  issn =         "1539-3755 (print), 1550-2376 (electronic)",
  issn-l =       "1539-3755",
  bibdate =      "Thu Feb 28 08:15:07 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  url =          "http://link.aps.org/doi/10.1103/PhysRevE.70.046109;
                 http://pre.aps.org/abstract/PRE/v70/i4/e046109",
  acknowledgement = ack-nhfb,
  fjournal =     "Physical Review E (Statistical physics, plasmas,
                 fluids, and related interdisciplinary topics)",
  issue =        "4",
  keywords =     "Linux; Unix; Zipf's Law",
  pagecount =    "5",
}

@Article{Chen:2004:MFM,
  author =       "Yanguang Chen and Yixing Zhou",
  title =        "Multi-fractal measures of city-size distributions
                 based on the three-parameter {Zipf} model",
  journal =      j-CHAOS-SOLITONS-FRACTALS,
  volume =       "22",
  number =       "4",
  pages =        "793--805",
  day =          "1",
  month =        nov,
  year =         "2004",
  coden =        "CSFOEH",
  doi =          "http://dx.doi.org/10.1016/j.chaos.2004.02.059",
  issn =         "0960-0779 (print), 1873-2887 (electronic)",
  issn-l =       "0960-0779",
  bibdate =      "Wed Feb 27 07:32:55 MST 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  url =          "http://www.sciencedirect.com/science/article/pii/S0960077904001031",
  acknowledgement = ack-nhfb,
  fjournal =     "Chaos, Solitons \& Fractals",
  keywords =     "Zipf's Law",
}

@Article{Cong:2004:WTP,
  author =       "Lin Cong and Zhipeng Li",
  title =        "On {Wilson}'s theorem and {Polignac} conjecture",
  journal =      "ArXiv e-prints",
  day =          "2",
  month =        aug,
  year =         "2004",
  bibdate =      "Mon Feb 18 07:03:53 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  url =          "http://arxiv.org/abs/math.NT/0408018",
  abstract =     "We introduce Wilson's theorem and Clement's result and
                 present a necessary and sufficient condition for $p$
                 and $p + 2 k$ to be primes where $k$ is a positive
                 integer. By using Simiov's Theorem, we derive an
                 improved version of Clement's result and
                 characterizations of Polignac twin primes which
                 parallel previous characterizations.",
  acknowledgement = ack-nhfb,
}

@TechReport{Diekmann:2004:DEE,
  author =       "Andreas Diekmann",
  title =        "{Datenf{\"a}lschung. Ergebnisse aus Experimenten mit
                 der Benford Verteilung}. ({German}) [{Data}
                 falsification. {Results} from experiments with the
                 {Benford} distribution]",
  type =         "Report",
  institution =  "ETH Z{\"u}rich",
  address =      "Z{\"u}rich, Switzerland",
  year =         "2004",
  bibdate =      "Fri Nov 18 12:09:49 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  language =     "German",
}

@TechReport{Diekmann:2004:FDU,
  author =       "Andreas Diekmann",
  title =        "Not the First Digit! {Using} {Benford's Law} to Detect
                 Fraudulent Scientific Data",
  type =         "Report",
  institution =  "ETH Z{\"u}rich",
  address =      "Z{\"u}rich, Switzerland",
  pages =        "26",
  month =        oct,
  year =         "2004",
  bibdate =      "Sat Dec 10 11:12:29 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  url =          "http://rfe.cs.oswego.edu/eps/othr/papers/0507/0507001.pdf",
  abstract =     "Digits in statistical data produced by natural or
                 social processes are often distributed in a manner
                 described by ``Benford's law''. Recently, a test
                 against this distribution was used to identify
                 fraudulent accounting data. This test is based on the
                 supposition that real data follow the Benford
                 distribution while fabricated data do not. Is it
                 possible to apply Benford tests to detect fabricated or
                 falsified scientific data as well as fraudulent
                 financial data? We approached this question in two
                 ways. First, we examined the use of the Benford
                 distribution as a standard by checking digit
                 frequencies in published statistical estimates. Second,
                 we conducted experiments in which subjects were asked
                 to fabricate statistical estimates (regression
                 coefficients). These experimental data were scrutinized
                 for possible deviations from the Benford distribution.
                 There were two main findings. First, the digits of the
                 published regression coefficients were approximately
                 Benford distributed. Second, the experimental results
                 yielded new insights into the strengths and weaknesses
                 of Benford tests. At least in the case of regression
                 coefficients, there were indications that checks for
                 digit-preference anomalies should focus less on the
                 first and more on the second and higher-digits",
  acknowledgement = ack-nhfb,
}

@Article{Durtschi:2004:EUB,
  author =       "C. Durtschi and W. Hillison and C. Pacini",
  title =        "The Effective Use of {Benford's Law} to Assist in
                 Detecting Fraud in Accounting Data",
  journal =      j-J-FORENSIC-ACCOUNT,
  volume =       "5",
  number =       "1",
  pages =        "17--34",
  month =        "????",
  year =         "2004",
  coden =        "????",
  issn =         "1524-5586",
  bibdate =      "Sun Nov 13 11:35:18 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Forensic Accounting",
}

@Article{Fontanari:2004:SNM,
  author =       "J. F. Fontanari and L. I. Perlovsky",
  title =        "Solvable null model for the distribution of word
                 frequencies",
  journal =      j-PHYS-REV-E,
  volume =       "70",
  number =       "??",
  pages =        "042901",
  day =          "25",
  month =        oct,
  year =         "2004",
  coden =        "PLEEE8",
  doi =          "http://dx.doi.org/10.1103/PhysRevE.70.042901",
  issn =         "1539-3755 (print), 1550-2376 (electronic)",
  issn-l =       "1539-3755",
  bibdate =      "Tue Feb 26 06:40:57 MST 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  url =          "http://link.aps.org/doi/10.1103/PhysRevE.70.042901",
  acknowledgement = ack-nhfb,
  fjournal =     "Physical Review E (Statistical physics, plasmas,
                 fluids, and related interdisciplinary topics)",
  keywords =     "Zipf's Law",
}

@Article{Fujiwara:2004:DPZ,
  author =       "Yoshi Fujiwara and Corrado {Di Guilmi} and Hideaki
                 Aoyama and Mauro Gallegati and Wataru Souma",
  title =        "Do {Pareto--Zipf} and {Gibrat} laws hold true? {An}
                 analysis with {European} firms",
  journal =      j-PHYSICA-A,
  volume =       "335",
  number =       "1--2",
  pages =        "197--216",
  day =          "1",
  month =        apr,
  year =         "2004",
  coden =        "PHYADX",
  doi =          "http://dx.doi.org/10.1016/j.physa.2003.12.015",
  issn =         "0378-4371 (print), 1873-2119 (electronic)",
  issn-l =       "0378-4371",
  bibdate =      "Wed Feb 27 07:32:55 MST 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  url =          "http://www.sciencedirect.com/science/article/pii/S0378437103011294",
  acknowledgement = ack-nhfb,
  fjournal =     "Physica A. Statistical Mechanics and its
                 Applications",
  keywords =     "Zipf's Law",
}

@Article{Fujiwara:2004:GPZ,
  author =       "Yoshi Fujiwara and Hideaki Aoyama and Corrado {Di
                 Guilmi} and Wataru Souma and Mauro Gallegati",
  title =        "{Gibrat} and {Pareto--Zipf} revisited with {European}
                 firms",
  journal =      j-PHYSICA-A,
  volume =       "344",
  number =       "1--2",
  pages =        "112--116",
  day =          "1",
  month =        dec,
  year =         "2004",
  coden =        "PHYADX",
  doi =          "http://dx.doi.org/10.1016/j.physa.2004.06.098",
  issn =         "0378-4371 (print), 1873-2119 (electronic)",
  issn-l =       "0378-4371",
  bibdate =      "Wed Feb 27 07:32:55 MST 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  url =          "http://www.sciencedirect.com/science/article/pii/S0378437104009173",
  acknowledgement = ack-nhfb,
  fjournal =     "Physica A. Statistical Mechanics and its
                 Applications",
  keywords =     "Zipf's Law",
}

@Article{Fujiwara:2004:ZLF,
  author =       "Yoshi Fujiwara",
  title =        "{Zipf} law in firms bankruptcy",
  journal =      j-PHYSICA-A,
  volume =       "337",
  number =       "1--2",
  pages =        "219--230",
  day =          "1",
  month =        jun,
  year =         "2004",
  coden =        "PHYADX",
  doi =          "http://dx.doi.org/10.1016/j.physa.2004.01.037",
  issn =         "0378-4371 (print), 1873-2119 (electronic)",
  issn-l =       "0378-4371",
  mrclass =      "91B38",
  mrnumber =     "2092316",
  bibdate =      "Wed Feb 27 07:32:55 MST 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  url =          "http://www.sciencedirect.com/science/article/pii/S0378437104001165",
  acknowledgement = ack-nhfb,
  fjournal =     "Physica A. Statistical Mechanics and its
                 Applications",
  keywords =     "Zipf's Law",
}

@Article{Geyer:2004:DFD,
  author =       "Christina Lynn Geyer and Patricia Pepple Williamson",
  title =        "Detecting fraud in data sets using {Benford's Law}",
  journal =      j-COMM-STAT,
  volume =       "B33",
  number =       "1",
  pages =        "229--246",
  month =        "????",
  year =         "2004",
  coden =        "CSSCDB",
  doi =          "http://dx.doi.org/10.1081/SAC-120028442",
  issn =         "0361-0918",
  issn-l =       "0361-0918",
  mrclass =      "62-07",
  mrnumber =     "2044866",
  bibdate =      "Sat Nov 12 09:13:23 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  ajournal =     "Comm. Statist. Simulation Comput.",
  fjournal =     "Communications in Statistics. Simulation and
                 Computation",
  keywords =     "Benford's Law; Law of Anomalous Numbers; Zipf's Law",
}

@Article{Hurlimann:2004:IPB,
  author =       "Werner H{\"u}rlimann",
  title =        "Integer powers and {Benford}'s law",
  journal =      j-INT-J-PURE-APPL-MATH,
  volume =       "11",
  number =       "1",
  pages =        "39--46",
  year =         "2004",
  coden =        "????",
  issn =         "1311-8080",
  issn-l =       "1314-3395",
  mrclass =      "62E15 (11B83 11K31 62E20)",
  mrnumber =     "2033394 (2005c:62030)",
  mrreviewer =   "I. N. Volodin",
  bibdate =      "Sat Nov 12 09:13:23 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Pure and Applied
                 Mathematics",
}

@Article{Ismail:2004:SES,
  author =       "Sanaa Isma{\"\i}l",
  title =        "A Simple Estimator for the Shape Parameter of the
                 {Pareto} Distribution with Economics and Medical
                 Applications",
  journal =      j-J-APPL-STAT,
  volume =       "31",
  number =       "1",
  pages =        "3--13",
  month =        jan,
  year =         "2004",
  coden =        "????",
  issn =         "0266-4763 (print), 1360-0532 (electronic)",
  issn-l =       "0266-4763",
  bibdate =      "Sat Dec 4 12:10:37 MST 2004",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 http://www.tandf.co.uk/journals/routledge/02664763.html",
  acknowledgement = ack-nhfb,
}

@Article{Janvresse:2004:UDB,
  author =       "{\'E}lise Janvresse and Thierry de la Rue",
  title =        "From uniform distributions to {Benford}'s law",
  journal =      j-J-APPL-PROBAB,
  volume =       "41",
  number =       "4",
  pages =        "1203--1210",
  year =         "2004",
  coden =        "JPRBAM",
  doi =          "http://dx.doi.org/10.1239/jap/1101840566",
  issn =         "0021-9002 (print), 1475-6072 (electronic)",
  issn-l =       "0021-9002",
  mrclass =      "60J20 (60J10)",
  mrnumber =     "2122815 (2006b:60161)",
  mrreviewer =   "Michael Drmota",
  bibdate =      "Sat Nov 12 09:13:23 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  url =          "http://projecteuclid.org/getRecord?id=euclid.jap/1101840566;
                 http://www.jstor.org/stable/4141393;
                 https://www.univ-rouen.fr/LMRS/Persopage/Delarue/Publis/PDF/uniform_distribution_to_Benford_law.pdf",
  abstract =     "We provide a new, probabilistic explanation for the
                 appearance of Benford's law in everyday-life numbers,
                 by showing that it arises naturally when we consider
                 mixtures of uniform distributions. Then we connect our
                 result to a result of Flehinger, for which we provide a
                 shorter proof, and the speed of convergence.",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Applied Probability",
}

@TechReport{Kollath-Romano:2004:DSD,
  author =       "P. Kollath-Romano",
  title =        "On the distribution of significant digits in numbers",
  type =         "Preprint",
  institution =  "Rensselaer Polytechnic Institute",
  address =      "Troy, NY, USA",
  year =         "2004",
  bibdate =      "Sat Feb 16 18:15:19 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
}

@InCollection{Kotz:2004:FDP,
  author =       "Samuel Kotz and N. Balakrishnan and Campbell B. Read
                 and Brani Vidakovic",
  editor =       "Samuel Kotz and N. Balakrishnan and Campbell B. Read
                 and Brani Vidakovic",
  booktitle =    "Encyclopedia of Statistical Sciences",
  title =        "First-Digit Problem",
  publisher =    pub-WILEY,
  address =      pub-WILEY:adr,
  edition =      "Second",
  pages =        "??--??",
  year =         "2004",
  doi =          "http://dx.doi.org/10.1002/0471667196.ess0783.pub2",
  isbn =         "0-471-66719-6 (e-book)",
  isbn-13 =      "978-0-471-66719-3 (e-book)",
  bibdate =      "Sun Feb 24 10:49:25 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Benford's Law",
}

@Article{Kristiansen:2004:BTZ,
  author =       "Kai de Lange Kristiansen and Geir Helgesen and Arne T.
                 Skjeltorp",
  title =        "Braid theory and {Zipf} relation used in dynamics of
                 magnetic microparticles",
  journal =      j-ECONOM-LETT,
  volume =       "30",
  number =       "1",
  pages =        "2387--2388",
  day =          "1",
  month =        may,
  year =         "2004",
  coden =        "ECLEDS",
  doi =          "http://dx.doi.org/10.1016/j.jmmm.2003.12.1288",
  issn =         "0165-1765 (print), 1873-7374 (electronic)",
  issn-l =       "0165-1765",
  bibdate =      "Wed Feb 27 07:32:55 MST 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  url =          "http://www.sciencedirect.com/science/article/pii/S0304885303019127",
  acknowledgement = ack-nhfb,
  fjournal =     "Economics Letters",
  keywords =     "Zipf's Law",
}

@Article{Kristiansen:2004:EOZ,
  author =       "Kai de Lange Kristiansen and Geir Helgesen and Arne T.
                 Skjeltorp",
  title =        "Experimental observation of {Zipf--Mandelbrot}
                 relation",
  journal =      j-PHYSICA-A,
  volume =       "335",
  number =       "3--4",
  pages =        "413--420",
  day =          "15",
  month =        apr,
  year =         "2004",
  coden =        "PHYADX",
  doi =          "http://dx.doi.org/10.1016/j.physa.2003.12.024",
  issn =         "0378-4371 (print), 1873-2119 (electronic)",
  issn-l =       "0378-4371",
  mrclass =      "82D10 (76T99 82-05)",
  mrnumber =     "2044153",
  bibdate =      "Wed Feb 27 07:32:55 MST 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  url =          "http://www.sciencedirect.com/science/article/pii/S0378437103011804",
  acknowledgement = ack-nhfb,
  fjournal =     "Physica A. Statistical Mechanics and its
                 Applications",
  keywords =     "Zipf's Law",
}

@Article{Kulikova:2004:OSS,
  author =       "A. A. Kulikova and Yu. V. Prokhorov",
  title =        "One-sided stable distributions and {Benford}'s law",
  journal =      "Teor. Veroyatn. Primen.",
  volume =       "49",
  number =       "1",
  pages =        "178--184",
  year =         "2004",
  coden =        "????",
  doi =          "http://dx.doi.org/10.1137/S0040585X97980944",
  issn =         "0040-361X",
  issn-l =       "0040-361X",
  mrclass =      "60E07 (60F05)",
  mrnumber =     "2141338 (2005m:60028)",
  mrreviewer =   "S{\'a}ndor Cs{\"o}rg{\H{o}}",
  bibdate =      "Sat Nov 12 09:13:23 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Rossi{\u\i}skaya Akademiya Nauk. Teoriya
                 Veroyatnoste{\u\i} i ee Primeneniya",
}

@Article{Lanza:2004:CBS,
  author =       "Richard B. Lanza",
  title =        "Comparing Best Software for Fraud Examinations: Fraud
                 Data Interrogation Tools",
  journal =      "Fraud Magazine",
  volume =       "??",
  number =       "??",
  pages =        "??--??",
  month =        nov # "\slash" # dec,
  year =         "2004",
  issn =         "1553-6645",
  issn-l =       "1553-6645",
  bibdate =      "Sun Feb 17 08:17:02 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  url =          "http://www.fraud-magazine.com/article.aspx?id=4294967837",
  acknowledgement = ack-nhfb,
  fjournal =     "Fraud Magazine. {A} Publication of the Association of
                 Certified Fraud Examiners",
  keywords =     "Benford's Law",
}

@Article{Li:2004:DBL,
  author =       "Zhi-peng Li and Lin Cong and Hua-jia Wang",
  title =        "Discussion on {Benford's Law} and its Application",
  journal =      "ArXiv e-prints",
  pages =        "1--13",
  year =         "2004",
  coden =        "????",
  issn =         "????",
  bibdate =      "Mon Nov 14 16:17:04 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  url =          "http://adsabs.harvard.edu/abs/2004math......8057L;
                 http://arxiv.org/abs/math/0408057",
  abstract =     "The probability that a number in many naturally
                 occurring tables of numerical data has first
                 significant digit $d$ is predicted by Benford's Law
                 ${\rm Prob} (d) = \log_{10} (1 + {\displaystyle{1\over
                 d}}), d = 1, 2, \ldots, 9$. Illustrations of Benford's
                 Law from both theoretical and real-life sources on both
                 science and social science areas are shown in detail
                 with some novel ideas and generalizations developed
                 solely by the authors of this paper. Three tests,
                 Chi-Square test, total variation distance, and maximum
                 deviations are adopted to examine the fitness of the
                 datasets to Benford's distribution. Finally,
                 applications of Benford's Law are summarized and
                 explored to reveal the power of this mathematical
                 principle.",
  acknowledgement = ack-nhfb,
  archiveprefix = "arXiv",
  eprint =       "math/0408057",
}

@Article{Lindsay:2004:DFD,
  author =       "D. H. Lindsay and P. S. Foote and A. Campbell and D.
                 R. Reilly",
  title =        "Detecting fraud in the data using automatic
                 intervention detection",
  journal =      "Fraud Magazine",
  volume =       "??",
  number =       "??",
  pages =        "??--??",
  month =        jan # "\slash " # feb,
  year =         "2004",
  issn =         "1553-6645",
  issn-l =       "1553-6645",
  bibdate =      "Sat Feb 16 18:32:22 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Fraud Magazine. {A} Publication of the Association of
                 Certified Fraud Examiners",
}

@TechReport{Miller:2004:STB,
  author =       "Steven J. Miller",
  title =        "Some thoughts on {Benford}'s law",
  type =         "Preprint",
  institution =  "Williams College",
  address =      "Williamstown, MA 01267 USA",
  year =         "2004",
  bibdate =      "Sat Feb 16 18:43:46 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  url =          "http://www.williams.edu/go/math/sjmiller/public_html/BrownClasses/1/BenfordTreatise.pdf",
  acknowledgement = ack-nhfb,
  remark =       "url not found on 17 February 2013; perhaps in ReCALL
                 2004 proceedings",
}

@Article{Molchanov:2004:BEL,
  author =       "Stanislav Molchanov and Xian Wang",
  title =        "On the {Benford}'s empirical law",
  journal =      "Random Oper. Stochastic Equations",
  volume =       "12",
  number =       "3",
  pages =        "201--210",
  year =         "2004",
  coden =        "????",
  doi =          "http://dx.doi.org/10.1163/1569397042222495",
  issn =         "0926-6364 (print), 1569-397X (electronic)",
  issn-l =       "0926-6364",
  mrclass =      "11K16 (11B39 60B15)",
  mrnumber =     "2084074 (2005h:11162)",
  mrreviewer =   "A. N. Philippou",
  bibdate =      "Sat Nov 12 09:13:23 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Random Operators and Stochastic Equations",
}

@Article{Nabeshima:2004:ZLP,
  author =       "Terutaka Nabeshima and Yukio-Pegio Gunji",
  title =        "{Zipf}'s law in phonograms and {Weibull} distribution
                 in ideograms: comparison of {English} with {Japanese}",
  journal =      j-BIOSYSTEMS,
  volume =       "73",
  number =       "2",
  pages =        "131--139",
  day =          "20",
  month =        feb,
  year =         "2004",
  coden =        "BSYMBO",
  doi =          "http://dx.doi.org/10.1016/j.biosystems.2003.11.002",
  issn =         "0303-2647 (print), 1872-8324 (electronic)",
  issn-l =       "0303-2647",
  bibdate =      "Wed Feb 27 07:32:55 MST 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  url =          "http://www.sciencedirect.com/science/article/pii/S0303264703002260",
  acknowledgement = ack-nhfb,
  fjournal =     "Biosystems (A6E)",
  keywords =     "Zipf's Law",
}

@InProceedings{Pericchi:2004:LNB,
  author =       "Luis R{\'a}ul Pericchi and David Torres",
  editor =       "????",
  booktitle =    "{Third Universidad Simon Bolivar Seminar on
                 Statistical Analyses of the Venezuelan Recall
                 Referendum}",
  title =        "La {Ley de Newcomb--Benford} y sus aplicaciones al
                 Referendum Revocatorio en {Venezuela}. ({Spanish}) [The
                 {Newcomb--Benford Law} and its applications to the
                 recall referendum in {Venezuela}]",
  publisher =    "????",
  address =      "????",
  pages =        "1--7",
  day =          "1",
  month =        oct,
  year =         "2004",
  bibdate =      "Fri Feb 15 18:25:14 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  note =         "Reporte T{\'e}cnico no-definitivo 2a. Presented on
                 September 23, 2004.",
  url =          "http://esdata.info/pdf/pericchi-torres.pdf;
                 https://sites.google.com/a/upr.edu/probability-and-statistics/home/techical-reports",
  acknowledgement = ack-nhfb,
  language =     "Spanish",
}

@TechReport{Posch:2004:BBH,
  author =       "Peter N. Posch",
  title =        "{Benford} or not-{Benford}? {How} to test for the
                 first digit law",
  type =         "Working paper.",
  institution =  "Department of Finance, University of Ulm",
  address =      "Ulm, Germany",
  year =         "2004",
  bibdate =      "Sat Feb 16 19:05:45 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
}

@TechReport{Posch:2004:SSD,
  author =       "Peter N. Posch",
  title =        "A survey on sequences and distribution functions
                 satisfying {Benford}'s law",
  type =         "Working paper.",
  institution =  "Department of Finance, University of Ulm",
  address =      "Ulm, Germany",
  day =          "25",
  month =        oct,
  year =         "2004",
  bibdate =      "Sat Feb 16 19:05:45 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  url =          "http://www.posch.org/paper/posch_benforddist.pdf",
  acknowledgement = ack-nhfb,
}

@TechReport{Posch:2004:ZFB,
  author =       "Peter N. Posch",
  title =        "{Ziffernanalyse in der F{\"a}lschungsaufsp{\"u}rung.
                 Benford's Gesetz und Steuererkl{\"a}rungen in Theorie
                 und Praxis}. ({German}) [Digit analysis in fake
                 tracing. {Benford's Law} and tax returns in theory and
                 practice]",
  type =         "Arbeitspapier",
  institution =  "Abteilung Finanzwirtschaft, University Ulm",
  address =      "Ulm, Germany",
  month =        oct,
  year =         "2004",
  bibdate =      "Sat Feb 16 19:03:27 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  language =     "German",
}

@Article{Pustet:2004:ZHH,
  author =       "Regina Pustet",
  title =        "{Zipf} and his heirs",
  journal =      j-LANG-SCI,
  volume =       "26",
  number =       "1",
  pages =        "1--25",
  day =          "1",
  month =        jan,
  year =         "2004",
  coden =        "????",
  doi =          "http://dx.doi.org/10.1016/S0388-0001(03)00018-4",
  issn =         "0388-0001 (print), 1873-5746 (electronic)",
  issn-l =       "0388-0001",
  bibdate =      "Wed Feb 27 07:32:55 MST 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 http://www.sciencedirect.com/",
  url =          "http://www.sciencedirect.com/science/article/pii/S0388000103000184",
  acknowledgement = ack-nhfb,
  fjournal =     "Language Sciences",
  journal-url =  "http://www.sciencedirect.com/science/journal/03880001",
  keywords =     "Benford's Law; George Kingsley Zipf; Zipf's Law",
}

@Article{Rawlings:2004:EBP,
  author =       "Philip K. Rawlings and David Reguera and Howard
                 Reiss",
  title =        "Entropic basis of the {Pareto} law",
  journal =      j-PHYSICA-A,
  volume =       "343",
  number =       "1--4",
  pages =        "643--652",
  year =         "2004",
  coden =        "PHYADX",
  doi =          "http://dx.doi.org/10.1016/j.physa.2004.06.152",
  issn =         "0378-4371 (print), 1873-2119 (electronic)",
  issn-l =       "0378-4371",
  mrclass =      "91B26 (91B82)",
  mrnumber =     "2094418 (2005e:91065)",
  bibdate =      "Mon Feb 18 17:05:26 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Physica A. Statistical Mechanics and its
                 Applications",
}

@Article{Rodriguez:2004:FSD,
  author =       "Ricardo J. Rodriguez",
  title =        "First Significant Digit Patterns From Mixtures of
                 Uniform Distributions",
  journal =      j-AMER-STAT,
  volume =       "58",
  number =       "1",
  pages =        "64--71",
  month =        feb,
  year =         "2004",
  coden =        "ASTAAJ",
  doi =          "http://dx.doi.org/10.1198/0003130042782",
  issn =         "0003-1305 (print), 1537-2731 (electronic)",
  issn-l =       "0003-1305",
  bibdate =      "Fri Feb 20 06:14:28 MST 2004",
  bibsource =    "http://www.amstat.org/publications/tas/;
                 http://www.math.utah.edu/pub/tex/bib/amstat2000.bib;
                 http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  url =          "http://oberon.ingentaselect.com/cgi-bin/linker?ini=asa&reqidx=/cw/asa/00031305/v58n1/s13/p64",
  acknowledgement = ack-nhfb,
  fjournal =     "The American Statistician",
  keywords =     "Benford's Law",
}

@TechReport{Saville:2004:SWN,
  author =       "A. Saville",
  title =        "Sorry, wrong number. {How} accounting data are wrong
                 and how the numbers can be fixed",
  type =         "Preprint",
  institution =  "????",
  address =      "????",
  month =        "????",
  year =         "2004",
  bibdate =      "Sat Feb 16 19:11:00 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
}

@Article{Sigurd:2004:WLS,
  author =       "Bengt Sigurd and Mats Eeg-Olofsson and Joost {Van
                 Weijer}",
  title =        "Word length, sentence length and frequency --- {Zipf}
                 revisited",
  journal =      j-STUD-LINGUISTICA,
  volume =       "58",
  number =       "1",
  pages =        "37--52",
  year =         "2004",
  doi =          "http://dx.doi.org/10.1111/j.0039-3193.2004.00109.x",
  issn =         "0039-3193 (print), 1467-9582 (electronic)",
  issn-l =       "0039-3193",
  bibdate =      "Mon Feb 25 06:13:56 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Studia Linguistica",
}

@Article{Skousen:2004:AUP,
  author =       "Christopher J. Skousen and Liming Guan and T. Sterling
                 Wetzel",
  title =        "Anomalies and Unusual Patterns in Reported Earnings:
                 {Japanese} Managers Round Earnings",
  journal =      j-J-INT-FINANC-MANAG-ACCOUNT,
  volume =       "15",
  number =       "3",
  pages =        "212--234",
  month =        oct,
  year =         "2004",
  coden =        "????",
  doi =          "http://dx.doi.org/10.1111/j.1467-646X.2004.00108.x",
  issn =         "0954-1314 (print), 1467-646X (electronic)",
  issn-l =       "0954-1314",
  bibdate =      "Fri Nov 25 11:11:38 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of International Financial Management and
                 Accounting",
}

@Book{Tijms:2004:UPC,
  author =       "Henk C. Tijms",
  title =        "Understanding probability: chance rules in everyday
                 life",
  publisher =    pub-CAMBRIDGE,
  address =      pub-CAMBRIDGE:adr,
  pages =        "x + 380",
  year =         "2004",
  isbn =         "0-521-83329-9 (hardcover), 0-521-54036-4 (paperback)",
  isbn-13 =      "978-0-521-83329-5 (hardcover), 978-0-521-54036-0
                 (paperback)",
  lccn =         "QA273 .T48 2004",
  bibdate =      "Mon Feb 18 06:48:08 MST 2013",
  bibsource =    "fsz3950.oclc.org:210/WorldCat;
                 http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Benford's Law",
  subject =      "Probabilities; Mathematical analysis; Chance;
                 Wahrscheinlichkeit; (Math.); Gesamtdarstellung",
}

@Article{Vanichpun:2004:OCU,
  author =       "Sarut Vanichpun and Armand M. Makowski",
  title =        "The output of a cache under the independent reference
                 model: where did the locality of reference go?",
  journal =      j-SIGMETRICS,
  volume =       "32",
  number =       "1",
  pages =        "295--306",
  month =        jun,
  year =         "2004",
  coden =        "????",
  doi =          "http://doi.acm.org/10.1145/1012888.1005722",
  issn =         "0163-5999 (print), 1557-9484 (electronic)",
  issn-l =       "0163-5999",
  bibdate =      "Fri Jun 27 09:21:18 MDT 2008",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 http://www.math.utah.edu/pub/tex/bib/sigmetrics.bib",
  abstract =     "We consider a cache operating under a demand-driven
                 replacement policy when document requests are modeled
                 according to the Independent Reference Model (IRM). We
                 characterize the popularity pmf of the stream of misses
                 from the cache, the so-called output of the cache, for
                 a large class of demand-driven cache replacement
                 policies. We measure strength of locality of reference
                 in a stream of requests through the skewness of its
                 popularity distribution. Using the notion of
                 majorization to capture this degree of skewness, we
                 show that for the policy $A_0$ and the random policy,
                 the output always has less locality of reference than
                 the input. However, we show by counterexamples that
                 this is not always the case under the LRU and CLIMB
                 policies when the input is selected according to a
                 Zipf-like pmf. In that case, conjectures are offered
                 (and supported by simulations) as to when LRU or CLIMB
                 caching indeed reduces locality of reference.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM SIGMETRICS Performance Evaluation Review",
  keywords =     "locality of reference; majorization; output of a
                 cache; popularity",
}

@Article{Anonymous:2005:UZL,
  author =       "Anonymous",
  title =        "The use of {Zipf}'s law in animal communication
                 analysis",
  journal =      j-ANIM-BEHAV,
  volume =       "69",
  number =       "1",
  pages =        "??--??",
  day =          "20",
  month =        jan,
  year =         "2005",
  coden =        "ANBEA8",
  doi =          "http://dx.doi.org/10.1016/j.anbehav.2004.08.004",
  issn =         "0003-3472 (print), 1095-8282 (electronic)",
  issn-l =       "0003-3472",
  bibdate =      "Wed Feb 27 07:32:55 MST 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  url =          "http://www.sciencedirect.com/science/article/pii/S0003347204003471",
  acknowledgement = ack-nhfb,
  fjournal =     "Animal Behaviour",
  journal-url =  "http://www.sciencedirect.com/science/journal/00033472",
  keywords =     "Zipf's Law",
}

@Article{Antonini:2005:RSC,
  author =       "Rita Giuliano Antonini and Georges Grekos",
  title =        "Regular sets and conditional density: an extension of
                 {Benford}'s law",
  journal =      j-COLLOQ-MATH,
  volume =       "103",
  number =       "2",
  pages =        "173--192",
  year =         "2005",
  coden =        "CQMAAQ",
  doi =          "http://dx.doi.org/10.4064/cm103-2-3",
  issn =         "0010-1354 (print), 1730-6302 (electronic)",
  issn-l =       "0010-1354",
  mrclass =      "11B05 (11K99)",
  mrnumber =     "2197847 (2006j:11012)",
  mrreviewer =   "Radhakrishnan Nair",
  bibdate =      "Sat Nov 12 09:13:23 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  zmnumber =     "1092.11009",
  acknowledgement = ack-nhfb,
  fjournal =     "Colloquium Mathematicum",
  keywords =     "asymptotic density; Benford's law; conditional
                 density; first digit problem; logarithmic density;
                 regular set; regular varying function",
  ZMclass =      "11B05 (Topology etc. of sets of numbers); 11K99
                 (Probabilistic theory)",
}

@Article{Berger:2005:BLP,
  author =       "Arno Berger",
  title =        "{Benford}'s law in power-like dynamical systems",
  journal =      j-STOCH-DYNAM,
  volume =       "5",
  number =       "4",
  pages =        "587--607",
  year =         "2005",
  coden =        "????",
  doi =          "http://dx.doi.org/10.1142/S0219493705001602",
  issn =         "0219-4937",
  issn-l =       "0219-4937",
  mrclass =      "37B55 (11K06 37A50 37E05)",
  mrnumber =     "2185507 (2008i:37029)",
  mrreviewer =   "Peter Raith",
  bibdate =      "Sat Nov 12 09:13:23 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  ajournal =     "Stoch. Dyn.",
  fjournal =     "Stochastics and Dynamics",
}

@InCollection{Berger:2005:DDU,
  author =       "A. Berger",
  booktitle =    "{EQUADIFF} 2003",
  title =        "Dynamics and digits: on the ubiquity of {Benford}'s
                 law",
  publisher =    "World Sci. Publ., Hackensack, NJ",
  pages =        "693--695",
  year =         "2005",
  doi =          "http://dx.doi.org/10.1142/9789812702067_0115",
  mrclass =      "37A45 (11K55)",
  mrnumber =     "2185113",
  bibdate =      "Sat Nov 12 09:13:23 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
}

@Article{Berger:2005:MDD,
  author =       "Arno Berger",
  title =        "Multi-dimensional dynamical systems and {Benford}'s
                 law",
  journal =      j-DISCRETE-CONTIN-DYN-SYST,
  volume =       "13",
  number =       "1",
  pages =        "219--237",
  year =         "2005",
  coden =        "????",
  doi =          "http://dx.doi.org/10.3934/dcds.2005.13.219",
  issn =         "1078-0947 (print), 1553-5231 (electronic)",
  issn-l =       "1078-0947",
  mrclass =      "37A45 (11K36 28D05 37A50 60F05)",
  mrnumber =     "2128801 (2005m:37016)",
  mrreviewer =   "Reinhard Winkler",
  bibdate =      "Sat Nov 12 09:13:23 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Discrete and Continuous Dynamical Systems. Series A",
}

@Article{Berger:2005:ODD,
  author =       "Arno Berger and Leonid A. Bunimovich and Theodore P.
                 Hill",
  title =        "One-dimensional dynamical systems and {Benford}'s
                 law",
  journal =      j-TRANS-AM-MATH-SOC,
  volume =       "357",
  number =       "1",
  pages =        "197--219",
  year =         "2005",
  coden =        "TAMTAM",
  doi =          "http://dx.doi.org/10.1090/S0002-9947-04-03455-5",
  issn =         "0002-9947 (print), 1088-6850 (electronic)",
  issn-l =       "0002-9947",
  mrclass =      "37A45 (11K06 37A50 37E05 60F05 82B05)",
  mrnumber =     "2098092 (2005m:37017)",
  mrreviewer =   "Peter Raith",
  bibdate =      "Sat Nov 12 09:13:23 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Transactions of the American Mathematical Society",
}

@Article{Bhattacharya:2005:CPA,
  author =       "Sukanto Bhattacharya and Kuldeep Kumar and Florentin
                 Smarandache",
  title =        "Conditional probability of actually detecting a
                 financial fraud --- a neutrosophic extension to
                 {Benford}'s law",
  journal =      "International Journal of Applied Mathematics",
  volume =       "17",
  number =       "1",
  pages =        "7--14",
  year =         "2005",
  coden =        "????",
  issn =         "1311-1728",
  mrclass =      "62G10 (91B28)",
  mrnumber =     "2170667",
  bibdate =      "Sat Nov 12 09:13:23 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  url =          "http://arxiv.org/abs/math/0504520",
  abstract =     "This study actually draws from and builds on an
                 earlier paper (Kumar and Bhattacharya, 2002). Here we
                 have basically added a neutrosophic dimension to the
                 problem of determining the conditional probability that
                 a financial fraud has been actually committed, given
                 that no Type I error occurred while rejecting the null
                 hypothesis H0: The observed first-digit frequencies
                 approximate a Benford distribution; and accepting the
                 alternative hypothesis H1: The observed first-digit
                 frequencies do not approximate a Benford distribution.
                 We have also suggested a conceptual model to implement
                 such a neutrosophic fraud detection system.",
  acknowledgement = ack-nhfb,
  ajournal =     "Int. J. Appl. Math.",
  fjournal =     "International Journal of Applied Mathematics",
}

@Article{Bhattacharyya:2005:COP,
  author =       "P. Bhattacharyya and A. Chatterjee and B. K.
                 Chakrabarti",
  title =        "A common origin of the power law distributions in
                 models of market and earthquake",
  journal =      "ArXiv e-prints",
  year =         "2005",
  bibdate =      "Sat Feb 16 17:25:18 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  url =          "http://arxiv.org/abs/physics/0510038",
  acknowledgement = ack-nhfb,
}

@Article{Brown:2005:BLS,
  author =       "Richard J. C. Brown",
  title =        "{Benford}'s law and the screening of analytical data:
                 the case of pollutant concentrations in ambient air",
  journal =      j-ANALYST,
  volume =       "130",
  number =       "9",
  pages =        "1280--1285",
  month =        "????",
  year =         "2005",
  coden =        "ANALAO",
  doi =          "http://dx.doi.org/10.1039/B504462F",
  issn =         "0003-2654 (print), 1364-5528 (electronic)",
  issn-l =       "0003-2654",
  bibdate =      "Sat Feb 16 17:27:51 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  url =          "http://www.ncbi.nlm.nih.gov/pubmed/16096674",
  acknowledgement = ack-nhfb,
  fjournal =     "The Analyst",
}

@Article{Campi:2005:ZLM,
  author =       "X. Campi and H. Krivine",
  title =        "{Zipf}'s law in multifragmentation",
  journal =      j-PHYS-REV-C,
  volume =       "72",
  number =       "??",
  pages =        "057602",
  day =          "30",
  month =        nov,
  year =         "2005",
  coden =        "PRVCAN",
  doi =          "http://dx.doi.org/10.1103/PhysRevC.72.057602",
  issn =         "0556-2813 (print), 1089-490X, 1538-4497",
  issn-l =       "0556-2813",
  bibdate =      "Tue Feb 26 06:40:57 MST 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  url =          "http://link.aps.org/doi/10.1103/PhysRevC.72.057602",
  acknowledgement = ack-nhfb,
  fjournal =     "Physical Review C (Nuclear Physics)",
  keywords =     "Zipf's Law",
}

@TechReport{Ciofalo:2005:EBF,
  author =       "Michele Ciofalo",
  title =        "Entropy, {Benford}'s first digit law, and the
                 distribution of everything",
  type =         "Report",
  institution =  "Dipartimento di Ingegneria Nucleare, Universit{\`a}
                 degli Studi di Palermo",
  address =      "Palermo, Italy",
  pages =        "34",
  year =         "2005",
  bibdate =      "Sun Feb 17 08:23:55 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  url =          "http://www.din.unipa.it/Struttura/Personale/Profili/ciofalo_allegati/Paper_Benford.pdf",
  acknowledgement = ack-nhfb,
}

@Article{Cleary:2005:ADA,
  author =       "Richard Cleary and Jay C. Thibodeau",
  title =        "Applying Digital Analysis Using {Benford's Law} to
                 Detect Fraud: The Dangers of Type {I} Errors",
  journal =      j-AUDITING,
  volume =       "24",
  number =       "1",
  pages =        "77--81",
  month =        may,
  year =         "2005",
  coden =        "????",
  doi =          "http://dx.doi.org/10.2308/aud.2005.24.1.77",
  issn =         "0278-0380 (print), 1558-7991 (electronic)",
  issn-l =       "0278-0380",
  bibdate =      "Tue Nov 15 09:17:46 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  url =          "http://aaapubs.org/loi/ajpt;
                 http://link.aip.org/link/AJPTXX/v24/i1/p77/s1",
  acknowledgement = ack-nhfb,
  fjournal =     "Auditing: A Journal of Practice \& Theory",
}

@Article{Cohen:2005:PCL,
  author =       "Edith Cohen and Carsten Lund",
  title =        "Packet classification in large {ISPs}: design and
                 evaluation of decision tree classifiers",
  journal =      j-SIGMETRICS,
  volume =       "33",
  number =       "1",
  pages =        "73--84",
  month =        jun,
  year =         "2005",
  coden =        "????",
  doi =          "http://doi.acm.org/10.1145/1064212.1064222",
  issn =         "0163-5999 (print), 1557-9484 (electronic)",
  issn-l =       "0163-5999",
  bibdate =      "Fri Jun 27 09:21:27 MDT 2008",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 http://www.math.utah.edu/pub/tex/bib/sigmetrics.bib",
  abstract =     "Packet classification, although extensively studied,
                 is an evolving problem. Growing and changing needs
                 necessitate the use of larger filters with more complex
                 rules. The increased complexity and size pose
                 implementation challenges on current hardware solutions
                 and drive the development of software classifiers, in
                 particular, decision-tree based classifiers. Important
                 performance measures for these classifiers are time and
                 memory due to required high throughput and use of
                 limited fast memory. We analyze Tier 1 ISP data that
                 includes filters and corresponding traffic from over a
                 hundred edge routers and thousands of interfaces. We
                 provide a comprehensive view on packet classification
                 in an operational network and glean insights that help
                 us design more effective classification algorithms. We
                 propose and evaluate decision tree classifiers with
                 {\em common branches}. These classifiers have linear
                 worst-case memory bounds and require much less memory
                 than standard decision tree classifiers, but
                 nonetheless, we show that on our data have similar
                 average and worst-case time performance. We argue that
                 common-branches exploit structure that is present in
                 real-life data sets. We observe a strong Zipf-like
                 pattern in the usage of rules in a classifier, where a
                 very small number of rules resolves the bulk of traffic
                 and most rules are essentially never used. Inspired by
                 this observation, we propose {\em traffic-aware\/}
                 classifiers that obtain superior average-case and
                 bounded worst-case performance. Good average-case can
                 boost performance of software classifiers that can be
                 used in small to medium sized routers and are also
                 important for traffic analysis and traffic
                 engineering.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM SIGMETRICS Performance Evaluation Review",
  keywords =     "access control lists; decision trees; packet
                 filtering; routing",
}

@Article{Dahui:2005:TRZ,
  author =       "Wang Dahui and Li Menghui and Di Zengru",
  title =        "True reason for {Zipf}'s law in language",
  journal =      j-PHYSICA-A,
  volume =       "358",
  number =       "2--4",
  pages =        "545--550",
  day =          "15",
  month =        dec,
  year =         "2005",
  coden =        "PHYADX",
  doi =          "http://dx.doi.org/10.1016/j.physa.2005.04.021",
  issn =         "0378-4371 (print), 1873-2119 (electronic)",
  issn-l =       "0378-4371",
  bibdate =      "Wed Feb 27 07:32:55 MST 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  url =          "http://www.sciencedirect.com/science/article/pii/S0378437105004085",
  acknowledgement = ack-nhfb,
  fjournal =     "Physica A. Statistical Mechanics and its
                 Applications",
  keywords =     "Zipf's Law",
}

@InProceedings{DelAcebo:2005:BLN,
  author =       "Esteve {Del Acebo} and Mateu Sbert",
  title =        "{Benford's Law} for Natural and Synthetic Images",
  crossref =     "Neumann:2005:CAE",
  pages =        "169--176",
  year =         "2005",
  doi =          "http://dx.doi.org/10.2312/COMPAESTH/COMPAESTH05/169-176",
  bibdate =      "Tue Nov 15 08:46:47 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  url =          "http://www.eg.org/EG/DL/WS/COMPAESTH/COMPAESTH05/169-176.pdf",
  acknowledgement = ack-nhfb,
}

@Book{Durrett:2005:PTE,
  author =       "Richard Durrett",
  title =        "Probability: theory and examples",
  publisher =    "Thomson Brooks\slash Cole",
  address =      "Belmont, CA, USA",
  edition =      "Third",
  pages =        "xi + 497",
  year =         "2005",
  isbn =         "0-534-42441-4",
  isbn-13 =      "978-0-534-42441-1",
  lccn =         "QA273 .D865 2005",
  bibdate =      "Mon Nov 21 10:00:11 MST 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 z3950.loc.gov:7090/Voyager",
  series =       "Duxbury advanced series",
  acknowledgement = ack-nhfb,
  remark =       "Benford's Law is treated on pp. 337ff. Hill \cite[page
                 893]{Hill:1995:BII} reports that the 1991 edition has a
                 proof that the $k$-th digit of powers of integers
                 follows Benford's Law.",
  subject =      "Probabilities",
}

@Book{Egghe:2005:PLI,
  author =       "Leo Egghe",
  title =        "Power laws in the information production process:
                 {Lotkaian} informetrics",
  publisher =    pub-ELSEVIER,
  address =      pub-ELSEVIER:adr,
  pages =        "xvii + 427",
  year =         "2005",
  isbn =         "0-12-088753-3, 0-08-048011-X (e-book)",
  isbn-13 =      "978-0-12-088753-8, 978-0-08-048011-4 (e-book)",
  lccn =         "Z669.8 .E44 2005",
  bibdate =      "Mon Feb 25 10:42:26 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  note =         "See pages 204--205 for Benford's Law discussion.",
  acknowledgement = ack-nhfb,
  keywords =     "Benford's Law",
  subject-dates = "Lotka, Alfred James, (1880--1949)",
  tableofcontents = "Basic theory of Lotkaian informetrics \\
                 Three-dimensional Lotkaian informetrics \\
                 Lotkaian concentration theory \\
                 Lotkaian fractal complexity theory \\
                 Lotkaian informetrics of systems in which items can
                 have multiple sources \\
                 Further applications in Lotkaian informetrics \\
                 Lotkaian informetrics: an introduction",
}

@Article{elSehity:2005:PDA,
  author =       "Tarek el Sehity and Erik Hoelzl and Erich Kirchler",
  title =        "Price developments after a nominal shock: {Benford's
                 Law} and psychological pricing after the euro
                 introduction",
  journal =      j-INT-J-RES-MARK,
  volume =       "22",
  number =       "4",
  pages =        "471--480",
  month =        dec,
  year =         "2005",
  coden =        "IJRME6",
  doi =          "http://dx.doi.org/10.1016/j.ijresmar.2005.09.002",
  issn =         "0167-8116 (print), 1873-8001 (electronic)",
  issn-l =       "0167-8116",
  bibdate =      "Tue Nov 22 11:28:19 MST 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 http://www.sciencedirect.com/",
  url =          "http://www.sciencedirect.com/science/article/pii/S0167811605000522",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Research in Marketing",
  keywords =     "Benford's Law",
}

@Article{Fairthorne:2005:PDE,
  author =       "Robert A. Fairthorne",
  title =        "Progress in Documentation: Empirical Hyperbolic
                 Distributions ({Bradford--Zipf--Mandelbrot}) for
                 Bibliometric Description and Prediction",
  journal =      j-J-DOC,
  volume =       "61",
  number =       "2",
  pages =        "171--193",
  month =        "????",
  year =         "2005",
  coden =        "JDOCAS",
  doi =          "http://dx.doi.org/10.1108/00220410510585179",
  issn =         "0022-0418 (print), 1758-7379 (electronic)",
  issn-l =       "0022-0418",
  bibdate =      "Fri Nov 25 06:27:27 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  note =         "Reprint of \cite{Fairthorne:1969:PDE}.",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Documentation",
  remark =       "According to \cite{Potter:1981:LLR}, this paper is the
                 first to link the distributions of Bradford, Zipf,
                 Mandelbrot, and Lotka.",
}

@Article{FerreriCancho:2005:CZL,
  author =       "Ramon {Ferrer i Cancho} and Oliver Riordan and
                 B{\'e}la Bollob{\'a}s",
  title =        "The consequences of {Zipf}'s law for syntax and
                 symbolic reference",
  journal =      j-PROC-R-SOC-LOND-SER-B-BIO-SCI,
  volume =       "272",
  number =       "1562",
  pages =        "561--565",
  day =          "7",
  month =        mar,
  year =         "2005",
  coden =        "PRLBA4",
  doi =          "http://dx.doi.org/10.1098/rspb.2004.2957",
  issn =         "0962-8452 (print), 1471-2954 (electronic)",
  issn-l =       "0962-8452",
  bibdate =      "Tue Nov 15 11:27:26 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  url =          "http://rspb.royalsocietypublishing.org/content/272/1562/561.full",
  acknowledgement = ack-nhfb,
  fjournal =     "Proceedings of the Royal Society of London. Series B.
                 Biological sciences",
}

@TechReport{Giles:2005:BLN,
  author =       "David E. Giles",
  title =        "{Benford's Law} and Naturally Occurring Prices in
                 Certain {ebaY} Auctions",
  type =         "Econometrics Working Paper",
  number =       "EWP0505",
  institution =  "Department of Economics, University of Victoria",
  address =      "Victoria, BC, Canada",
  month =        may,
  year =         "2005",
  issn =         "1485-6441",
  bibdate =      "Thu Feb 15 16:24:39 2007",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  url =          "http://web.uvic.ca/econ/ewp0505.pdf",
  abstract =     "We show that certain the winning bids for certain ebaY
                 auctions obey Benford's Law. One implication of this is
                 that it is unlikely that these bids are subject to
                 collusion among bidders, or ``shilling'' on the part of
                 sellers. Parenthetically, we also show that numbers
                 from the naturally occurring Fibonacci and Lucas
                 sequences also obey Benford's Law.",
  acknowledgement = ack-nhfb,
  keywords =     "Benford's Law; Law of Anomalous Numbers; Zipf's Law",
}

@Article{Harremoes:2005:ZLHa,
  author =       "Peter Harremo{\"e}s and Flemming Topsoe",
  title =        "{Zipf}'s law, hyperbolic distributions and entropy
                 loss",
  journal =      j-PHYSICA-A,
  volume =       "328",
  number =       "3--4",
  pages =        "315--318",
  day =          "1",
  month =        aug,
  year =         "2005",
  coden =        "PHYADX",
  doi =          "http://dx.doi.org/10.1016/j.endm.2005.07.075",
  issn =         "0378-4371 (print), 1873-2119 (electronic)",
  issn-l =       "0378-4371",
  bibdate =      "Wed Feb 27 07:32:55 MST 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  url =          "http://www.sciencedirect.com/science/article/pii/S1571065305051450",
  acknowledgement = ack-nhfb,
  fjournal =     "Physica A. Statistical Mechanics and its
                 Applications",
  keywords =     "Zipf's Law",
}

@InCollection{Harremoes:2005:ZLHb,
  author =       "Peter Harremo{\"e}s and Flemming Topsoe",
  editor =       "Rudolf Ahlswede and others",
  booktitle =    "General theory of information transfer and
                 combinatorics.",
  title =        "{Zipf}'s law, hyperbolic distributions and entropy
                 loss",
  volume =       "21",
  publisher =    pub-ELSEVIER,
  address =      pub-ELSEVIER:adr,
  pages =        "315--318",
  year =         "2005",
  doi =          "http://dx.doi.org/10.1016/j.endm.2005.07.075",
  bibdate =      "Sat Nov 12 11:07:14 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  series =       "Electronic Notes in Discrete Mathematics",
  zmnumber =     "1158.91482",
  abstract =     "Zipf's law --- or Estoup-Zipf's law --- is an
                 empirical fact of computational linguistics which
                 relates rank and frequency of words in natural
                 languages. The law suggests modelling by distributions
                 of ``hyperbolic type''. We present a satisfactory
                 general definition and an information-theoretical
                 characterization of the resulting hyperbolic
                 distributions. When applied to linguistics this leads
                 to a property of stability and flexibility, explaining
                 that a language can develop towards higher and higher
                 expressive powers without changing its basic
                 structure.",
  acknowledgement = ack-nhfb,
  classmath =    "91F20 (Linguistics) 94A15 (General topics of
                 information theory) 94A17 (Measures of information)",
  keywords =     "entropy loss; hyperbolic distributions; Zipf's law",
}

@Article{Hill:2005:RDS,
  author =       "Theodore P. Hill and Klaus Sch{\"u}rger",
  title =        "Regularity of digits and significant digits of random
                 variables",
  journal =      j-STOCH-PROC-APPL,
  volume =       "115",
  number =       "10",
  pages =        "1723--1743",
  month =        oct,
  year =         "2005",
  coden =        "STOPB7",
  doi =          "http://dx.doi.org/10.1016/j.spa.2005.05.003",
  issn =         "0304-4149 (print), 1879-209X (electronic)",
  issn-l =       "0304-4149",
  bibdate =      "Tue Nov 22 11:28:19 MST 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 http://www.sciencedirect.com/",
  url =          "http://www.sciencedirect.com/science/article/pii/S0304414905000657",
  acknowledgement = ack-nhfb,
  fjournal =     "Stochastic Processes and Their Applications",
  keywords =     "Benford's Law; digit-regular random variable;
                 floating-point numbers; law of least significant
                 digits; nonleading digits; normal numbers; significant
                 digits; significant-digit-regular random variable;
                 trailing digits",
}

@InProceedings{Hjorland:2005:BLS,
  author =       "Birger Hj{\o}rland and Jeppe Nicolaisen",
  editor =       "Fabio Crestani and Ian Ruthven",
  booktitle =    "Context: nature, impact, and role: {5th International
                 Conference on Conceptions of Library and Information
                 Sciences, CoLIS 2005, Glasgow, UK, June 4--8, 2005;
                 proceedings}",
  title =        "{Bradford}'s law of scattering: ambiguities in the
                 concept of ``subject''",
  volume =       "3507",
  publisher =    pub-SV,
  address =      pub-SV:adr,
  pages =        "96--106",
  year =         "2005",
  isbn =         "3-540-26178-8",
  isbn-13 =      "978-3-540-26178-0",
  lccn =         "Z672.5 .I5616 2005",
  bibdate =      "Fri Nov 25 11:52:37 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  series =       ser-LNCS,
  acknowledgement = ack-nhfb,
  bookpages =    "xiii + 250",
}

@Article{Ioannidis:2005:WMP,
  author =       "John P. A. Ioannidis",
  title =        "Why Most Published Research Findings Are False",
  journal =      j-PLOS-MED,
  volume =       "2",
  number =       "8",
  pages =        "696--701",
  month =        aug,
  year =         "2005",
  coden =        "PMLEAC",
  doi =          "http://dx.doi.org/10.1371/journal.pmed.0020124",
  issn =         "1549-1277 (print), 1549-1676 (electronic)",
  issn-l =       "1549-1277",
  bibdate =      "Fri Nov 18 12:42:05 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  url =          "http://www.plosmedicine.org/article/info:doi/10.1371/journal.pmed.0020124",
  abstract =     "There is increasing concern that most current
                 published research findings are false. The probability
                 that a research claim is true may depend on study power
                 and bias, the number of other studies on the same
                 question, and, importantly, the ratio of true to no
                 relationships among the relationships probed in each
                 scientific field. In this framework, a research finding
                 is less likely to be true when the studies conducted in
                 a field are smaller; when effect sizes are smaller;
                 when there is a greater number and lesser preselection
                 of tested relationships; where there is greater
                 flexibility in designs, definitions, outcomes, and
                 analytical modes; when there is greater financial and
                 other interest and prejudice; and when more teams are
                 involved in a scientific field in chase of statistical
                 significance. Simulations show that for most study
                 designs and settings, it is more likely for a research
                 claim to be false than true. Moreover, for many current
                 scientific fields, claimed research findings may often
                 be simply accurate measures of the prevailing bias. In
                 this essay, I discuss the implications of these
                 problems for the conduct and interpretation of
                 research.",
  acknowledgement = ack-nhfb,
  articleno =    "e124",
  fjournal =     "PLoS Medicine",
  remark =       "This article does not discuss Benford's Law, but is
                 related to the use of that law in the detection of
                 fraud in research data. Ioannidis discusses the abuse
                 of statistics for limited experimental data, a topic
                 that receives book-length treatment in
                 \cite{Ziliak:2008:CSS}.",
}

@Article{Jolissaint:2005:LBR,
  author =       "Paul Jolissaint",
  title =        "Loi de {Benford}, relations de r{\'e}currence et
                 suites {\'e}quidistribu{\'e}es. ({French}) [{Benford}'s
                 Law, recurrence relations, and equidistributed
                 sequences]",
  journal =      j-ELEM-MATH,
  volume =       "60",
  number =       "1",
  pages =        "10--18",
  year =         "2005",
  coden =        "????",
  doi =          "http://dx.doi.org/10.4171/EM/2",
  issn =         "0013-6018 (print), 1420-8962 (electronic)",
  issn-l =       "0013-6018",
  mrclass =      "11K36 (37A45 60E99)",
  mrnumber =     "2188341 (2006j:11109)",
  mrreviewer =   "Radhakrishnan Nair",
  bibdate =      "Sat Nov 12 09:13:23 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Elemente der Mathematik",
  language =     "French",
}

@Article{Kechedzhi:2005:RDW,
  author =       "K. E. Kechedzhi and O. V. Usatenko and V. A.
                 Yampol{\cprime}skii",
  title =        "Rank distributions of words in correlated symbolic
                 systems and the {Zipf} law",
  journal =      j-PHYS-REV-E,
  volume =       "72",
  number =       "4",
  pages =        "046138",
  day =          "28",
  month =        oct,
  year =         "2005",
  coden =        "PLEEE8",
  doi =          "http://dx.doi.org/10.1103/PhysRevE.72.046138",
  issn =         "1539-3755 (print), 1550-2376 (electronic)",
  issn-l =       "1539-3755",
  mrclass =      "82C31",
  mrnumber =     "2183723 (2006f:82069)",
  bibdate =      "Tue Feb 26 06:40:57 MST 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  url =          "http://link.aps.org/doi/10.1103/PhysRevE.72.046138",
  acknowledgement = ack-nhfb,
  fjournal =     "Physical Review E (Statistical physics, plasmas,
                 fluids, and related interdisciplinary topics)",
  keywords =     "Zipf's Law",
  pagecount =    "6",
}

@Article{Kontorovich:2005:BLV,
  author =       "Alex V. Kontorovich and Steven J. Miller",
  title =        "{Benford}'s law, values of {$L$}-functions and the {$3
                 x + 1$} problem",
  journal =      j-ACTA-ARITHMETICA,
  volume =       "120",
  number =       "3",
  pages =        "269--297",
  year =         "2005",
  coden =        "AARIA9",
  doi =          "http://dx.doi.org/10.4064/aa120-3-4",
  issn =         "0065-1036 (print), 1730-6264 (electronic)",
  issn-l =       "0065-1036",
  mrclass =      "11K06 (11B37 11M06 37A45)",
  mrnumber =     "2188844 (2007c:11085)",
  mrreviewer =   "J. C. Lagarias",
  bibdate =      "Sat Nov 12 09:13:23 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  url =          "http://adsabs.harvard.edu/abs/2005AcAri.120..269K;
                 http://arxiv.org/abs/math/0412003",
  abstract =     "We show the leading digits of a variety of systems
                 satisfying certain conditions follow Benford's Law. For
                 each system proving this involves two main ingredients.
                 One is a structure theorem of the limiting
                 distribution, specific to the system. The other is a
                 general technique of applying Poisson Summation to the
                 limiting distribution. We show the distribution of
                 values of $L$-functions near the central line and (in
                 some sense) the iterates of the $3 x + 1$ Problem are
                 Benford.",
  acknowledgement = ack-nhfb,
  fjournal =     "Acta Arithmetica",
}

@Article{Kulikova:2005:CAS,
  author =       "A. A. Kulikova and Yu. V. Prokhorov",
  title =        "Completely Asymmetric Stable Laws and {Benford's
                 Law}",
  journal =      j-THEORY-PROBAB-APPL,
  volume =       "49",
  number =       "1",
  pages =        "163--169",
  month =        mar,
  year =         "2005",
  coden =        "TPRBAU",
  doi =          "http://dx.doi.org/10.1137/S0040585X97980944",
  issn =         "0040-585X (print), 1095-7219 (electronic)",
  issn-l =       "0040-585X",
  bibdate =      "Thu Jul 7 19:15:48 MDT 2005",
  bibsource =    "http://epubs.siam.org/sam-bin/dbq/toc/TVP/49/1;
                 http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  url =          "http://epubs.siam.org/sam-bin/dbq/article/98094",
  acknowledgement = ack-nhfb,
  fjournal =     "Theory of probability and its applications",
  keywords =     "Benford's Law; Zipf's Law",
}

@Article{Kulikova:2005:HFD,
  author =       "A. A. Kulikova and Yu. V. Prokhorov and V. I.
                 Khokhlov",
  title =        "{H. F. D.} ({$H$}-function distribution) and the
                 {Benford} law. {I}",
  journal =      "Teor. Veroyatn. Primen.",
  volume =       "50",
  number =       "2",
  pages =        "366--371",
  year =         "2005",
  coden =        "????",
  doi =          "http://dx.doi.org/10.1137/S0040585X97981706",
  issn =         "0040-361X",
  issn-l =       "0040-361X",
  mrclass =      "60E07 (60F05)",
  mrnumber =     "2221718 (2007b:60029)",
  mrreviewer =   "S{\'a}ndor Cs{\"o}rg{\H{o}}",
  bibdate =      "Sat Nov 12 09:13:23 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Rossi{\u\i}skaya Akademiya Nauk. Teoriya
                 Veroyatnoste{\u\i} i ee Primeneniya",
}

@Article{Lagarias:2005:BLF,
  author =       "J. C. Lagarias and K. Soundararajan",
  title =        "{Benford}'s law for the $3 x + 1$ function",
  journal =      "ArXiv Mathematics e-prints",
  month =        sep,
  year =         "2005",
  coden =        "????",
  issn =         "????",
  bibdate =      "Tue Nov 15 06:34:24 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  url =          "http://adsabs.harvard.edu/abs/2005math......9175L;
                 http://arxiv.org/abs/math/0509175",
  acknowledgement = ack-nhfb,
  eprint =       "arXiv:math/0509175",
  keywords =     "Mathematics - Number Theory, Mathematics -
                 Probability",
}

@Article{Li:2005:ZLP,
  author =       "Yujian Li and Chuangbai Xiao",
  title =        "{Zipf}'s law probably existing in protein sequences",
  journal =      "J. Beijing Univ. Technol.",
  volume =       "31",
  number =       "4",
  pages =        "366--368",
  year =         "2005",
  coden =        "????",
  issn =         "????",
  bibdate =      "Sat Nov 12 11:10:06 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  zmnumber =     "1084.92019",
  abstract =     "In order to analyze whether Zipf's law in linguistics
                 exists in protein sequences, this paper uses $
                 1.735\,7\times 10^4 $ protein sequences labeled with
                 secondary structures which are selected from the DSSP
                 database. The segments of successive amino acid
                 residues with a same code of secondary structure are
                 defined as words. The results show that the
                 distribution of words emerging frequency follows Zipf's
                 law with the exponent $ 0.981 $.",
  acknowledgement = ack-nhfb,
  classmath =    "92C40 (Biochemistry, etc.); 62P10 (Appl. of statistics
                 to biology): 92D20 (Protein sequences, DNA sequences)",
  language =     "Chinese. English summary",
  xxremark =     "Which journal is this? Beijing gong ye da xue xue bao
                 = Journal of Beijing Polytechnic University (issn
                 0254-0037), or Beijing ke ji da xue xue bao = Journal
                 of University of Science and Technology, Beijing (issn
                 1001-053X), or something different?",
}

@Article{Lu:2005:CZL,
  author =       "Tim Lu and Christine M. Costello and Peter J. P.
                 Croucher and Robert H{\"a}sler and G{\"u}nther Deuschl
                 and Stefan Schreiber",
  title =        "Can {Zipf}'s law be adapted to normalize
                 microarrays?",
  journal =      "BMC Bioinformatics",
  volume =       "6",
  number =       "??",
  pages =        "37--49",
  month =        "????",
  year =         "2005",
  coden =        "????",
  doi =          "http://dx.doi.org/10.1186/1471-2105-6-37",
  issn =         "1471-2105",
  issn-l =       "1471-2105",
  bibdate =      "Sat Feb 16 18:38:50 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  url =          "http://www.biomedcentral.com/1471-2105/6/37",
  acknowledgement = ack-nhfb,
}

@InProceedings{Lu:2005:DFH,
  author =       "Fletcher Lu and J. Efrim Boritz",
  title =        "Detecting Fraud in Health Insurance Data: Learning to
                 Model Incomplete {Benford's Law} Distributions",
  crossref =     "Gama:2005:MLE",
  pages =        "633--640",
  year =         "2005",
  doi =          "http://dx.doi.org/10.1007/11564096_63",
  bibdate =      "Tue Nov 15 08:55:45 2011",
  bibsource =    "DBLP;
                 http://dblp.uni-trier.de/db/conf/ecml/ecml2005.html#LuB05;
                 http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  series =       ser-LNCS,
  acknowledgement = ack-nhfb,
}

@Article{Ma:2005:CBL,
  author =       "Y. G. Ma and J. B. Natowitz and R. Wada and K. Hagel
                 and J. Wang and T. Keutgen and Z. Majka and M. Murray
                 and L. Qin and P. Smith and R. Alfaro and J. Cibor and
                 M. Cinausero and Y. El Masri and D. Fabris and E.
                 Fioretto and A. Keksis and M. Lunardon and A. Makeev
                 and N. Marie and E. Martin and A. Martinez-Davalos and
                 A. Menchaca-Rocha and G. Nebbia and G. Prete and V.
                 Rizzi and A. Ruangma and D. V. Shetty and G. Souliotis
                 and P. Staszel and M. Veselsky and G. Viesti and E. M.
                 Winchester and S. J. Yennello",
  title =        "Critical behavior in light nuclear systems:
                 Experimental aspects",
  journal =      j-PHYS-REV-C,
  volume =       "71",
  number =       "5",
  pages =        "054606",
  day =          "26",
  month =        may,
  year =         "2005",
  coden =        "PRVCAN",
  doi =          "http://dx.doi.org/10.1103/PhysRevC.71.054606",
  issn =         "0556-2813 (print), 1089-490X, 1538-4497",
  issn-l =       "0556-2813",
  bibdate =      "Tue Feb 26 06:40:57 MST 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  url =          "http://link.aps.org/doi/10.1103/PhysRevC.71.054606",
  acknowledgement = ack-nhfb,
  fjournal =     "Physical Review C (Nuclear Physics)",
  keywords =     "Zipf's Law",
}

@Article{Manaris:2005:ZLM,
  author =       "Bill Manaris and Juan Romero and Penousal Machado and
                 Dwight Krehbiel and Timothy Hirzel and Walter Pharr and
                 Robert B. Davis",
  title =        "{Zipf}'s law, music classification, and aesthetics",
  journal =      j-COMP-MUSIC-J,
  volume =       "29",
  number =       "1",
  pages =        "55--69",
  month =        "Spring",
  year =         "2005",
  coden =        "CMUJDY",
  issn =         "0148-9267 (print), 1531-5169 (electronic)",
  issn-l =       "0148-9267",
  bibdate =      "Sat Feb 16 18:40:14 2013",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/m/mandelbrot-benoit.bib;
                 http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  url =          "http://muse.jhu.edu/journals/cmj/summary/v029/29.1manaris.html;
                 http://muse.jhu.edu/journals/computer_music_journal/v029/29.1manaris.pdf",
  acknowledgement = ack-nhfb,
  fjournal =     "Computer Music Journal",
  keywords =     "Benford's Law; Zipf's Law; Zipf--Mandelbrot Law",
}

@Article{Maslov:2005:GTS,
  author =       "V. P. Maslov",
  title =        "On a general theorem of set theory that leads to the
                 {Gibbs}, {Bose--Einstein}, and {Pareto} distributions
                 and to the {Zipf--Mandelbrot} law for the stock
                 market",
  journal =      j-MAT-ZAMETKI,
  volume =       "78",
  number =       "6",
  pages =        "870--877",
  year =         "2005",
  coden =        "????",
  doi =          "http://dx.doi.org/10.1007/s11006-005-0186-9",
  issn =         "0025-567X",
  issn-l =       "0025-567X",
  mrclass =      "91B28 (90C29)",
  mrnumber =     "2249037 (2007b:91077)",
  bibdate =      "Sat Nov 12 09:13:23 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Rossi{\u\i}skaya Akademiya Nauk. Matematicheskie
                 Zametki",
}

@Article{Maslov:2005:RZLa,
  author =       "V. P. Maslov",
  title =        "Refining {Zipf}'s law for frequency dictionaries",
  journal =      j-DOKL-AKAD-NAUK,
  volume =       "405",
  number =       "5",
  pages =        "591--594",
  year =         "2005",
  coden =        "DANKAS",
  issn =         "0869-5652",
  issn-l =       "0869-5652",
  mrclass =      "94A15 (60C05)",
  mrnumber =     "2340762",
  bibdate =      "Sat Nov 12 09:13:23 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Rossi{\u\i}skaya Akademiya Nauk. Doklady Akademii
                 Nauk",
}

@Article{Maslov:2005:RZLb,
  author =       "V. P. Maslov",
  title =        "Refinement of {Zipf}'s law for frequency
                 dictionaries",
  journal =      j-DOKL-MATH,
  volume =       "72",
  number =       "3",
  pages =        "942--945",
  year =         "2005",
  coden =        "????",
  issn =         "1064-5624 (print), 1531-8362 (electronic)",
  issn-l =       "1064-5624",
  bibdate =      "Sat Nov 12 11:05:14 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  zmnumber =     "1206.82009",
  acknowledgement = ack-nhfb,
  classmath =    "82B10 (Quantum equilibrium statistical mechanics
                 (general)) 68T50 (Natural language processing) 68Q45
                 (Formal languages)",
  fjournal =     "Doklady Mathematics",
  keywords =     "Bose--Einstein statistics",
  language =     "English. Russian original",
}

@Article{Maslov:2005:ZML,
  author =       "V. P. Maslov",
  title =        "The {Zipf--Mandelbrot} law: quantization and an
                 application to the stock market",
  journal =      j-RUSS-J-MATH-PHYS,
  volume =       "12",
  number =       "4",
  pages =        "483--488",
  year =         "2005",
  coden =        "RJMPEL",
  issn =         "1061-9208",
  issn-l =       "1061-9208",
  mrclass =      "91B28 (82B99)",
  mrnumber =     "2201312 (2006i:91053)",
  bibdate =      "Sat Nov 12 09:13:23 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Russian Journal of Mathematical Physics",
}

@Article{McAllister:2005:ACE,
  author =       "James W. McAllister",
  title =        "Algorithmic compression of empirical data: reply to
                 {Twardy}, {Gardner}, and {Dowe}",
  journal =      j-STUD-HIST-PHILOS-SCI,
  volume =       "36",
  number =       "2",
  pages =        "403--410",
  month =        jun,
  year =         "2005",
  coden =        "SHPSB5",
  doi =          "http://dx.doi.org/10.1016/j.shpsa.2005.04.005",
  issn =         "0039-3681 (print), 1879-2510 (electronic)",
  issn-l =       "0039-3681",
  bibdate =      "Mon Nov 7 12:11:58 MST 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 http://www.math.utah.edu/pub/tex/bib/shps-a.bib;
                 http://www.sciencedirect.com/science/journal/00393681",
  note =         "See \cite{McAllister:2003:ARE,Twardy:2005:EDS}.",
  url =          "http://www.sciencedirect.com/science/article/pii/S0039368105000221",
  acknowledgement = ack-nhfb,
  fjournal =     "Studies in History and Philosophy of Science Part A",
}

@Article{McCowan:2005:AUZ,
  author =       "B. McCowan and L. R. Doyle and J. M. Jenkins and S. F.
                 Hanser",
  title =        "The appropriate use of {Zipf}'s law in animal
                 communication studies",
  journal =      j-ANIM-BEHAV,
  volume =       "69",
  number =       "1",
  pages =        "F1--F7",
  day =          "20",
  month =        jan,
  year =         "2005",
  coden =        "ANBEA8",
  doi =          "http://dx.doi.org/10.1016/j.anbehav.2004.09.002",
  issn =         "0003-3472 (print), 1095-8282 (electronic)",
  issn-l =       "0003-3472",
  bibdate =      "Wed Feb 27 07:32:55 MST 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  url =          "http://www.sciencedirect.com/science/article/pii/S000334720400346X",
  acknowledgement = ack-nhfb,
  fjournal =     "Animal Behaviour",
  journal-url =  "http://www.sciencedirect.com/science/journal/00033472",
  keywords =     "Zipf's Law",
}

@Article{Miller:2005:BLV,
  author =       "S. J. Miller and A. Kontorovich",
  title =        "{Benford}'s law, values of {$L$}-functions and the $ 3
                 x + 1 $ problem",
  journal =      j-ACTA-ARITHMETICA,
  volume =       "120",
  number =       "3",
  pages =        "269--297",
  month =        "????",
  year =         "2005",
  coden =        "AARIA9",
  doi =          "http://dx.doi.org/10.4064/aa120-3-4",
  issn =         "0065-1036 (print), 1730-6264 (electronic)",
  issn-l =       "0065-1036",
  mrclass =      "11K06, 60A10, 11B83, 11M06 (60F05, 11J86, 60J65, 46F12)",
  bibdate =      "Tue Feb 26 06:11:26 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Acta Arithmetica",
}

@InProceedings{Nagasaka:2005:BLD,
  author =       "Kenji Nagasaka",
  editor =       "G. Barat and H. Daud{\'e} and M. Laurent and P.
                 Liardet and S. Louboutin and A. Thomas",
  booktitle =    "{Journ{\'e}es Arithm{\'e}tiques XXIV, Marseilles, July
                 4--8, 2005, Universit{\'e} de Provence and
                 Universit{\'e} de la M{\'e}diterran{\'e}e and CNRS
                 Marseilles, France}",
  title =        "{Benford}'s law with different basis",
  publisher =    "????",
  address =      "????",
  pages =        "1--2",
  year =         "2005",
  isbn =         "????",
  isbn-13 =      "????",
  lccn =         "????",
  bibdate =      "Sat Feb 16 18:49:26 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  url =          "http://atlas-conferences.com/c/a/r/e/47.htm",
  acknowledgement = ack-nhfb,
}

@Article{Newman:2005:PLP,
  author =       "M. E. J. Newman",
  title =        "Power laws, {Pareto} distributions and {Zipf}'s law",
  journal =      j-CONTEMP-PHYS,
  volume =       "46",
  number =       "5",
  pages =        "323--351",
  month =        sep,
  year =         "2005",
  coden =        "CTPHAF",
  doi =          "http://dx.doi.org/10.1080/00107510500052444",
  issn =         "0010-7514 (print), 1366-5812 (electronic)",
  issn-l =       "0010-7514",
  bibdate =      "Fri Jul 09 16:33:18 2010",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  abstract =     "When the probability of measuring a particular value
                 of some quantity varies inversely as a power of that
                 value, the quantity is said to follow a power law, also
                 known variously as Zipf's law or the Pareto
                 distribution. Power laws appear widely in physics,
                 biology, earth and planetary sciences, economics and
                 finance, computer science, demography and the social
                 sciences. For instance, the distributions of the sizes
                 of cities, earthquakes, forest fires, solar flares,
                 moon craters and people's personal fortunes all appear
                 to follow power laws. The origin of power-law behaviour
                 has been a topic of debate in the scientific community
                 for more than a century. Here we review some of the
                 empirical evidence for the existence of power-law forms
                 and the theories proposed to explain them.",
  acknowledgement = ack-nhfb,
  fjournal =     "Contemporary physics",
  keywords =     "Benford's Law; critical phenomena; Legendre beta
                 function; Pareto distribution; percolation; phase
                 transitions; power-law distributions; random walks;
                 Riemann zeta function; scale-free distributions; Yule
                 process; Zipf's Law",
  remark =       "This article is an excellent survey of continuous and
                 discrete distributions that follow a power law, and
                 some that do not. It is well worth reading.",
  subject =      "astrophysics; atomic and nuclear physics; chemical
                 physics; computational physics; condensed matter
                 physics; environmental physics; experimental physics;
                 general physics; particle and high energy physics;
                 plasma physics; space science; theoretical physics",
}

@Article{Nitsch:2005:ZZ,
  author =       "Volker Nitsch",
  title =        "{Zipf} zipped",
  journal =      j-J-URBAN-ECON,
  volume =       "57",
  number =       "1",
  pages =        "86--100",
  day =          "15",
  month =        jan,
  year =         "2005",
  coden =        "JUECDW",
  doi =          "http://dx.doi.org/10.1016/j.jue.2004.09.002",
  issn =         "0094-1190 (print), 1095-9068 (electronic)",
  issn-l =       "0094-1190",
  bibdate =      "Wed Feb 27 07:32:55 MST 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  url =          "http://www.sciencedirect.com/science/article/pii/S0094119004000981",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Urban Economics",
  journal-url =  "http://www.sciencedirect.com/science/journal/00941190",
  keywords =     "Zipf's Law",
}

@Article{Perline:2005:SWF,
  author =       "Richard Perline",
  title =        "Strong, weak and false inverse power laws",
  journal =      j-STAT-SCI,
  volume =       "20",
  number =       "1",
  pages =        "68--88",
  month =        "????",
  year =         "2005",
  coden =        "STSCEP",
  issn =         "0883-4237",
  issn-l =       "0883-4237",
  bibdate =      "Fri Nov 18 12:15:56 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Statistical Science",
  keywords =     "Benford's Law",
}

@Book{Posch:2005:ZTP,
  author =       "Peter N. Posch",
  title =        "{Ziffernanalyse in Theorie und Praxis: Testverfahren
                 zur F{\"a}lschungsaufsp{\"u}rung mit Benfords Gesetz}",
  publisher =    "Shaker",
  address =      "Aachen, Germany",
  pages =        "iv + 87 + v",
  year =         "2005",
  isbn =         "3-8322-4492-1",
  isbn-13 =      "978-3-8322-4492-7",
  lccn =         "????",
  bibdate =      "Mon Feb 18 18:01:33 MST 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 z3950.gbv.de:20011/gvk",
  price =        "EUR 29.80 (DE)",
  series =       "Berichte aus der Statistik",
  url =          "http://www.gbv.de/dms/hbz/toc/ht014717371.pdf",
  acknowledgement = ack-nhfb,
}

@Article{Rousseau:2005:RFE,
  author =       "Ronald Rousseau",
  title =        "{Robert Fairthorne} and the empirical power laws",
  journal =      j-J-DOC,
  volume =       "61",
  number =       "2",
  pages =        "194--202",
  month =        "????",
  year =         "2005",
  coden =        "JDOCAS",
  doi =          "http://dx.doi.org/10.1108/00220410510585188",
  issn =         "0022-0418 (print), 1758-7379 (electronic)",
  issn-l =       "0022-0418",
  bibdate =      "Fri Nov 25 06:42:00 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Documentation",
  remark =       "Review of
                 \cite{Fairthorne:1969:PDE,Fairthorne:2005:PDE}.",
}

@Article{Rowlands:2005:EAD,
  author =       "Ian Rowlands",
  title =        "{Emerald} authorship data, {Lotka}'s law and research
                 productivity",
  journal =      j-ASLIB-PROC,
  volume =       "57",
  number =       "1",
  pages =        "5--10",
  month =        "????",
  year =         "2005",
  coden =        "ASLPAO",
  doi =          "http://dx.doi.org/10.1108/00012530510579039",
  issn =         "0001-253X (print), 1758-3748 (electronic)",
  issn-l =       "0001-253X",
  bibdate =      "Fri Nov 25 07:25:01 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ASLIB Proceedings",
  keywords =     "brand loyalty; publishing; research results",
  remark =       "This paper applies Lotka's Law to the question of the
                 likelihood of an author remaining with a particular
                 publisher.",
}

@Article{Shan:2005:GZD,
  author =       "Shi Shan",
  title =        "On the generalized {Zipf} distribution. {Part I}",
  journal =      j-INFO-PROC-MAN,
  volume =       "41",
  number =       "6",
  pages =        "1369--1386",
  day =          "1",
  month =        dec,
  year =         "2005",
  coden =        "IPMADK",
  doi =          "http://dx.doi.org/10.1016/j.ipm.2005.03.003",
  issn =         "0306-4573 (print), 1873-5371 (electronic)",
  issn-l =       "0306-4573",
  bibdate =      "Wed Feb 27 07:32:55 MST 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  url =          "http://www.sciencedirect.com/science/article/pii/S030645730500018X",
  acknowledgement = ack-nhfb,
  fjournal =     "Information Processing and Management",
  keywords =     "Zipf's Law",
}

@Article{Soo:2005:ZLC,
  author =       "Kwok Tong Soo",
  title =        "{Zipf's Law} for cities: a cross-country
                 investigation",
  journal =      j-REG-SCI-URBAN-ECON,
  volume =       "35",
  number =       "3",
  pages =        "239--263",
  day =          "1",
  month =        may,
  year =         "2005",
  coden =        "RSUEDM",
  doi =          "http://dx.doi.org/10.1016/j.regsciurbeco.2004.04.004",
  issn =         "0166-0462 (print), 1879-2308 (electronic)",
  issn-l =       "0166-0462",
  bibdate =      "Wed Feb 27 07:32:55 MST 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  url =          "http://www.sciencedirect.com/science/article/pii/S016604620400033X",
  acknowledgement = ack-nhfb,
  fjournal =     "Regional Science and Urban Economics",
  journal-url =  "http://www.sciencedirect.com/science/journal/01660462",
  keywords =     "Zipf's Law",
}

@Article{Stadje:2005:APD,
  author =       "Wolfgang Stadje",
  title =        "Asymptotic properties of digit sequences of random
                 numbers",
  journal =      j-MATH-NACHR,
  volume =       "278",
  number =       "10",
  pages =        "1209--1229",
  month =        "????",
  year =         "2005",
  coden =        "MTMNAQ",
  doi =          "http://dx.doi.org/10.1002/mana.200310303",
  issn =         "0025-584X",
  issn-l =       "0025-584X",
  bibdate =      "Mon Feb 18 06:36:36 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  zmnumber =     "1073.11053",
  acknowledgement = ack-nhfb,
  fjournal =     "Mathematische Nachrichten",
  keywords =     "ergodicity; limit theorem; Markov chain; moments;
                 occurrence probability; random digit sequence;
                 stationary digits; transition function",
  ZMclass =      "11K31 (Special sequences); 60G10 (Stationary
                 processes); 60J05 (Discrete-time Markov processes on
                 general state spaces); 60F99 (Limit theorems
                 (probability))",
}

@TechReport{Taylor:2005:TMT,
  author =       "Jonathan Taylor",
  title =        "Too many ties? An empirical analysis of the
                 {Venezuelan} recall referendum counts",
  type =         "Technical report",
  number =       "??",
  institution =  "Department of Statistics, Stanford University",
  address =      "Stanford, CA 94305, USA",
  year =         "2005",
  bibdate =      "Fri Feb 15 18:29:53 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  url =          "http://esdata.info/pdf/Taylor-Ties.pdf;
                 http://www.benfordonline.net/fullreference/577",
  acknowledgement = ack-nhfb,
  remark =       "Cited in \cite{Pericchi:2011:QAD}, with ``Statist.
                 Sci. To appear 2009''. However, the article is not yet
                 found there in February 2013. This report was issued as
                 a result of the Carter Center's investigation of
                 fairness of 2004 voting in Venezuela. Its conclusion,
                 that there was no demonstrable electoral fraud, has
                 been challenged; see \cite{Pericchi:2011:QAD}.",
}

@Article{Twardy:2005:EDS,
  author =       "Charles Twardy and Steve Gardner and David L. Dowe",
  title =        "Empirical data sets are algorithmically compressible:
                 reply to {McAllister}?",
  journal =      j-STUD-HIST-PHILOS-SCI,
  volume =       "36",
  number =       "2",
  pages =        "391--402",
  month =        jun,
  year =         "2005",
  coden =        "SHPSB5",
  doi =          "http://dx.doi.org/10.1016/j.shpsa.2005.04.004",
  issn =         "0039-3681 (print), 1879-2510 (electronic)",
  issn-l =       "0039-3681",
  bibdate =      "Mon Nov 7 12:11:58 MST 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 http://www.math.utah.edu/pub/tex/bib/shps-a.bib;
                 http://www.sciencedirect.com/science/journal/00393681",
  note =         "See \cite{McAllister:2003:ARE,McAllister:2005:ACE}.",
  url =          "http://www.sciencedirect.com/science/article/pii/S003936810500021X",
  acknowledgement = ack-nhfb,
  fjournal =     "Studies in History and Philosophy of Science Part A",
}

@Article{vanLeijenhorst:2005:FDH,
  author =       "D. C. van Leijenhorst and Th. P. van der Weide",
  title =        "A formal derivation of {Heaps}' law",
  journal =      j-INFO-SCI,
  volume =       "170",
  number =       "2--4",
  pages =        "263--272",
  year =         "2005",
  coden =        "ISIJBC",
  doi =          "http://dx.doi.org/10.1016/j.ins.2004.03.006",
  issn =         "0020-0255 (print), 1872-6291 (electronic)",
  issn-l =       "0020-0255",
  mrclass =      "60C05",
  mrnumber =     "2120894 (2005h:60024)",
  bibdate =      "Sat Nov 12 10:28:06 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  abstract =     "Word frequencies in text documents can be reasonably
                 described by the Mandelbrot distribution, which has
                 Zipf's law as a special case. Furthermore, the growth
                 of vocabulary size as a function of the text size (its
                 number of words) has been described in Heaps' law. It
                 has been shown that these two experimental laws are
                 related. In this paper we go a step further, and
                 provide a (formal) derivation of Heaps' law from the
                 Mandelbrot distribution. We also provide a
                 specification of the validity area for applying Heaps'
                 law.",
  acknowledgement = ack-nhfb,
  ajournal =     "Inform. Sci.",
  fjournal =     "Information Sciences. An International Journal",
}

@Article{Aban:2006:PET,
  author =       "Inmaculada B. Aban and Mark M. Meerschaert and Anna K.
                 Panorska",
  title =        "Parameter Estimation for the Truncated {Pareto}
                 Distribution",
  journal =      j-J-AM-STAT-ASSOC,
  volume =       "101",
  number =       "473",
  pages =        "270--277",
  month =        mar,
  year =         "2006",
  coden =        "JSTNAL",
  doi =          "http://dx.doi.org/10.1198/016214505000000411",
  issn =         "0162-1459 (print), 1537-274X (electronic)",
  issn-l =       "0162-1459",
  bibdate =      "Thu Aug 26 11:26:31 MDT 2010",
  bibsource =    "http://www.amstat.org/publications/jasa/;
                 http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 http://www.math.utah.edu/pub/tex/bib/jamstatassoc2000.bib",
  acknowledgement = ack-nhfb,
}

@Article{Baskerville:2006:SEM,
  author =       "Kim Baskerville and Maya Paczuski",
  title =        "Subgraph ensembles and motif discovery using an
                 alternative heuristic for graph isomorphism",
  journal =      j-PHYS-REV-E,
  volume =       "74",
  number =       "??",
  pages =        "051903",
  day =          "3",
  month =        nov,
  year =         "2006",
  coden =        "PLEEE8",
  doi =          "http://dx.doi.org/10.1103/PhysRevE.74.051903",
  issn =         "1539-3755 (print), 1550-2376 (electronic)",
  issn-l =       "1539-3755",
  bibdate =      "Tue Feb 26 06:40:57 MST 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  url =          "http://link.aps.org/doi/10.1103/PhysRevE.74.051903",
  acknowledgement = ack-nhfb,
  fjournal =     "Physical Review E (Statistical physics, plasmas,
                 fluids, and related interdisciplinary topics)",
  keywords =     "Zipf's Law",
}

@Article{Bohachevsky:2006:DBL,
  author =       "Ihor O. Bohachevsky and Mark E. Johnson and Myron L.
                 Stein",
  title =        "A derivation of {Benford}'s law",
  journal =      j-AM-J-MATH-MANAGE-SCI,
  volume =       "26",
  number =       "3--4",
  pages =        "355--370",
  year =         "2006",
  coden =        "AMMSDX",
  issn =         "0196-6324",
  issn-l =       "0196-6324",
  mrclass =      "60E99 (11K36)",
  mrnumber =     "2312400 (2008h:60062)",
  mrreviewer =   "Radhakrishnan Nair",
  bibdate =      "Sat Nov 12 09:13:23 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "American Journal of Mathematical and Management
                 Sciences",
}

@InProceedings{Dallacasa:2006:TBS,
  author =       "F. Dallacasa and Valerio Dallacasa",
  editor =       "????",
  booktitle =    "{5th International Conference: APLIMAT 2006, Slovak
                 University of Technology, Bratislava}",
  title =        "Temporal behaviour of stock data from {Benford}'s
                 law",
  publisher =    "????",
  address =      "????",
  pages =        "425--432",
  year =         "2006",
  isbn =         "????",
  isbn-13 =      "????",
  lccn =         "????",
  bibdate =      "Sat Feb 16 17:32:15 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  price =        "US\$",
  url =          "http://archiv.aplimat.com/2006/Aplimat/Proceedings/Communications/Financial_Actuary_math/Dallasca-Dallasca.pdf",
  acknowledgement = ack-nhfb,
}

@Article{Dorogovtsev:2006:FON,
  author =       "S. N. Dorogovtsev and J. F. F. Mendes and J. G.
                 Oliveira",
  title =        "Frequency of occurrence of numbers in the {World Wide
                 Web}",
  journal =      j-PHYSICA-A,
  volume =       "360",
  number =       "2",
  pages =        "548--556",
  month =        feb,
  year =         "2006",
  coden =        "PHYADX",
  doi =          "http://dx.doi.org/10.1016/j.physa.2005.06.064",
  issn =         "0378-4371 (print), 1873-2119 (electronic)",
  issn-l =       "0378-4371",
  bibdate =      "Tue Nov 22 11:28:19 MST 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 http://www.sciencedirect.com/",
  url =          "http://arxiv.org/abs/physics/0504185;
                 http://www.sciencedirect.com/science/article/pii/S0378437105006874",
  acknowledgement = ack-nhfb,
  fjournal =     "Physica A: Statistical Mechanics and its
                 Applications",
  keywords =     "Benford's Law",
}

@Article{Duranton:2006:SFZ,
  author =       "Gilles Duranton",
  title =        "Some foundations for {Zipf}'s law: Product
                 proliferation and local spillovers",
  journal =      j-REG-SCI-URBAN-ECON,
  volume =       "36",
  number =       "4",
  pages =        "542--563",
  day =          "1",
  month =        jul,
  year =         "2006",
  coden =        "RSUEDM",
  doi =          "http://dx.doi.org/10.1016/j.regsciurbeco.2006.03.008",
  issn =         "0166-0462 (print), 1879-2308 (electronic)",
  issn-l =       "0166-0462",
  bibdate =      "Wed Feb 27 07:32:55 MST 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  url =          "http://www.sciencedirect.com/science/article/pii/S0166046206000354",
  acknowledgement = ack-nhfb,
  fjournal =     "Regional Science and Urban Economics",
  keywords =     "Zipf's Law",
}

@Article{Egghe:2006:DHL,
  author =       "L. Egghe",
  title =        "The dependence of the height of a {Lorenz} curve of a
                 {Zipf} function on the size of the system",
  journal =      j-MATH-COMP-MODELLING,
  volume =       "43",
  number =       "7--8",
  pages =        "870--879",
  day =          "15",
  month =        apr,
  year =         "2006",
  coden =        "MCMOEG",
  doi =          "http://dx.doi.org/10.1016/j.mcm.2005.09.033",
  issn =         "0895-7177 (print), 1872-9479 (electronic)",
  issn-l =       "0895-7177",
  mrclass =      "94A15 (91B82)",
  mrnumber =     "2218323 (2006k:94033)",
  mrreviewer =   "Ulrich Tamm",
  bibdate =      "Wed Feb 27 07:32:55 MST 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  url =          "http://www.sciencedirect.com/science/article/pii/S089571770500508X",
  acknowledgement = ack-nhfb,
  fjournal =     "Mathematical and Computer Modelling",
  keywords =     "Zipf's Law",
}

@Article{Gaite:2006:CSZ,
  author =       "Jos{\'e} Gaite",
  title =        "Cut-out sets and the {Zipf} law for fractal voids",
  journal =      j-PHYSICA-D,
  volume =       "223",
  number =       "2",
  pages =        "248--255",
  day =          "15",
  month =        nov,
  year =         "2006",
  coden =        "PDNPDT",
  doi =          "http://dx.doi.org/10.1016/j.physd.2006.09.021",
  issn =         "0167-2789 (print), 1872-8022 (electronic)",
  issn-l =       "0167-2789",
  mrclass =      "28A80",
  mrnumber =     "2307212",
  bibdate =      "Wed Feb 27 07:32:55 MST 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  url =          "http://www.sciencedirect.com/science/article/pii/S0167278906003848",
  acknowledgement = ack-nhfb,
  fjournal =     "Physica. D, Nonlinear phenomena",
  keywords =     "Zipf's Law",
}

@Article{Gan:2006:ZLS,
  author =       "Li Gan and Dong Li and Shunfeng Song",
  title =        "Is the {Zipf} law spurious in explaining city-size
                 distributions?",
  journal =      j-ECONOM-LETT,
  volume =       "92",
  number =       "2",
  pages =        "256--262",
  day =          "1",
  month =        aug,
  year =         "2006",
  coden =        "ECLEDS",
  doi =          "http://dx.doi.org/10.1016/j.econlet.2006.03.004",
  issn =         "0165-1765 (print), 1873-7374 (electronic)",
  issn-l =       "0165-1765",
  bibdate =      "Wed Feb 27 07:32:55 MST 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  url =          "http://www.sciencedirect.com/science/article/pii/S0165176506000772",
  acknowledgement = ack-nhfb,
  fjournal =     "Economics Letters",
  keywords =     "Zipf's Law",
}

@Article{Handurukande:2006:PSB,
  author =       "S. B. Handurukande and A.-M. Kermarrec and F. {Le
                 Fessant} and L. Massouli{\'e} and S. Patarin",
  title =        "Peer sharing behaviour in the {eDonkey} network, and
                 implications for the design of server-less file sharing
                 systems",
  journal =      j-OPER-SYS-REV,
  volume =       "40",
  number =       "4",
  pages =        "359--371",
  month =        oct,
  year =         "2006",
  coden =        "OSRED8",
  doi =          "http://doi.acm.org/10.1145/1218063.1217970",
  issn =         "0163-5980 (print), 1943-586X (electronic)",
  issn-l =       "0163-5980",
  bibdate =      "Fri Jun 20 17:14:10 MDT 2008",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  abstract =     "In this paper we present an empirical study of a
                 workload gathered by crawling the eDonkey network --- a
                 dominant peer-to-peer file sharing system --- for over
                 50 days. We first confirm the presence of some known
                 features, in particular the prevalence of free-riding
                 and the Zipf-like distribution of file popularity. We
                 also analyze the evolution of document popularity. We
                 then provide an in-depth analysis of several clustering
                 properties of such workloads. We measure the
                 geographical clustering of peers offering a given file.
                 We find that most files are offered mostly by peers of
                 a single country, although popular files don't have
                 such a clear home country. We then analyze the overlap
                 between contents offered by different peers. We find
                 that peer contents are highly clustered according to
                 several metrics of interest. We propose to leverage
                 this property by allowing peers to search for content
                 without server support, by querying suitably identified
                 semantic neighbours. We find via trace-driven
                 simulations that this approach is generally effective,
                 and is even more effective for rare files. If we
                 further allow peers to query both their semantic
                 neighbours, and in turn their neighbours' neighbours,
                 we attain hit rates as high as over 55\% for neighbour
                 lists of size 20.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM SIGOPS Operating Systems Review",
  keywords =     "file sharing; peer-to-peer; simulation; trace",
}

@InCollection{Harremoes:2006:ZLH,
  author =       "P. Harremo{\"e}s and F. Topsoe",
  editor =       "Rudolf Ahlswede and others",
  booktitle =    "General theory of information transfer and
                 combinatorics",
  title =        "{Zipf}'s law, hyperbolic distributions and entropy
                 loss",
  volume =       "4123",
  publisher =    pub-SV,
  address =      pub-SV:adr,
  pages =        "788--792",
  year =         "2006",
  doi =          "http://dx.doi.org/10.1007/11889342_50",
  bibdate =      "Sat Nov 12 11:15:28 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  series =       ser-LNCS,
  zmnumber =     "1158.91481",
  abstract =     "Zipf's law --- or Estoup-Zipf's law --- is an
                 empirical fact of computational linguistics which
                 relates rank and frequency of words in natural
                 languages. The law suggests modelling by distributions
                 of ``hyperbolic type''. We present a satisfactory
                 general definition and an information-theoretical
                 characterization of the resulting hyperbolic
                 distributions. When applied to linguistics this leads
                 to a property of stability and flexibility, explaining
                 that a language can develop towards higher and higher
                 expressive powers without changing its basic
                 structure.",
  acknowledgement = ack-nhfb,
  classmath =    "91F20 (Linguistics) 94A15 (General topics of
                 information theory) 94A17 (Measures of information)",
  keywords =     "entropy loss; hyperbolic distributions; Zipf's law",
}

@TechReport{Humenberger:2006:BGV,
  author =       "Hans Humenberger",
  title =        "{Das ,,Benford-Gesetz'' {\"u}ber die Verteilung der
                 ersten Ziffer von Zahn}. ({German}) [{Benford}'s Law on
                 the distribution of the first digit of numbers]",
  type =         "Report",
  institution =  "Institut f{\"u}r Mathematik und Angewandte Statistik,
                 Universit{\"a}t f{\"u}r Bodenkultur",
  address =      "Gregor Mendel-Stra{\ss}e 33, A-1180, Wien, Austria",
  month =        aug,
  year =         "2006",
  bibdate =      "Sun Feb 17 09:37:40 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  url =          "http://www.mathematik.uni-kassel.de/didaktik/HomePersonal/fischer/StochScan/1996-3_Hum.pdf",
  acknowledgement = ack-nhfb,
  language =     "German",
}

@TechReport{Hurlimann:2006:BLB,
  author =       "Werner H{\"u}rlimann",
  title =        "{Benford's Law} from 1881 to 2006: a bibliography",
  type =         "Report",
  address =      "Feldstrasse 145, CH-8004 Z{\"u}rich, Switzerland",
  pages =        "15",
  day =          "5",
  month =        jul,
  year =         "2006",
  bibdate =      "Fri Mar 30 11:32:30 2007",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  url =          "http://arxiv.org/pdf/math.ST/0607168",
  abstract =     "On the occasion of the 125-th anniversary of Newcomb's
                 paper, a bibliography of academic work related to
                 Benford's law from its year of origin 1881 to 2006 has
                 been compiled.",
  acknowledgement = ack-nhfb,
  keywords =     "Benford's Law; Law of Anomalous Numbers; Zipf's Law",
  remark =       "This bibliography lists 325 references on the title
                 subject, with these (years) and counts: (1881) 1,
                 (1912) 1, (1916) 1, (1917) 1, (1936) 1, (1938) 1,
                 (1944) 1, (1945) 1, (1948) 2, (1950) 1, (1952) 1,
                 (1953) 1, (1954) 1, (1957) 3, (1960) 1, (1961) 2,
                 (1963) 1, (1964) 2, (1965) 2, (1966) 1, (1967) 1,
                 (1968) 2, (1969) 5, (1970) 1, (1971) 4, (1972) 2,
                 (1973) 7, (1974) 2, (1975) 1, (1976) 5, (1977) 3,
                 (1978) 3, (1979) 2, (1981) 6, (1982) 3, (1983) 4,
                 (1984) 7, (1985) 2, (1986) 7, (1987) 5, (1988) 1,
                 (1988) 5, (1989) 2, (1990) 1, (1991) 4, (1992) 6,
                 (1993) 5, (1994) 5, (1995) 1, (1995) 2, (1996) 4,
                 (1997) 1, (1997) 9, (1998) 1, (1998) 6, (1999) 12,
                 (2000) 10, (2001) 19, (2002) 30, (2003) 22, (2004) 29,
                 (2005) 34, (2006) 18.",
}

@Article{Hurlimann:2006:GBL,
  author =       "W. Hurlimann",
  title =        "Generalizing {Benford}'s law using power laws:
                 application to integer sequences",
  journal =      "ArXiv Mathematics e-prints",
  month =        jul,
  year =         "2006",
  coden =        "????",
  issn =         "????",
  bibdate =      "Tue Nov 15 06:34:24 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  url =          "http://adsabs.harvard.edu/abs/2006math......7166H",
  acknowledgement = ack-nhfb,
  eprint =       "arXiv:math/0607166",
  keywords =     "Mathematics - Statistics, Mathematics - Number Theory,
                 11B73, 11B83, 11K31, 62E15, 62E17",
}

@Article{Izsak:2006:MLE,
  author =       "F. Izs{\'a}k",
  title =        "Maximum likelihood estimation for constrained
                 parameters of multinomial distributions --- Application
                 to {Zipf--Mandelbrot} models",
  journal =      j-COMPUT-STAT-DATA-ANAL,
  volume =       "51",
  number =       "3",
  pages =        "1575--1583",
  day =          "1",
  month =        dec,
  year =         "2006",
  coden =        "CSDADW",
  doi =          "http://dx.doi.org/10.1016/j.csda.2006.05.008",
  issn =         "0167-9473 (print), 1872-7352 (electronic)",
  issn-l =       "0167-9473",
  mrnumber =     "2307527",
  bibdate =      "Wed Feb 27 07:32:55 MST 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  url =          "http://www.sciencedirect.com/science/article/pii/S016794730600154X",
  acknowledgement = ack-nhfb,
  fjournal =     "Computational Statistics \& Data Analysis",
  keywords =     "Zipf's Law",
}

@TechReport{Judge:2006:DPS,
  author =       "George Judge and Laura Schechter",
  title =        "Detecting problems in survey data using {Benford}'s
                 law",
  type =         "Preprint",
  institution =  "University of California at Berkeley and University of
                 Wisconsin at Madison",
  address =      "Berkeley, CA, USA and Madison, WI, USA",
  pages =        "30",
  day =          "1",
  month =        nov,
  year =         "2006",
  bibdate =      "Sat Feb 16 18:12:29 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  url =          "http://www.aae.wisc.edu/lschechter/benford.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "Benford's Law",
}

@Article{Kossovsky:2006:TBU,
  author =       "Alex Ely Kossovsky",
  title =        "Towards a Better Understanding of the Leading Digits
                 Phenomena",
  journal =      "ArXiv Mathematics e-prints",
  year =         "2006",
  bibdate =      "Mon Nov 21 06:46:43 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  url =          "http://arxiv.org/abs/math/0612627",
  abstract =     "This article on leading digits (Benford's Law)
                 contains the following: (i) An attempt at a
                 comprehensive account on the leading digits phenomena,
                 incorporating many of its existing explanations,
                 proofs, and differing points of view. (ii) The finding
                 that leading digits of random numbers derived from a
                 chain of distributions that are linked via parameter
                 selection are logarithmic in the limit as the number of
                 sequences approaches infinity, and that empirically
                 only around 5 or 6 sequences of such a distribution
                 chain are needed to obtain results that are close
                 enough to the logarithmic (i.e., rapid convergence).
                 (iii) An outright exact logarithmic behavior for a
                 2-sequence chain whenever parametrical density is
                 exactly logarithmic. (iv) An account on the existence
                 of singularities in exponential growth rates with
                 regards to the leading digits distributions of their
                 series. (v) An account on several distributions that
                 are intrinsically logarithmic or approximately so. (vi)
                 A conceptual justification of Flehinger's iterated
                 averaging scheme --- an algorithm that was presented
                 without any clear motivation. (vii) A note on the close
                 relationship of Flehinger's scheme and the chain of
                 distribution to Hill's super distribution. (viii) A
                 conceptual argument justifying the scale invariance
                 principle --- a principle invoked in derivations of
                 Benford's law. (ix) A note on the intimate connection
                 between one-sided tail to the right in density
                 distributions and logarithmic leading digit behavior.",
  acknowledgement = ack-nhfb,
  remark =       "On 18 February 2013, the archive has 17 revisions of
                 this article.",
  xxjournal =    "CoRR",
}

@Article{Kristiansen:2006:BTZ,
  author =       "K. de Lange Kristiansen and G. Helgesen and A. T.
                 Skjeltorp",
  title =        "Braid theory and {Zipf--Mandelbrot} relation used in
                 microparticle dynamics",
  journal =      j-EUR-PHYS-J-B,
  volume =       "51",
  number =       "3",
  pages =        "363--371",
  month =        jun,
  year =         "2006",
  coden =        "EPJBFY",
  doi =          "http://dx.doi.org/10.1140/epjb/e2006-00241-7",
  issn =         "1434-6028 (print), 1434-6036 (electronic)",
  issn-l =       "1434-6028",
  bibdate =      "Sat Sep 8 18:31:14 2012",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/m/mandelbrot-benoit.bib;
                 http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "European Physical Journal B: Condensed Matter and
                 Complex Systems",
}

@Book{Kuipers:2006:UDS,
  author =       "Lauwerens Kuipers and Harald Niederreiter",
  title =        "Uniform distribution of sequences",
  publisher =    pub-DOVER,
  address =      pub-DOVER:adr,
  pages =        "xviii + 390",
  year =         "2006",
  isbn =         "0-486-45019-8 (paperback)",
  isbn-13 =      "978-0-486-45019-3 (paperback)",
  lccn =         "QA292 .K84 2006",
  bibdate =      "Sat Nov 12 15:42:53 MST 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 z3950.loc.gov:7090/Voyager",
  url =          "http://www.loc.gov/catdir/enhancements/fy0625/2005056064-d.html;
                 http://www.loc.gov/catdir/toc/fy0612/2005056064.html",
  acknowledgement = ack-nhfb,
  remark =       "Originally published in \cite{Kuipers:1974:UDS}.",
  subject =      "Sequences (Mathematics); Uniform distribution
                 (Probability theory)",
}

@Article{Kulikova:2006:HFD,
  author =       "A. A. Kulikova and Yu. V. Prokhorov and V. I.
                 Khokhlov",
  title =        "{H.F.D.} ({$H$}-function Distribution) and {Benford's
                 Law}. {I}",
  journal =      j-THEORY-PROBAB-APPL,
  volume =       "50",
  number =       "2",
  pages =        "311--315",
  month =        jan,
  year =         "2006",
  coden =        "TPRBAU",
  doi =          "http://dx.doi.org/10.1137/S0040585X97981706",
  issn =         "0040-585X (print), 1095-7219 (electronic)",
  issn-l =       "0040-585X",
  bibdate =      "Wed May 19 18:14:51 MDT 2010",
  bibsource =    "http://epubs.siam.org/sam-bin/dbq/toc/TVP/50/2;
                 http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  url =          "http://epubs.siam.org/tvp/resource/1/tprbau/v50/i2/p311_s1",
  acknowledgement = ack-nhfb,
  fjournal =     "Theory of probability and its applications",
}

@Article{Lagarias:2006:BLF,
  author =       "Jeffrey C. Lagarias and K. Soundararajan",
  title =        "{Benford}'s law for the $3 x + 1$ function",
  journal =      "J. London Math. Soc. (2)",
  volume =       "74",
  number =       "2",
  pages =        "289--303",
  year =         "2006",
  coden =        "JLMSAK",
  doi =          "http://dx.doi.org/10.1112/S0024610706023131",
  issn =         "0024-6107 (print), 1469-7750 (electronic)",
  issn-l =       "0024-6107",
  mrclass =      "37A45",
  mrnumber =     "2269630 (2007h:37007)",
  mrreviewer =   "Radhakrishnan Nair",
  bibdate =      "Sat Nov 12 09:13:23 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of the London Mathematical Society. Second
                 Series",
}

@Article{Leinicke:2006:FFN,
  author =       "Linda M. Leinicke and Joyce A. Ostrosky and W. Max
                 Rexroad",
  title =        "Fighting fraud by the numbers: Digital analysis
                 primer",
  journal =      "Fraud Magazine",
  volume =       "??",
  number =       "??",
  pages =        "??--??",
  month =        jan # "\slash " # feb,
  year =         "2006",
  issn =         "1553-6645",
  issn-l =       "1553-6645",
  bibdate =      "Sun Feb 17 08:13:02 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  url =          "http://www.fraud-magazine.com/article.aspx?id=4294967620",
  acknowledgement = ack-nhfb,
  fjournal =     "Fraud Magazine. {A} Publication of the Association of
                 Certified Fraud Examiners",
  keywords =     "Benford's Law",
}

@Article{Leydesdorff:2006:CPL,
  author =       "Loet Leydesdorff and Stephen Bensman",
  title =        "Classification and power laws: the logarithmic
                 transformation",
  journal =      j-J-AM-SOC-INF-SCI-TECHNOL,
  volume =       "57",
  number =       "11",
  pages =        "1470--1486",
  month =        sep,
  year =         "2006",
  coden =        "JASIEF",
  doi =          "http://dx.doi.org/10.1002/asi.20467",
  issn =         "1532-2882 (print), 1532-2890 (electronic)",
  issn-l =       "1532-2882",
  bibdate =      "Sat Feb 16 18:31:04 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of the American Society for Information
                 Science and Technology",
  journal-url =  "http://onlinelibrary.wiley.com/journal/10.1002/(issn)1532-2890",
  keywords =     "Benford's Law",
}

@InCollection{Lu:2006:AFD,
  author =       "Fletcher Lu and J. Efrim Boritz and Dominic Covvey",
  booktitle =    "Advances in artificial intelligence",
  title =        "Adaptive fraud detection using {Benford}'s law",
  volume =       "4013",
  publisher =    pub-SV,
  address =      pub-SV:adr,
  pages =        "347--358",
  year =         "2006",
  doi =          "http://dx.doi.org/10.1007/11766247_30",
  mrnumber =     "2280590",
  bibdate =      "Sat Nov 12 09:13:23 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  series =       ser-LNCS,
  acknowledgement = ack-nhfb,
}

@InProceedings{Lu:2006:BCF,
  author =       "F. Lu and J. E. Boritz",
  editor =       "????",
  booktitle =    "{Uncertainty in Artificial Intelligence: Proceedings
                 of the 22nd Conference}",
  title =        "Building a case for fraud using {Benford}'s law with
                 reinforcement learning",
  publisher =    "????",
  address =      "????",
  pages =        "??--??",
  year =         "2006",
  bibdate =      "Sat Feb 16 18:34:47 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Manaris:2006:IES,
  author =       "Bill Manaris and Luca Pellicoro and George Pothering
                 and Harland Hodges",
  editor =       "????",
  booktitle =    "{2006 IASTED International Conference on Artificial
                 Intelligence and Applications (AIA 2006), February
                 13--16, 2006, Innsbruck, Austria}",
  title =        "Investigating {Esperanto}'s statistical proportions
                 relative to other languages using neural networks and
                 {Zipf}'s law",
  publisher =    "Acta Press",
  address =      "????",
  pages =        "1--7",
  year =         "2006",
  isbn =         "????",
  isbn-13 =      "????",
  lccn =         "????",
  bibdate =      "Sat Feb 16 18:41:37 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  url =          "http://www.cs.cofc.edu/~manaris/uploads/Main/IASTED2006.pdf",
  acknowledgement = ack-nhfb,
}

@Article{Marchi:2006:AAS,
  author =       "Scott Marchi and James Hamilton",
  title =        "Assessing the Accuracy of Self-Reported Data: an
                 Evaluation of the Toxics Release Inventory",
  journal =      "Journal of Risk and Uncertainty",
  volume =       "32",
  number =       "1",
  pages =        "57--76",
  month =        jan,
  year =         "2006",
  coden =        "JRUNEN",
  doi =          "http://dx.doi.org/10.1007/s10797-006-6666-3",
  issn =         "0895-5646 (print), 1573-0476 (electronic)",
  issn-l =       "0895-5646",
  bibdate =      "Fri Nov 25 11:25:49 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
}

@Article{Maslov:2006:BGA,
  author =       "V. P. Maslov",
  title =        "{Bose} gas of anharmonic oscillators and a refinement
                 of {Zipf}'s law",
  journal =      j-TEORET-MATH-FIZ,
  volume =       "148",
  number =       "3",
  pages =        "495--496",
  year =         "2006",
  coden =        "TMFZAL",
  doi =          "http://dx.doi.org/10.1007/s11232-006-0117-2",
  issn =         "0564-6162",
  issn-l =       "0564-6162",
  mrclass =      "82B10",
  mrnumber =     "2283664",
  bibdate =      "Sat Nov 12 09:13:23 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Rossi{\u\i}skaya Akademiya Nauk. Teoreticheskaya i
                 Matematicheskaya Fizika",
}

@Article{Maslov:2006:NAD,
  author =       "V. P. Maslov",
  title =        "Negative asymptotic dimension, a new condensate, and
                 their relation to the quantized {Zipf} law",
  journal =      j-MAT-ZAMETKI,
  volume =       "80",
  number =       "6",
  pages =        "856--863",
  year =         "2006",
  coden =        "????",
  doi =          "http://dx.doi.org/10.1007/s11006-006-0203-7",
  issn =         "0025-567X",
  issn-l =       "0025-567X",
  mrclass =      "82B10 (20F69 53C23 81S10 91F20)",
  mrnumber =     "2311613 (2008e:82005)",
  mrreviewer =   "Artur E. Ruuge",
  bibdate =      "Sat Nov 12 09:13:23 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Rossi{\u\i}skaya Akademiya Nauk. Matematicheskie
                 Zametki",
}

@Article{Maslov:2006:RZM,
  author =       "V. P. Maslov",
  title =        "A refinement of the {Zipf--Mandelbrot} law and
                 lacunarity in an ideal gas",
  journal =      j-TEORET-MATH-FIZ,
  volume =       "147",
  number =       "3",
  pages =        "511--512",
  year =         "2006",
  coden =        "TMFZAL",
  doi =          "http://dx.doi.org/10.1007/s11232-006-0083-8",
  issn =         "0564-6162",
  issn-l =       "0564-6162",
  mrclass =      "82B10",
  mrnumber =     "2254729 (2007d:82007)",
  bibdate =      "Sat Nov 12 09:13:23 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Rossi{\u\i}skaya Akademiya Nauk. Teoreticheskaya i
                 Matematicheskaya Fizika",
}

@Article{Maslov:2006:ZLR,
  author =       "V. P. Maslov and T. V. Maslova",
  title =        "On {Zipf}'s law and rank distributions in linguistics
                 and semiotics",
  journal =      j-MAT-ZAMETKI,
  volume =       "80",
  number =       "5",
  pages =        "718--732",
  year =         "2006",
  coden =        "????",
  doi =          "http://dx.doi.org/10.1007/s11006-006-0189-1",
  issn =         "0025-567X",
  issn-l =       "0025-567X",
  mrclass =      "60C05 (62-07 62P99)",
  mrnumber =     "2311586 (2008g:60027)",
  mrreviewer =   "Konstantin E. Feldman",
  bibdate =      "Sat Nov 12 09:13:23 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  zmnumber =     "Zbl 1134.62086",
  acknowledgement = ack-nhfb,
  fjournal =     "Rossi{\u\i}skaya Akademiya Nauk. Matematicheskie
                 Zametki",
}

@Article{Maslova:2006:ZLM,
  author =       "T. V. Maslova",
  title =        "{Zipf}'s law and {Maslov}'s formula as applied to
                 semiotic systems",
  journal =      j-DOKL-MATH,
  volume =       "74",
  number =       "3",
  pages =        "917--920",
  year =         "2006",
  coden =        "????",
  doi =          "http://dx.doi.org/10.1134/S1064562406060330",
  issn =         "1064-5624 (print), 1531-8362 (electronic)",
  issn-l =       "1064-5624",
  bibdate =      "Sat Nov 12 11:13:35 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  zmnumber =     "pre05824774",
  acknowledgement = ack-nhfb,
  classmath =    "62E20 (Asymptotic distribution theory in statistics)
                 82B03 (Foundations of equilibrium statistical
                 mechanics)",
  fjournal =     "Doklady Mathematics",
  language =     "English. Russian original",
}

@Article{Maslova:2006:ZLV,
  author =       "T. V. Maslova",
  title =        "On the {Zipf} law and the {V. P. Maslov} formula for
                 semiotic systems",
  journal =      j-DOKL-AKAD-NAUK,
  volume =       "411",
  number =       "6",
  pages =        "754--757",
  year =         "2006",
  coden =        "DANKAS",
  issn =         "0869-5652",
  issn-l =       "0869-5652",
  mrclass =      "62E20 (82B03)",
  mrnumber =     "2451374",
  bibdate =      "Sat Nov 12 09:13:23 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Rossi{\u\i}skaya Akademiya Nauk. Doklady Akademii
                 Nauk",
}

@InProceedings{Mebane:2006:DAE,
  author =       "Walter R. {Mebane, Jr.}",
  editor =       "????",
  booktitle =    "{2006 Annual Meeting of the Midwest Political Science
                 Association, April 20--23, Palmer House, Chicago}",
  title =        "Detecting Attempted Election Theft: Vote Counts,
                 Voting Machines and {Benford's Law}",
  publisher =    "????",
  address =      "????",
  pages =        "i + 50",
  day =          "19",
  month =        apr,
  year =         "2006",
  isbn =         "????",
  isbn-13 =      "????",
  lccn =         "????",
  bibdate =      "Sat Feb 16 12:14:14 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  url =          "http://www.umich.edu/~wmebane/mw06.pdf",
  acknowledgement = ack-nhfb,
}

@InProceedings{Mebane:2006:EFS,
  author =       "Walter R. {Mebane, Jr.}",
  editor =       "????",
  booktitle =    "{Election Fraud Conference, Salt Lake City, Utah,
                 September 29--30, 2006}",
  title =        "Election Forensics: The Second-digit {Benford's Law}
                 Test and Recent {American Presidential} Elections",
  publisher =    "????",
  address =      "????",
  pages =        "??--??",
  year =         "2006",
  isbn =         "????",
  isbn-13 =      "????",
  lccn =         "????",
  bibdate =      "Fri Feb 15 18:22:27 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  url =          "http://www-personal.umich.edu/~wmebane/fraud06.pdf",
  acknowledgement = ack-nhfb,
}

@InProceedings{Mebane:2006:EFV,
  author =       "Walter R. {Mebane, Jr.}",
  editor =       "????",
  booktitle =    "{2006 Summer Meeting of the Political Methodology
                 Society, UC-Davis, July 20--22, 2006}",
  title =        "Election Forensics: Vote Counts and {Benford's Law}",
  publisher =    "????",
  address =      "????",
  pages =        "ii + 48",
  day =          "18",
  month =        jul,
  year =         "2006",
  isbn =         "????",
  isbn-13 =      "????",
  lccn =         "????",
  bibdate =      "Sat Feb 16 12:01:26 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  url =          "http://www.umich.edu/~wmebane/pm06.pdf",
  acknowledgement = ack-nhfb,
}

@Article{Mellor:2006:GKZ,
  author =       "Andy Mellor",
  title =        "Book Review: {G. K. Zipf, \booktitle The
                 Psycho-biology of Language (1935) MIT Press, Cambridge,
                 MA}",
  journal =      j-SYSTEM,
  volume =       "34",
  number =       "3",
  pages =        "455--457",
  day =          "20",
  month =        sep,
  year =         "2006",
  coden =        "????",
  doi =          "http://dx.doi.org/10.1016/j.system.2006.07.004",
  issn =         "0346-251X (print), 1879-3282 (electronic)",
  issn-l =       "0346-251X",
  bibdate =      "Wed Feb 27 07:32:55 MST 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  url =          "http://www.sciencedirect.com/science/article/pii/S0346251X06000674",
  acknowledgement = ack-nhfb,
  fjournal =     "System",
  journal-url =  "http://www.sciencedirect.com/science/journal/0346251X",
  keywords =     "Zipf's Law",
}

@Article{Metwally:2006:IES,
  author =       "Ahmed Metwally and Divyakant Agrawal and Amr {El
                 Abbadi}",
  title =        "An integrated efficient solution for computing
                 frequent and top-$k$ elements in data streams",
  journal =      j-TODS,
  volume =       "31",
  number =       "3",
  pages =        "1095--1133",
  month =        sep,
  year =         "2006",
  coden =        "ATDSD3",
  doi =          "http://doi.acm.org/10.1145/1166074.1166084",
  issn =         "0362-5915 (print), 1557-4644 (electronic)",
  issn-l =       "0362-5915",
  bibdate =      "Tue Oct 17 05:41:01 MDT 2006",
  bibsource =    "http://www.acm.org/pubs/contents/journals/tods/;
                 http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  note =         "See comments in \cite{Liu:2010:CIE}.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Database Systems",
}

@Article{Miller:2006:MCL,
  author =       "S. J. Miller and M. J. Nigrini",
  title =        "The {Modulo 1 Central Limit Theorem} and {Benford's
                 Law} for Products",
  journal =      "International Journal of Algebra",
  volume =       "3",
  number =       "3",
  pages =        "119--130",
  month =        jul,
  year =         "2006",
  coden =        "????",
  issn =         "1312-8868",
  issn-l =       "1312-8868",
  bibdate =      "Tue Nov 15 06:34:24 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  url =          "http://adsabs.harvard.edu/abs/2006math......7686M;
                 http://arxiv.org/abs/math/0607686",
  abstract =     "We derive a necessary and sufficient condition for the
                 sum of $M$ independent continuous random variables
                 modulo $1$ to converge to the uniform distribution in
                 $L^1([0,1])$, and discuss generalizations to discrete
                 random variables. A consequence is that if $X_1,
                 \ldots{}, X_M$ are independent continuous random
                 variables with densities $f_1, \ldots{}, f_M$, for any
                 base $B$ as $M \to \infty$ for many choices of the
                 densities the distribution of the digits of $X_1 *
                 \cdots{} * X_M$ converges to Benford's law base $B$.
                 The rate of convergence can be quantified in terms of
                 the Fourier coefficients of the densities, and provides
                 an explanation for the prevalence of Benford behavior
                 in many diverse systems.",
  acknowledgement = ack-nhfb,
  eprint =       "arXiv:math/0607686",
  keywords =     "Mathematics - Probability, Mathematics - Classical
                 Analysis and ODEs, 60F05, 60F25, 11K06 (Primary),
                 42A10, 42A61, 62E15 (Secondary)",
}

@Article{Miller:2006:OSB,
  author =       "S. J. Miller and M. J. Nigrini",
  title =        "Order Statistics and {Benford's Law}",
  journal =      "ArXiv Mathematics e-prints",
  month =        jan,
  year =         "2006",
  coden =        "????",
  issn =         "????",
  bibdate =      "Tue Nov 15 06:34:24 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  url =          "http://adsabs.harvard.edu/abs/2006math......1344M",
  acknowledgement = ack-nhfb,
  eprint =       "arXiv:math/0601344",
  keywords =     "Mathematics - Probability, Mathematics - Number
                 Theory, 11K06, 60A10 (Primary), 46F12, 60F05, 42A16
                 (Secondary)",
}

@Article{Moret:2006:NBL,
  author =       "M. A. Moret and V. de Senna and M. G. Pereira and G.
                 F. Zebende",
  title =        "{Newcomb--Benford} Law in Astrophysical Sources",
  journal =      j-INT-J-MOD-PHYS-C,
  volume =       "17",
  number =       "11",
  pages =        "1597--1604",
  month =        "????",
  year =         "2006",
  coden =        "IJMPEO",
  issn =         "0129-1831 (print), 1793-6586 (electronic)",
  issn-l =       "0129-1831",
  bibdate =      "Mon Nov 14 17:37:59 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  url =          "http://adsabs.harvard.edu/abs/2006IJMPC..17.1597M",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Modern Physics C [Physics and
                 Computers]",
  journal-url =  "http://www.worldscientific.com/loi/ijmpc",
}

@TechReport{Morrow:2006:BLF,
  author =       "John Morrow",
  title =        "{Benford's Law}, Families of Distributions and a Test
                 Basis",
  type =         "Report",
  institution =  "University of Wisconsin--Madison",
  address =      "Madison, WI, USA",
  month =        "????",
  year =         "2006",
  bibdate =      "Tue Nov 22 20:44:23 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  note =         "Revised draft of 9 October 2010.",
  url =          "http://www.johnmorrow.info/projects/benford/benfordMain.pdf",
  acknowledgement = ack-nhfb,
  lastaccess =   "22 November 2011",
}

@Article{Moura:2006:ZLB,
  author =       "Newton J. Moura Jr. and Marcelo B. Ribeiro",
  title =        "{Zipf} law for {Brazilian} cities",
  journal =      j-J-THEOR-BIOL,
  volume =       "219",
  number =       "4",
  pages =        "441--448",
  day =          "15",
  month =        jul,
  year =         "2006",
  coden =        "JTBIAP",
  doi =          "http://dx.doi.org/10.1016/j.physa.2005.11.038",
  issn =         "0022-5193 (print), 1095-8541 (electronic)",
  issn-l =       "0022-5193",
  bibdate =      "Wed Feb 27 07:32:55 MST 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  url =          "http://www.sciencedirect.com/science/article/pii/S0378437105012422",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Theoretical Biology",
  keywords =     "Zipf's Law",
}

@TechReport{Nigrini:2006:BLA,
  author =       "M. J. Nigrini and S. J. Miller",
  title =        "{Benford}'s law applied to hydrology data --- results
                 and relevance to other geophysical data",
  type =         "Preprint",
  institution =  "????",
  address =      "????",
  month =        "????",
  year =         "2006",
  bibdate =      "Sat Feb 16 18:58:34 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
}

@Article{Ogasawara:2006:ZLH,
  author =       "Osamu Ogasawara and Shoko Kawamoto and Kousaku Okubo",
  title =        "{Zipf}'s law and human transcriptomes: an explanation
                 with an evolutionary model",
  journal =      j-C-R-BIOL,
  volume =       "326",
  number =       "10--11",
  pages =        "1097--1101",
  day =          "1",
  month =        jul,
  year =         "2006",
  coden =        "CRBOCM",
  doi =          "http://dx.doi.org/10.1016/j.crvi.2003.09.031",
  issn =         "1631-0691 (print), 1768-3238 (electronic)",
  issn-l =       "1631-0691",
  bibdate =      "Wed Feb 27 07:32:55 MST 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  url =          "http://www.sciencedirect.com/science/article/pii/S1631069103002294",
  acknowledgement = ack-nhfb,
  fjournal =     "Comptes Rendus Biologies",
  journal-url =  "http://sciencedirect.com/science/journal/16310691",
  keywords =     "Zipf's Law",
}

@Article{Pocheau:2006:SDL,
  author =       "A. Pocheau",
  title =        "The significant digit law: a paradigm of statistical
                 scale symmetries",
  journal =      j-EUR-PHYS-J-B,
  volume =       "49",
  number =       "4",
  pages =        "491--511",
  month =        feb,
  year =         "2006",
  coden =        "EPJBFY",
  doi =          "http://dx.doi.org/10.1140/epjb/e2006-00084-2",
  issn =         "1434-6028 (print), 1434-6036 (electronic)",
  issn-l =       "1434-6028",
  bibdate =      "Sat Feb 16 15:06:20 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  url =          "http://link.springer.com/article/10.1140/epjb/e2006-00084-2",
  acknowledgement = ack-nhfb,
  fjournal =     "European Physical Journal B: Condensed Matter and
                 Complex Systems",
}

@Article{Posch:2006:ADP,
  author =       "Peter N. Posch and Welf A. Kreiner",
  title =        "Analysing digits for portfolio formation and index
                 tracking",
  journal =      j-J-ASSET-MANAGE,
  volume =       "7",
  number =       "1",
  pages =        "69--80",
  month =        may,
  year =         "2006",
  coden =        "????",
  doi =          "http://dx.doi.org/10.1057/palgrave.jam.2240203",
  issn =         "1470-8272 (print), 1479-179X (electronic)",
  issn-l =       "1470-8272",
  bibdate =      "Fri Nov 25 11:19:38 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  abstract =     "A general methodology is proposed for using digit
                 distributions as an approach to examining arbitrary
                 datasets. With the Newcomb--Benford law as a starting
                 point, a more general framework for digital analysis is
                 developed. A new measure is proposed based on this
                 framework, namely the Digital-Fit Factor (DFF). The use
                 of index comparison on the S\&P500 and the Dow Jones
                 Industrial Average is demonstrated. The DFF is then
                 used to construct portfolios and measure their
                 performance compared with that of the index. The
                 average returns using the measure exceed the index
                 composition by 6--14 percentage points per year by
                 being more stable at the same time. Furthermore, these
                 measures require only a very small proportion of the
                 available information and are thus very efficient.",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Asset Management",
  keywords =     "Benford's Law",
}

@Article{Ree:2006:PLD,
  author =       "Suhan Ree",
  title =        "Power-law distributions from additive preferential
                 redistributions",
  journal =      j-PHYS-REV-E,
  volume =       "73",
  number =       "??",
  pages =        "026115",
  day =          "15",
  month =        feb,
  year =         "2006",
  coden =        "PLEEE8",
  doi =          "http://dx.doi.org/10.1103/PhysRevE.73.026115",
  issn =         "1539-3755 (print), 1550-2376 (electronic)",
  issn-l =       "1539-3755",
  bibdate =      "Tue Feb 26 06:40:57 MST 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  url =          "http://link.aps.org/doi/10.1103/PhysRevE.73.026115",
  acknowledgement = ack-nhfb,
  fjournal =     "Physical Review E (Statistical physics, plasmas,
                 fluids, and related interdisciplinary topics)",
  keywords =     "Zipf's Law",
}

@InProceedings{Sanches:2006:IRU,
  author =       "Jo{\~a}o M. Sanches and Jorge S. Marques",
  booktitle =    "{2006 IEEE International Conference on Image
                 Processing, Atlanta, Georgia, 8--11 October 2006}",
  title =        "Image Reconstruction using the {Benford Law}",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "2029--2032",
  year =         "2006",
  doi =          "http://dx.doi.org/10.1109/ICIP.2006.312845",
  isbn =         "1-4244-0480-0",
  isbn-13 =      "978-1-4244-0480-3",
  issn =         "1522-4880",
  bibdate =      "Tue Nov 15 09:03:24 2011",
  bibsource =    "DBLP;
                 http://dblp.uni-trier.de/db/conf/icip/icip2006.html#SanchesM06;
                 http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  abstract =     "Tt has been claimed that the first digit of real
                 signals follows a logarithmic distribution, called
                 Benford law. This paper shows that this distribution is
                 a natural prior for the gradient of several types of
                 medical images (MRI, CT, ultrasound) and proposes a
                 reconstruction algorithm based on the Benford law which
                 does not require any parameter tuning. Experimental
                 results are presented to illustrate the performance of
                 the reconstruction algorithm",
  acknowledgement = ack-nhfb,
}

@Article{Schneider:2006:RAS,
  author =       "Reto U. Schneider",
  title =        "{Das R{\"a}tsel der abgegriffenen Seiten: Vor {\"u}ber
                 hundert Jahren stiess ein Astronom auf ein
                 merkw{\"u}rdiges statistisches Gesetz, das heute
                 Steuerbetr{\"u}ger entlarven soll}. ({German}) [{The}
                 puzzle of the worn pages: More than a hundred years ago
                 an astronomer came across a strange statistical law
                 that will now expose tax cheats]",
  journal =      "{NZZ Folio: Die Zeitschrift der Neuen Z{\"u}rcher
                 Zeitung}",
  number =       "1/06",
  month =        "????",
  year =         "2006",
  bibdate =      "Fri Nov 18 12:18:17 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  url =          "http://www-x.nzz.ch/folio/curr/articles/schneider_2.html;
                 http://www.nzzfolio.ch/www/d80bd71b-b264-4db4-afd0-277884b93470/showarticle/4c9a5444-883e-4e6b-8a4c-6c31f32c02f3.aspx",
  acknowledgement = ack-nhfb,
  language =     "German",
}

@Article{Schuette:2006:TFZ,
  author =       "Paul Schuette and Marcus C. Spruill",
  title =        "Tail fit and the {Zipf--Pareto} law",
  journal =      "Extremes",
  volume =       "9",
  number =       "3--4",
  pages =        "243--261",
  year =         "2006",
  coden =        "????",
  doi =          "http://dx.doi.org/10.1007/s10687-007-0030-6",
  issn =         "1386-1999",
  issn-l =       "1386-1999",
  mrnumber =     "2367837",
  bibdate =      "Sat Nov 12 09:13:23 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Extremes. Statistical Theory and Applications in
                 Science, Engineering and Economics",
  xxyear =       "2007",
}

@Article{Sugimoto:2006:AFP,
  author =       "Toyoaki Sugimoto and Naoto Miyoshi",
  title =        "On the asymptotics of fault probability in
                 least-recently-used caching with {Zipf}-type request
                 distribution",
  journal =      j-RAND-STRUCT,
  volume =       "29",
  number =       "3",
  pages =        "296--323",
  year =         "2006",
  coden =        "RSALFD",
  doi =          "http://dx.doi.org/10.1002/rsa.20098",
  issn =         "1042-9832",
  issn-l =       "1042-9832",
  mrclass =      "68N25 (60C05 62E20 62P30 68P05 68U35)",
  mrnumber =     "2254493 (2008h:68028)",
  bibdate =      "Sat Nov 12 09:13:23 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Random Structures and Algorithms",
  keywords =     "distributional tail asymptotics; least-recently-used
                 caching; move-to-front algorithm; negative association;
                 Zipf-type distribution",
}

@MastersThesis{TorresNunez:2006:NBL,
  author =       "David A. {Torres N{\'u}{\~n}ez}",
  title =        "{Newcomb--Benford's Law}: Applications to Electoral
                 Processes, Bioinformatics, and the Stock Index",
  type =         "{M.S.} thesis",
  school =       "Center for Bioststatistics and Bioinformatics,
                 University of Puerto Rico, R{\'\i}o Piedras Campus",
  address =      "PO Box 23355, San Juan, PR 00931-3355",
  month =        may,
  year =         "2006",
  bibdate =      "Fri Feb 15 18:34:47 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  advisor =      "Luis R{\'a}ul Pericchi Guerra",
}

@Article{VandeWalle:2006:ZGK,
  author =       "J. {Van de Walle} and K. Willems",
  title =        "{Zipf, George Kingsley (1902--1950)}",
  journal =      j-J-ECON-DYN-CONTROL,
  volume =       "31",
  number =       "7",
  pages =        "756--757",
  day =          "15",
  month =        jul,
  year =         "2006",
  coden =        "JEDCDH",
  doi =          "http://dx.doi.org/10.1016/B0-08-044854-2/04726-X",
  issn =         "0165-1889 (print), 1879-1743 (electronic)",
  issn-l =       "0165-1889",
  bibdate =      "Wed Feb 27 07:32:55 MST 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  url =          "http://www.sciencedirect.com/science/article/pii/B008044854204726X",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Economic Dynamics and Control",
  keywords =     "Zipf's Law",
}

@Article{Wilkinson:2006:RPC,
  author =       "Leland Wilkinson",
  title =        "Revising the {Pareto} Chart",
  journal =      j-AMER-STAT,
  volume =       "60",
  number =       "4",
  pages =        "332--334",
  month =        nov,
  year =         "2006",
  coden =        "ASTAAJ",
  doi =          "http://pubs.amstat.org/doi/pdfplus/10.1198/000313006X152243",
  issn =         "0003-1305 (print), 1537-2731 (electronic)",
  issn-l =       "0003-1305",
  bibdate =      "Thu Aug 26 21:48:27 MDT 2010",
  bibsource =    "http://www.amstat.org/publications/tas/;
                 http://www.math.utah.edu/pub/tex/bib/amstat.bib;
                 http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
}

@Article{Ackermann:2007:DMB,
  author =       "Heiner Ackermann and Alantha Newman and Heiko
                 R{\"o}glin and Berthold V{\"o}cking",
  title =        "Decision-making based on approximate and smoothed
                 {Pareto} curves",
  journal =      j-THEOR-COMP-SCI,
  volume =       "378",
  number =       "3",
  pages =        "253--270",
  day =          "9",
  month =        jun,
  year =         "2007",
  coden =        "TCSCDI",
  issn =         "0304-3975 (print), 1879-2294 (electronic)",
  issn-l =       "0304-3975",
  bibdate =      "Tue Mar 29 08:55:49 MDT 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 http://www.sciencedirect.com/science/journal/03043975",
  acknowledgement = ack-nhfb,
  fjournal =     "Theoretical Computer Science",
}

@Article{Amin:2007:TVA,
  author =       "Zeinab H. Amin",
  title =        "Tests for the Validity of the Assumption that the
                 Underlying Distribution of Life is {Pareto}",
  journal =      j-J-APPL-STAT,
  volume =       "34",
  number =       "2",
  pages =        "195--201",
  year =         "2007",
  coden =        "????",
  issn =         "0266-4763 (print), 1360-0532 (electronic)",
  issn-l =       "0266-4763",
  bibdate =      "Wed Aug 25 11:41:54 MDT 2010",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 http://www.tandf.co.uk/journals/routledge/02664763.html",
  acknowledgement = ack-nhfb,
}

@Article{Bakulina:2007:AZL,
  author =       "M. P. Bakulina",
  title =        "Application of {Zipf}'s law for text compression",
  journal =      "Diskretn. Anal. Issled. Oper. Ser. 2",
  volume =       "14",
  number =       "2",
  pages =        "3--13",
  year =         "2007",
  coden =        "????",
  issn =         "1560-9901",
  issn-l =       "1560-9901",
  mrclass =      "94A15",
  mrnumber =     "2542308 (2010i:94076)",
  mrreviewer =   "I. Vajda",
  bibdate =      "Sat Nov 12 09:13:23 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Diskretny{\u\i} Analiz i Issledovanie Operatsi{\u\i}.
                 Seriya 2",
}

@Article{Baskerville:2007:GAS,
  author =       "Kim Baskerville and Peter Grassberger and Maya
                 Paczuski",
  title =        "Graph animals, subgraph sampling, and motif search in
                 large networks",
  journal =      j-PHYS-REV-E,
  volume =       "76",
  number =       "??",
  pages =        "036107",
  day =          "11",
  month =        sep,
  year =         "2007",
  coden =        "PLEEE8",
  doi =          "http://dx.doi.org/10.1103/PhysRevE.76.036107",
  issn =         "1539-3755 (print), 1550-2376 (electronic)",
  issn-l =       "1539-3755",
  bibdate =      "Tue Feb 26 06:40:57 MST 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  url =          "http://link.aps.org/doi/10.1103/PhysRevE.76.036107",
  acknowledgement = ack-nhfb,
  fjournal =     "Physical Review E (Statistical physics, plasmas,
                 fluids, and related interdisciplinary topics)",
  keywords =     "Zipf's Law",
}

@Article{Benguigui:2007:DMC,
  author =       "Lucien Benguigui and Efrat Blumenfeld-Lieberthal",
  title =        "A dynamic model for city size distribution beyond
                 {Zipf}'s law",
  journal =      j-PHYSICA-A,
  volume =       "384",
  number =       "2",
  pages =        "613--627",
  day =          "15",
  month =        oct,
  year =         "2007",
  coden =        "PHYADX",
  doi =          "http://dx.doi.org/10.1016/j.physa.2007.05.059",
  issn =         "0378-4371 (print), 1873-2119 (electronic)",
  issn-l =       "0378-4371",
  bibdate =      "Wed Feb 27 07:32:55 MST 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  url =          "http://www.sciencedirect.com/science/article/pii/S0378437107006061",
  acknowledgement = ack-nhfb,
  fjournal =     "Physica A. Statistical Mechanics and its
                 Applications",
  keywords =     "Zipf's Law",
}

@Article{Berger:2007:DMN,
  author =       "A. Berger and S. Siegmund",
  title =        "On the distribution of mantissae in nonautonomous
                 difference equations",
  journal =      j-J-DIFFERENCE-EQU-APPL,
  volume =       "13",
  number =       "8--9",
  pages =        "829--845",
  month =        "????",
  year =         "2007",
  coden =        "JDEAEA",
  doi =          "http://dx.doi.org/10.1080/10236190701388039",
  issn =         "1023-6198 (print), 1563-5120 (electronic)",
  issn-l =       "1023-6198",
  mrclass =      "37A45 (37B55 39A11)",
  mrnumber =     "2343033 (2008j:37010)",
  mrreviewer =   "Reinhard Winkler",
  bibdate =      "Tue Feb 19 09:37:52 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  note =         "Second Memorial Issue in Honour of Bernd Aulbach.",
  url =          "http://www.math.ualberta.ca/~aberger/benford_bibliography/berger_siegmund_07.pdf",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Difference Equations and Applications",
  journal-url =  "http://www.informaworld.com/1023-6198",
}

@Article{Berger:2007:NMO,
  author =       "Arno Berger and Theodore P. Hill",
  title =        "{Newton}'s Method Obeys {Benford}'s Law",
  journal =      j-AMER-MATH-MONTHLY,
  volume =       "114",
  number =       "7",
  pages =        "588--601",
  month =        aug # "\slash " # sep,
  year =         "2007",
  coden =        "AMMYAE",
  issn =         "0002-9890 (print), 1930-0972 (electronic)",
  issn-l =       "0002-9890",
  mrclass =      "65G50 (37N30)",
  mrnumber =     "2341322 (2008h:65016)",
  mrreviewer =   "Uwe Sch{\"a}fer",
  bibdate =      "Mon Jan 30 12:00:29 MST 2012",
  bibsource =    "http://www.jstor.org/journals/00029890.html;
                 http://www.jstor.org/stable/i27642270;
                 http://www.math.utah.edu/pub/tex/bib/amermathmonthly2000.bib;
                 http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  url =          "http://www.jstor.org/stable/27642274",
  acknowledgement = ack-nhfb,
  fjournal =     "American Mathematical Monthly",
}

@Article{Bernik:2007:BLA,
  author =       "V. I. Bernik and N. I. Kalosha",
  title =        "{Benford}'s law and the approximation of logarithms of
                 natural numbers by rational numbers",
  journal =      "Vests{\=\i} Nats. Akad. Navuk Belarus{\=\i} Ser.
                 F{\=\i}z.-Mat. Navuk",
  volume =       "??",
  number =       "3",
  pages =        "68--73, 127",
  year =         "2007",
  coden =        "????",
  issn =         "0002-3574",
  issn-l =       "0002-3574",
  mrclass =      "11J83 (11A63 11K36)",
  mrnumber =     "2398318 (2008j:11084)",
  bibdate =      "Sat Nov 12 09:13:23 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Vests{\=\i} Natsyyanal\cprime na{\u\i}
                 Akad{\`e}m{\=\i} {\=\i} Navuk Belarus{\=\i}. Seryya
                 F{\=\i}z{\=\i}ka-Mat{\`e}matychnykh Navuk. Izvestiya
                 Natsional\cprime no{\u\i} Akademii Nauk Belarusi.
                 Seriya Fiziko-Matematicheskikh Nauk. Proceedings of the
                 National Academy of Sciences of Belarus. Physics and
                 Mathematics Series",
}

@Article{Brown:2007:UZL,
  author =       "R. J. C. Brown",
  title =        "The use of {Zipf}'s law in the screening of analytical
                 data: a step beyond {Benford}",
  journal =      j-ANALYST,
  volume =       "132",
  number =       "4",
  pages =        "344",
  year =         "2007",
  coden =        "ANALAO",
  doi =          "http://dx.doi.org/10.1039/b618255k",
  issn =         "0003-2654 (print), 1364-5528 (electronic)",
  issn-l =       "0003-2654",
  bibdate =      "Tue Nov 15 06:34:24 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  url =          "http://adsabs.harvard.edu/abs/2007Ana...132..344B",
  abstract =     "This study shows for the first time the effectiveness
                 of Zipf's law in screening analytical data sets for
                 outliers, data formatting and data transcription
                 errors, particularly when the data sets are small. In
                 the case of pollutant concentrations in ambient air,
                 the multivariate nature of the measurement, and the
                 relationship between the measured values of these
                 multivariant quantities are the characteristics that
                 allow a Zipf's law approach to data screening to be
                 successful. Furthermore, it has been shown that Zipf's
                 law has advantages over other novel data screening
                 techniques, such as Benford's law, in terms of
                 sensitivity and scope",
  acknowledgement = ack-nhfb,
  fjournal =     "The Analyst",
}

@Article{Chacko:2007:EPB,
  author =       "Manoj Chacko and P. Yageen Thomas",
  title =        "Estimation of a Parameter of Bivariate {Pareto}
                 Distribution by Ranked Set Sampling",
  journal =      j-J-APPL-STAT,
  volume =       "34",
  number =       "6",
  pages =        "703--714",
  year =         "2007",
  coden =        "????",
  issn =         "0266-4763 (print), 1360-0532 (electronic)",
  issn-l =       "0266-4763",
  bibdate =      "Wed Aug 25 11:41:54 MDT 2010",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 http://www.tandf.co.uk/journals/routledge/02664763.html",
  acknowledgement = ack-nhfb,
}

@Article{Cho:2007:BBL,
  author =       "Wendy K. Tam Cho and Brian J. Gaines",
  title =        "Breaking the ({Benford}) law: statistical fraud
                 detection in campaign finance",
  journal =      j-AMER-STAT,
  volume =       "61",
  number =       "3",
  pages =        "218--223",
  month =        aug,
  year =         "2007",
  coden =        "ASTAAJ",
  doi =          "http://dx.doi.org/10.1198/000313007X223496",
  issn =         "0003-1305 (print), 1537-2731 (electronic)",
  issn-l =       "0003-1305",
  mrnumber =     "2393725",
  bibdate =      "Sat Nov 12 09:13:23 2011",
  bibsource =    "http://www.amstat.org/publications/tas/;
                 http://www.math.utah.edu/pub/tex/bib/amstat2000.bib;
                 http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  url =          "http://pubs.amstat.org/doi/pdfplus/10.1198/000313007X223496;
                 http://www.tandfonline.com/doi/abs/10.1198/000313007X223496",
  abstract =     "Benford's law is seeing increasing use as a diagnostic
                 tool for isolating pockets of large datasets with
                 irregularities that deserve closer inspection. Popular
                 and academic accounts of campaign finance are rife with
                 tales of corruption, but the complete dataset of
                 transactions for federal campaigns is enormous.
                 Performing a systematic sweep is extremely arduous;
                 hence, these data are a natural candidate for initial
                 screening by comparison to Benford's distributions.",
  acknowledgement = ack-nhfb,
  fjournal =     "The American Statistician",
}

@Article{Clauset:2007:FST,
  author =       "Aaron Clauset and Maxwell Young and Kristian Skrede
                 Gleditsch",
  title =        "On the Frequency of Severe Terrorist Events",
  journal =      j-J-CONFL-RESOLUT,
  volume =       "51",
  number =       "1",
  pages =        "58--87",
  month =        feb,
  year =         "2007",
  coden =        "JCFRAL",
  doi =          "http://dx.doi.org/10.1177/0022002706296157",
  issn =         "0022-0027 (print), 1552-8766 (electronic)",
  issn-l =       "0022-0027",
  bibdate =      "Thu Nov 24 14:07:17 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  url =          "http://jcr.sagepub.com;
                 http://jcr.sagepub.com/content/51/1/58.abstract;
                 http://www.jstor.org/journals/00220027.html",
  abstract =     "In the spirit of Lewis Richardson's original study of
                 the statistics of deadly conflicts, we study the
                 frequency and severity of terrorist attacks worldwide
                 since 1968. We show that these events are uniformly
                 characterized by the phenomenon of ``scale
                 invariance,'' that is, the frequency scales as an
                 inverse power of the severity, $P(x) \approx
                 x{-\alpha}$. We find that this property is a robust
                 feature of terrorism, persisting when we control for
                 economic development of the target country, the type of
                 weapon used, and even for short time scales. Further,
                 we show that the center of the distribution oscillates
                 slightly with a period of roughly 13 years, that there
                 exist significant temporal correlations in the
                 frequency of severe events, and that current models of
                 event incidence cannot account for these variations or
                 the scale invariance property of global terrorism.
                 Finally, we describe a simple toy model for the
                 generation of these statistics and briefly discuss its
                 implications.",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Conflict Resolution",
}

@Article{Clauset:2007:PLD,
  author =       "Aaron Clauset and Cosma Rohilla Shalizi and M. E. J.
                 Newman",
  title =        "Power-law distributions in empirical data",
  journal =      "ArXiv Physics e-prints",
  day =          "7",
  month =        jun,
  year =         "2007",
  bibdate =      "Thu Feb 28 08:52:43 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  note =         "arXiv:0706.1062.",
  url =          "http://arxiv.org/abs/0706.1062v1",
  acknowledgement = ack-nhfb,
  pagecount =    "27",
}

@Article{Clauset:2007:PLDa,
  author =       "Aaron Clauset and Cosma Rohilla Shalizi and M. E. J.
                 Newman",
  title =        "Power-law distributions in empirical data",
  journal =      "ArXiv Physics e-prints",
  day =          "2",
  month =        feb,
  year =         "2009",
  doi =          "http://dx.doi.org/10.1137/070710111",
  bibdate =      "Thu Feb 28 08:52:43 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  note =         "arXiv:0706.1062.",
  url =          "http://arxiv.org/abs/0706.1062v1",
  acknowledgement = ack-nhfb,
  pagecount =    "43",
}

@Article{Decker:2007:GPC,
  author =       "Ethan H. Decker and Andrew J. Kerkhoff and Melanie E.
                 Moses",
  title =        "Global Patterns of City Size Distributions and Their
                 Fundamental Drivers",
  journal =      j-PLOS-ONE,
  volume =       "2",
  number =       "9",
  pages =        "e934",
  month =        sep,
  year =         "2007",
  coden =        "POLNCL",
  doi =          "http://dx.doi.org/10.1371/journal.pone.0000934",
  issn =         "1932-6203",
  bibdate =      "Wed Feb 27 06:29:22 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  url =          "http://www.plosone.org/article/info%3Adoi%2F10.1371%2Fjournal.pone.0000934",
  abstract =     "Urban areas and their voracious appetites are
                 increasingly dominating the flows of energy and
                 materials around the globe. Understanding the size
                 distribution and dynamics of urban areas is vital if we
                 are to manage their growth and mitigate their negative
                 impacts on global ecosystems. For over 50 years, city
                 size distributions have been assumed to universally
                 follow a power function, and many theories have been
                 put forth to explain what has become known as Zipf's
                 law (the instance where the exponent of the power
                 function equals unity). Most previous studies, however,
                 only include the largest cities that comprise the tail
                 of the distribution. Here we show that national,
                 regional and continental city size distributions,
                 whether based on census data or inferred from cluster
                 areas of remotely-sensed nighttime lights, are in fact
                 lognormally distributed through the majority of cities
                 and only approach power functions for the largest
                 cities in the distribution tails. To explore generating
                 processes, we use a simple model incorporating only two
                 basic human dynamics, migration and reproduction, that
                 nonetheless generates distributions very similar to
                 those found empirically. Our results suggest that
                 macroscopic patterns of human settlements may be far
                 more constrained by fundamental ecological principles
                 than more fine-scale socioeconomic factors.",
  acknowledgement = ack-nhfb,
  fjournal =     "PLoS One",
  keywords =     "Zipf's Law",
  pagecount =    "6",
}

@Article{Diekmann:2007:FDU,
  author =       "Andreas Diekmann",
  title =        "Not the First Digit! {Using} {Benford's Law} to Detect
                 Fraudulent Scientific Data",
  journal =      j-J-APPL-STAT,
  volume =       "34",
  number =       "3--4",
  pages =        "321--329",
  year =         "2007",
  coden =        "????",
  doi =          "http://dx.doi.org/10.1080/02664760601004940",
  issn =         "0266-4763 (print), 1360-0532 (electronic)",
  issn-l =       "0266-4763",
  mrnumber =     "2380543",
  bibdate =      "Sat Nov 12 09:13:23 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 http://www.tandf.co.uk/journals/routledge/02664763.html",
  url =          "http://www.tandfonline.com/doi/abs/10.1080/02664760601004940",
  abstract =     "Digits in statistical data produced by natural or
                 social processes are often distributed in a manner
                 described by `Benford's law'. Recently, a test against
                 this distribution was used to identify fraudulent
                 accounting data. This test is based on the supposition
                 that first, second, third, and other digits in real
                 data follow the Benford distribution while the digits
                 in fabricated data do not. Is it possible to apply
                 Benford tests to detect fabricated or falsified
                 scientific data as well as fraudulent financial data?
                 We approached this question in two ways. First, we
                 examined the use of the Benford distribution as a
                 standard by checking the frequencies of the nine
                 possible first and ten possible second digits in
                 published statistical estimates. Second, we conducted
                 experiments in which subjects were asked to fabricate
                 statistical estimates (regression coefficients). The
                 digits in these experimental data were scrutinized for
                 possible deviations from the Benford distribution.
                 There were two main findings. First, both digits of the
                 published regression coefficients were approximately
                 Benford distributed or at least followed a pattern of
                 monotonic decline. Second, the experimental results
                 yielded new insights into the strengths and weaknesses
                 of Benford tests. Surprisingly, first digits of faked
                 data also exhibited a pattern of monotonic decline,
                 while second, third, and fourth digits were distributed
                 less in accordance with Benford's law. At least in the
                 case of regression coefficients, there were indications
                 that checks for digit-preference anomalies should focus
                 less on the first (i.e., leftmost) and more on later
                 digits.",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Applied Statistics",
  keywords =     "Benford's Law; data fabrication; digital analysis;
                 distribution of digits from regression coefficients;
                 first digit law; Zipf's Law",
}

@Article{Dumbgen:2007:EBA,
  author =       "L. D{\"u}mbgen and C. Leuenberger",
  title =        "Explicit bounds for the approximation error in
                 {Benford}'s law",
  journal =      "ArXiv e-prints",
  month =        may,
  year =         "2007",
  coden =        "????",
  issn =         "????",
  bibdate =      "Tue Nov 15 06:34:24 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  url =          "http://adsabs.harvard.edu/abs/2007arXiv0705.4488D",
  acknowledgement = ack-nhfb,
  archiveprefix = "arXiv",
  eprint =       "0705.4488",
  keywords =     "Mathematics - Probability, 60E15, 60F99",
  primaryclass = "math.PR",
}

@Article{Egghe:2007:UHL,
  author =       "Leo Egghe",
  title =        "Untangling {Herdan's Law} and {Heaps' Law}:
                 Mathematical and informetric arguments",
  journal =      j-J-AM-SOC-INF-SCI-TECHNOL,
  volume =       "58",
  number =       "5",
  pages =        "702--709",
  year =         "2007",
  coden =        "JASIEF",
  doi =          "http://dx.doi.org/10.1002/asi.20524",
  issn =         "1532-2890",
  issn-l =       "1532-2882",
  bibdate =      "Mon Feb 25 08:31:49 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of the American Society for Information Science and Technology",
  keywords =     "Herdan's law in linguistics; Heaps' law in
                 information retrieval",
}

@InProceedings{Fu:2007:GBL,
  author =       "D. Fu and Y. Q. Shi and W. Su",
  editor =       "Edward J. {Delp III} and Ping Wah Wong",
  booktitle =    "{Society of Photo-Optical Instrumentation Engineers
                 (SPIE)} Conference Series",
  title =        "A generalized {Benford}'s law for {JPEG} coefficients
                 and its applications in image forensics",
  volume =       "6505",
  publisher =    pub-SPIE,
  address =      pub-SPIE:adr,
  month =        feb,
  year =         "2007",
  doi =          "http://dx.doi.org/10.1117/12.704723",
  issn =         "0277-786X (print), 1996-756X (electronic)",
  bibdate =      "Tue Nov 15 06:34:24 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  series =       "Society of Photo-Optical Instrumentation Engineers
                 (SPIE) Conference Series",
  url =          "http://adsabs.harvard.edu/abs/2007SPIE.6505E..55F",
  acknowledgement = ack-nhfb,
}

@Article{Giles:2007:BLN,
  author =       "D. E. Giles",
  title =        "{Benford's Law} and naturally occurring prices in
                 certain {eBay} auctions",
  journal =      j-APPL-ECON-LETT,
  volume =       "14",
  number =       "3",
  pages =        "157--161",
  year =         "2007",
  coden =        "????",
  doi =          "http://dx.doi.org/10.1080/13504850500425667",
  issn =         "1350-4851 (print), 1466-4291 (electronic)",
  issn-l =       "1350-4851",
  bibdate =      "Wed Nov 16 09:49:53 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  url =          "http://www.tandfonline.com/toc/rael20/current",
  acknowledgement = ack-nhfb,
  fjournal =     "Applied Economics Letters",
  keywords =     "Benford's Law; Fibonacci sequences; Lucas sequences",
}

@Article{Grendar:2007:ENP,
  author =       "Marian Grendar and George Judge and Laura Schechter",
  title =        "An empirical non-parametric likelihood family of
                 data-based {Benford}-like distributions",
  journal =      j-PHYSICA-A,
  volume =       "380",
  number =       "??",
  pages =        "429--438",
  day =          "1",
  month =        jul,
  year =         "2007",
  coden =        "PHYADX",
  doi =          "http://dx.doi.org/10.1016/j.physa.2007.02.062",
  issn =         "0378-4371 (print), 1873-2119 (electronic)",
  issn-l =       "0378-4371",
  bibdate =      "Tue Nov 22 11:28:19 MST 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 http://www.sciencedirect.com/",
  url =          "http://adsabs.harvard.edu/abs/2007PhyA..380..429G;
                 http://www.sciencedirect.com/science/article/pii/S0378437107001963",
  acknowledgement = ack-nhfb,
  fjournal =     "Physica A: Statistical Mechanics and its
                 Applications",
  keywords =     "Benford's Law",
}

@Article{Guo:2007:DIM,
  author =       "Lei Guo and Enhua Tan and Songqing Chen and Zhen Xiao
                 and Xiaodong Zhang",
  title =        "Does {Internet} media traffic really follow
                 {Zipf}-like distribution?",
  journal =      j-SIGMETRICS,
  volume =       "35",
  number =       "1",
  pages =        "359--360",
  month =        jun,
  year =         "2007",
  coden =        "????",
  doi =          "http://doi.acm.org/10.1145/1254882.1254929",
  issn =         "0163-5999 (print), 1557-9484 (electronic)",
  issn-l =       "0163-5999",
  bibdate =      "Fri Jun 27 09:42:48 MDT 2008",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 http://www.math.utah.edu/pub/tex/bib/sigmetrics.bib",
  abstract =     "It is commonly agreed that Web traffic follows the
                 Zipf-like distribution, which is an analytical
                 foundation for improving Web access performance by
                 client-server based proxy caching systems on the
                 Internet. However, some recent studies have observed
                 non-Zipf-like distributions of Internet media traffic
                 in different content delivery systems. Due to the
                 variety of media delivery systems and the diversity of
                 media content, existing studies on media traffic are
                 largely workload specific, and the observed access
                 patterns are often different from or even conflict with
                 each other. For Web media systems, study [3] reports
                 that the access pattern of streaming media is Zipf-like
                 in a university campus network, while study [2] finds
                 that it is not Zipf-like in an enterprise media
                 server.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM SIGMETRICS Performance Evaluation Review",
  keywords =     "media; stretched exponential; Zipf-like",
}

@Article{Gupta:2007:IMS,
  author =       "Arjun K. Gupta and Saralees Nadarajah",
  title =        "Information matrices for some bivariate {Pareto}
                 distributions",
  journal =      j-APPL-MATH-COMP,
  volume =       "184",
  number =       "2",
  pages =        "1069--1079",
  day =          "15",
  month =        jan,
  year =         "2007",
  coden =        "AMHCBQ",
  issn =         "0096-3003 (print), 1873-5649 (electronic)",
  issn-l =       "0096-3003",
  bibdate =      "Sat Jul 12 09:03:01 MDT 2008",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/applmathcomput2005.bib;
                 http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 http://www.sciencedirect.com/science/journal/00963003",
  acknowledgement = ack-nhfb,
  fjournal =     "Applied Mathematics and Computation",
}

@Article{Hand:2007:DDD,
  author =       "David Hand",
  title =        "Deception and Dishonesty with Data: Fraud in Science",
  journal =      j-SIGNIF,
  volume =       "4",
  number =       "1",
  pages =        "22--25",
  month =        mar,
  year =         "2007",
  coden =        "????",
  doi =          "http://dx.doi.org/10.1111/j.1740-9713.2007.00215.x",
  issn =         "1740-9705 (print), 1740-9713 (electronic)",
  issn-l =       "1740-9705",
  bibdate =      "Thu Nov 17 19:17:58 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Significance ({Oxford, England})",
}

@Article{Hasumi:2007:ITS,
  author =       "Tomohiro Hasumi",
  title =        "Interoccurrence time statistics in the two-dimensional
                 {Burridge--Knopoff} earthquake model",
  journal =      j-PHYS-REV-E,
  volume =       "76",
  number =       "??",
  pages =        "026117",
  day =          "29",
  month =        aug,
  year =         "2007",
  coden =        "PLEEE8",
  doi =          "http://dx.doi.org/10.1103/PhysRevE.76.026117",
  issn =         "1539-3755 (print), 1550-2376 (electronic)",
  issn-l =       "1539-3755",
  bibdate =      "Tue Feb 26 06:40:57 MST 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  url =          "http://link.aps.org/doi/10.1103/PhysRevE.76.026117",
  acknowledgement = ack-nhfb,
  fjournal =     "Physical Review E (Statistical physics, plasmas,
                 fluids, and related interdisciplinary topics)",
  keywords =     "Zipf--Mandelbrot law",
}

@TechReport{Hungerbuhler:2007:BGF,
  author =       "Norbert H{\"u}ngerb{\"u}hler",
  title =        "{Benfords Gesetz {\"u}ber f{\"u}hrende Ziffern. Wie
                 die Mathematik Steuers{\"u}ndern das F{\"u}rchten
                 lehrt} [{Benford's Law} on leading digits. Mathematics
                 teaches tax evaders to fear]",
  type =         "Report",
  institution =  "EducETH",
  address =      "Z{\"u}rich, Switzerland",
  pages =        "24",
  day =          "2",
  month =        mar,
  year =         "2007",
  bibdate =      "Fri Nov 18 12:02:21 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  url =          "http://www.educ.ethz.ch/unt/um/mathe/ana/benford/Benford_Fuehrende_Ziffern.pdf",
  acknowledgement = ack-nhfb,
  language =     "German",
  lastaccess =   "18 November 2011",
  remark =       "This report has several nice figures, including
                 photographs of Newcomb, Benford, and worn pages of log
                 tables, and an amazing plot of the agreement of
                 200,125,088 mathematical constants with Benford's
                 Law.",
}

@Article{Kumar:2007:DDD,
  author =       "Kuldeep Kumar and Sukanto Bhattacharya",
  title =        "Detecting the dubious digits: {Benford}'s law in
                 forensic accounting",
  journal =      j-SIGNIF,
  volume =       "4",
  number =       "2",
  pages =        "81--83",
  month =        jun,
  year =         "2007",
  coden =        "????",
  doi =          "http://dx.doi.org/10.1111/j.1740-9713.2007.00234.x",
  issn =         "1740-9705 (print), 1740-9713 (electronic)",
  issn-l =       "1740-9705",
  mrnumber =     "2380610",
  bibdate =      "Sat Nov 12 09:13:23 2011",
  bibsource =    "http://onlinelibrary.wiley.com/;
                 http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Significance ({Oxford, England})",
  onlinedate =   "7 Jun 2007",
}

@Article{Mansury:2007:EZL,
  author =       "Yuri Mansury and L{\'a}szl{\'o} Guly{\'a}s",
  title =        "The emergence of {Zipf's Law} in a system of cities:
                 an agent-based simulation approach",
  journal =      j-J-ECON-DYN-CONTROL,
  volume =       "31",
  number =       "7",
  pages =        "2438--2460",
  day =          "15",
  month =        jul,
  year =         "2007",
  coden =        "JEDCDH",
  doi =          "http://dx.doi.org/10.1016/j.jedc.2006.08.002",
  issn =         "0165-1889 (print), 1879-1743 (electronic)",
  issn-l =       "0165-1889",
  bibdate =      "Wed Feb 27 07:32:55 MST 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  url =          "http://www.sciencedirect.com/science/article/pii/S0165188906001527",
  zmnumber =     "1163.91504",
  abstract =     "This paper develops a spatial agent-based model to
                 generate a system of cities that exhibits the
                 statistical properties of the Zipf's Law. The numerical
                 results suggest that the combination of bounded
                 rationality and maximum heterogeneity of agents can
                 produce a generic power-law relationship in the size
                 distribution of cities, but does not always generate
                 the Zipf's Law. We found sufficient conditions on the
                 probability distribution of spatial reach to generate
                 the Zipf's Law associated with unit power coefficient.
                 Our model also indicates that the Zipf's Law breaks
                 down unless the extent of agglomeration economies
                 overwhelms the negative disagglomerating forces.",
  acknowledgement = ack-nhfb,
  classmath =    "91B72 (Spatial models)",
  fjournal =     "Journal of Economic Dynamics and Control",
  keywords =     "complex systems; power laws; spatial agent based
                 models; Zipf's Law",
}

@Article{Maslov:2007:PTZ,
  author =       "V. P. Maslov",
  title =        "Phase transitions of the zeroth kind and the
                 quantization of the {Zipf} law",
  journal =      j-TEORET-MATH-FIZ,
  volume =       "150",
  number =       "1",
  pages =        "118--142",
  year =         "2007",
  coden =        "TMFZAL",
  doi =          "http://dx.doi.org/10.1007/s11232-007-0008-1",
  issn =         "0564-6162",
  issn-l =       "0564-6162",
  mrclass =      "82B26 (82B03)",
  mrnumber =     "2325869 (2008g:82037)",
  mrreviewer =   "N. N. Ganikhodjaev",
  bibdate =      "Sat Nov 12 09:13:23 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Rossi{\u\i}skaya Akademiya Nauk. Teoreticheskaya i
                 Matematicheskaya Fizika",
}

@InProceedings{Mebane:2007:SD,
  author =       "Walter R. {Mebane, Jr.}",
  editor =       "????",
  booktitle =    "{2007 Summer Meeting of the Political Methodology
                 Society, Pennsylvania State University, July 18--21,
                 2007}",
  title =        "Statistics for Digits",
  publisher =    "????",
  address =      "????",
  pages =        "1--21",
  day =          "2",
  month =        jul,
  year =         "2007",
  isbn =         "????",
  isbn-13 =      "????",
  lccn =         "????",
  bibdate =      "Sat Feb 16 12:03:01 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  url =          "http://www.umich.edu/~wmebane/pm07.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "Benford's Law",
}

@Article{Nadarajah:2007:CPG,
  author =       "Saralees Nadarajah and Samuel Kotz",
  title =        "On the convolution of {Pareto} and gamma
                 distributions",
  journal =      j-COMP-NET-AMSTERDAM,
  volume =       "51",
  number =       "12",
  pages =        "3650--3654",
  day =          "22",
  month =        aug,
  year =         "2007",
  coden =        "????",
  issn =         "1389-1286 (print), 1872-7069 (electronic)",
  issn-l =       "1389-1286",
  bibdate =      "Sat Apr 2 08:42:20 MDT 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 http://www.sciencedirect.com/science/journal/13891286",
  acknowledgement = ack-nhfb,
  fjournal =     "Computer Networks",
}

@Article{Nicolaisen:2007:PPB,
  author =       "Jeppe Nicolaisen and Birger Hj{\o}rland",
  title =        "Practical potentials of {Bradford}'s law: a critical
                 examination of the received view",
  journal =      j-J-DOC,
  volume =       "63",
  number =       "3",
  pages =        "359--377",
  month =        "????",
  year =         "2007",
  coden =        "JDOCAS",
  doi =          "http://dx.doi.org/10.1108/00220410710743298",
  issn =         "0022-0418 (print), 1758-7379 (electronic)",
  issn-l =       "0022-0418",
  bibdate =      "Fri Nov 25 11:58:03 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Documentation",
}

@Article{Nigrini:2007:BLA,
  author =       "Mark J. Nigrini and Steven J. Miller",
  title =        "{Benford's Law} Applied to Hydrology Data --- Results
                 and Relevance to Other Geophysical Data",
  journal =      j-MATH-GEOL,
  volume =       "39",
  number =       "5",
  pages =        "469--490",
  month =        jul,
  year =         "2007",
  coden =        "MATGED",
  doi =          "http://dx.doi.org/10.1007/s11004-007-9109-5",
  issn =         "0882-8121 (print), 1573-8868 (electronic)",
  issn-l =       "0882-8121",
  bibdate =      "Sun Feb 17 13:35:42 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  url =          "http://link.springer.com/article/10.1007%2Fs11004-007-9109-5;
                 http://www.springerlink.com/content/m2274ng70435u3x6/",
  acknowledgement = ack-nhfb,
  fjournal =     "Mathematical Geology",
}

@Article{Nye:2007:PEN,
  author =       "J. Nye and C. Moul",
  title =        "The Political Economy of Numbers: On the Application
                 of {Benford's Law} to International Macroeconomic
                 Statistics",
  journal =      "{B. E.} Journal of Macroeconomics",
  volume =       "7",
  number =       "1",
  pages =        "??--??",
  month =        "????",
  year =         "2007",
  coden =        "????",
  doi =          "http://dx.doi.org/10.2202/1935-1690.1449",
  issn =         "1935-1690",
  issn-l =       "1935-1690",
  bibdate =      "Tue Nov 22 20:48:42 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  url =          "http://www.bepress.com/bejm/vol7/iss1/art17",
  acknowledgement = ack-nhfb,
  articleno =    "17",
  fjournal =     "Berkeley Electronic Press Journal of Macroeconomics",
}

@Article{Oteo:2007:DPE,
  author =       "J. A. Oteo and J. Ros",
  title =        "Double precision errors in the logistic map:
                 Statistical study and dynamical interpretation",
  journal =      j-PHYS-REV-E,
  volume =       "76",
  pages =        "036214",
  month =        sep,
  year =         "2007",
  coden =        "PLEEE8",
  doi =          "http://dx.doi.org/10.1103/PhysRevE.76.036214",
  issn =         "1539-3755 (print), 1550-2376 (electronic)",
  issn-l =       "1539-3755",
  bibdate =      "Tue Feb 26 06:35:43 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  url =          "http://link.aps.org/doi/10.1103/PhysRevE.76.036214",
  acknowledgement = ack-nhfb,
  fjournal =     "Physical Review E (Statistical physics, plasmas,
                 fluids, and related interdisciplinary topics)",
  issue =        "3",
  pagecount =    "8",
  remark =       "From the abstract: ``a comparison with Benford?s law
                 for the distribution of the leading digit of
                 compilation of numbers is discussed.''",
}

@Article{Paech:2007:ZLN,
  author =       "Kerstin Paech and Wolfgang Bauer and Scott Pratt",
  title =        "{Zipf}'s law in nuclear multifragmentation and
                 percolation theory",
  journal =      j-PHYS-REV-C,
  volume =       "76",
  number =       "??",
  pages =        "054603",
  day =          "15",
  month =        nov,
  year =         "2007",
  coden =        "PRVCAN",
  doi =          "http://dx.doi.org/10.1103/PhysRevC.76.054603",
  issn =         "0556-2813 (print), 1089-490X, 1538-4497",
  issn-l =       "0556-2813",
  bibdate =      "Tue Feb 26 06:40:57 MST 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  url =          "http://link.aps.org/doi/10.1103/PhysRevC.76.054603",
  acknowledgement = ack-nhfb,
  fjournal =     "Physical Review C (Nuclear Physics)",
  keywords =     "Zipf's Law",
}

@Article{Simons:2007:SIP,
  author =       "John L. Simons",
  title =        "A simple (inductive) proof for the non-existence of
                 2-cycles of the $3 x + 1$ problem",
  journal =      j-J-NUMBER-THEORY,
  volume =       "123",
  number =       "1",
  pages =        "10--17",
  month =        mar,
  year =         "2007",
  coden =        "JNUTA9",
  doi =          "http://dx.doi.org/10.1016/j.jnt.2006.05.011",
  issn =         "0022-314X (print), 1096-1658 (electronic)",
  issn-l =       "0022-314X",
  bibdate =      "Tue Nov 22 11:28:19 MST 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 http://www.sciencedirect.com/",
  url =          "http://www.sciencedirect.com/science/article/pii/S0022314X06001223",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Number Theory",
  keywords =     "Benford's Law",
}

@Book{Tijms:2007:UPC,
  author =       "H. C. Tijms",
  title =        "Understanding probability: chance rules in everyday
                 life",
  publisher =    pub-CAMBRIDGE,
  address =      pub-CAMBRIDGE:adr,
  edition =      "Second",
  pages =        "x + 442",
  year =         "2007",
  isbn =         "0-511-34626-3 (e-book), 0-511-35003-1 (e-book),
                 0-521-70172-4 (paperback)",
  isbn-13 =      "978-0-511-34626-2 (e-book), 978-0-511-35003-0
                 (e-book), 978-0-521-70172-3 (paperback)",
  lccn =         "QA273 .T48 2007",
  bibdate =      "Mon Feb 18 06:48:08 MST 2013",
  bibsource =    "fsz3950.oclc.org:210/WorldCat;
                 http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Benford's Law",
  subject =      "Probabilities; Mathematical analysis; Chance;
                 Mathematics; Probability and Statistics; General;
                 Waarschijnlijkheidstheorie;
                 Wahrscheinlichkeitsverteilung",
  tableofcontents = "Probability questions \\
                 The law of large numbers and simulation \\
                 Probabilities in everyday life \\
                 Rare events and lotteries \\
                 Probability and statistics \\
                 Chance trees and Bayes' rule \\
                 Foundations of probability theory \\
                 Conditional probability and Bayes \\
                 Basic rules for discrete random variables \\
                 Continuous random variables \\
                 Jointly distributed random variables \\
                 Multivariate normal distribution \\
                 Conditional distributions \\
                 Generating functions \\
                 Markov chains",
}

@Article{Torres:2007:HDN,
  author =       "J. Torres and S. Fern{\'a}ndez and A. Gamero and A.
                 Sola",
  title =        "How do numbers begin? (the first digit law)",
  journal =      j-EUR-J-PHYS,
  volume =       "28",
  number =       "3",
  pages =        "L17--L25",
  month =        may,
  year =         "2007",
  coden =        "EJPHD4",
  doi =          "http://dx.doi.org/10.1088/0143-0807/28/3/N04",
  issn =         "0143-0807 (print), 1361-6404 (electronic)",
  issn-l =       "0143-0807",
  bibdate =      "Fri Feb 15 18:37:16 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  url =          "http://iopscience.iop.org/0143-0807/28/3/N04",
  acknowledgement = ack-nhfb,
  fjournal =     "European Journal of Physics",
  keywords =     "Benford's Law; Frank Benford; Simon Newcomb",
  remark-1 =     "From page L19: ``He [Newcomb] founded the American
                 Astronomical Society, and was its first president; he
                 was a successful scientist.''.",
  remark-2 =     "From page L19: ``His [Newcomb's] discovery went
                 unnoticed by the scientific community, in spite of the
                 fact that Newcomb was already a famous scientist at the
                 time. He continued working in physical and mathematical
                 astronomy, receiving honours for his career --- a
                 crater of Mars takes his name --- but he was also
                 responsible for a famous funny mistake: he tried to
                 demonstrate that an object heavier than air could not
                 fly, just months before the Wright brothers' first
                 one-man aeroplane flew in 1903. Far from retracting,
                 Newcomb said that an aeroplane for two or more people
                 could not fly, so aeroplanes would not be worthwhile
                 pursuing [3, 4]. He died in 1909, without even
                 remembering the matter of the first significant digit
                 law.'',",
  remark-3 =     "From page L19: ``Frank Benford, a physicist working at
                 General Electric (who was the inventor of the electric
                 light pointer), \ldots{}''.",
}

@Article{Wells:2007:QPV,
  author =       "K. Wells and J. Chiverton and M. Partridge and M.
                 Barry and H. Kadhem and B. Ott",
  title =        "Quantifying the Partial Volume Effect in {PET} Using
                 {Benford's Law}",
  journal =      j-IEEE-TRANS-NUCL-SCI,
  volume =       "54",
  number =       "5",
  pages =        "1616--1625",
  month =        oct,
  year =         "2007",
  coden =        "IRNSAM",
  doi =          "http://dx.doi.org/10.1109/TNS.2007.903182",
  issn =         "0018-9499 (print), 1558-1578 (electronic)",
  issn-l =       "0018-9499",
  bibdate =      "Tue Nov 15 06:34:24 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  url =          "http://adsabs.harvard.edu/abs/2007ITNS...54.1616W",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Nuclear Science",
}

@Article{Yeh:2007:SMD,
  author =       "Hsiaw-Chan Yeh",
  title =        "Some multivariate discrete time series models for
                 dependent multivariate {Zipf} counts",
  journal =      "Bulletin of the Institute of Mathematics. Academia
                 Sinica. New Series",
  volume =       "2",
  number =       "1",
  pages =        "29--53",
  year =         "2007",
  coden =        "????",
  issn =         "0304-9825",
  issn-l =       "0304-9825",
  mrclass =      "62M10 (62H20)",
  mrnumber =     "2294107",
  bibdate =      "Sat Nov 12 09:13:23 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  ajournal =     "Bull. Inst. Math. Acad. Sin. (N.S.)",
  fjournal =     "Bulletin of the Institute of Mathematics. Academia
                 Sinica. New Series",
}

@Article{Aono:2008:ISO,
  author =       "June Y. Aono and Liming Guan",
  title =        "The impact of {Sarbanes--Oxley} act on cosmetic
                 earnings management",
  journal =      "Research in Accounting Regulation",
  volume =       "20",
  number =       "??",
  pages =        "205--215",
  month =        oct,
  year =         "2008",
  coden =        "????",
  doi =          "http://dx.doi.org/10.1016/S1052-0457(07)00212-3",
  issn =         "1052-0457",
  issn-l =       "1052-0457",
  bibdate =      "Tue Nov 22 11:28:19 MST 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 http://www.sciencedirect.com/",
  url =          "http://www.sciencedirect.com/science/article/pii/S1052045707002123",
  acknowledgement = ack-nhfb,
  fjournal =     "Research in Accounting Regulation",
  keywords =     "Benford's Law",
}

@Article{Batty:2008:PSS,
  author =       "Michael Batty",
  title =        "Perspective: The Size, Scale, and Shape of Cities",
  journal =      j-SCIENCE,
  volume =       "318",
  number =       "5864",
  pages =        "769--771",
  day =          "8",
  month =        feb,
  year =         "2008",
  coden =        "SCIEAS",
  doi =          "http://dx.doi.org/10.1126/science.1151419",
  issn =         "0036-8075 (print), 1095-9203 (electronic)",
  issn-l =       "0036-8075",
  bibdate =      "Wed Feb 27 06:02:28 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  url =          "http://www.sciencemag.org/content/319/5864/769.abstract",
  acknowledgement = ack-nhfb,
  fjournal =     "Science",
  keywords =     "US cities of one million (or more) population; 200 tallest buildings in world;
Zipf's law",
}

@Article{Bhattacharya:2008:FAB,
  author =       "S. Bhattacharya and K. Kumar",
  title =        "Forensic Accounting and {Benford's Law} [In the
                 Spotlight]",
  journal =      j-IEEE-SIGNAL-PROCESS-MAG,
  volume =       "25",
  number =       "2",
  pages =        "152--150",
  month =        mar,
  year =         "2008",
  coden =        "ISPRE6",
  doi =          "http://dx.doi.org/10.1109/MSP.2007.914724",
  issn =         "1053-5888 (print), 1558-0792 (electronic)",
  issn-l =       "1053-5888",
  bibdate =      "Tue Nov 15 06:34:24 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  url =          "http://adsabs.harvard.edu/abs/2008ISPM...25..152B",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE signal processing magazine",
}

@Article{Chakravorty:2008:TAE,
  author =       "Douglas N. Hales and V. Sridharan and Abirami
                 Radhakrishnan and Satya S. Chakravorty and Samia M.
                 Siha",
  title =        "Testing the accuracy of employee-reported data: An
                 inexpensive alternative approach to traditional
                 methods",
  journal =      j-EUR-J-OPER-RES,
  volume =       "189",
  number =       "3",
  pages =        "583--593",
  day =          "16",
  month =        sep,
  year =         "2008",
  coden =        "EJORDT",
  doi =          "http://dx.doi.org/10.1016/j.ejor.2006.09.092",
  issn =         "0377-2217 (print), 1872-6860 (electronic)",
  issn-l =       "0377-2217",
  bibdate =      "Tue Nov 22 11:28:19 MST 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 http://www.sciencedirect.com/",
  url =          "http://www.sciencedirect.com/science/article/pii/S0377221706011702",
  acknowledgement = ack-nhfb,
  fjournal =     "European Journal of Operational Research",
  keywords =     "Benford's Law",
  xxauthor =     "S. Chakravorty and Samia M. Siha",
}

@Article{Costas:2008:NCC,
  author =       "Eduardo Costas and Victoria L{\'o}pez-Rodas and F.
                 Javier Toro and Antonio Flores-Moya",
  title =        "The number of cells in colonies of the cyanobacterium
                 {{\em Microcystis aeruginosa\/}} satisfies {Benford}'s
                 law",
  journal =      j-AQUAT-BOT,
  volume =       "89",
  number =       "3",
  pages =        "341--343",
  month =        oct,
  year =         "2008",
  coden =        "AQBODS",
  doi =          "http://dx.doi.org/10.1016/j.aquabot.2008.03.011",
  issn =         "0304-3770 (print), 1879-1522 (electronic)",
  issn-l =       "0304-3770",
  bibdate =      "Tue Nov 22 11:28:19 MST 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 http://www.sciencedirect.com/",
  url =          "http://www.sciencedirect.com/science/article/pii/S0304377008000533",
  acknowledgement = ack-nhfb,
  fjournal =     "Aquatic Botany",
  keywords =     "Benford's Law",
}

@Article{Depken:2008:BZB,
  author =       "Craig A. {Depken II}",
  title =        "{Benford}, {Zipf} and the blogosphere",
  journal =      j-APPL-ECON-LETT,
  volume =       "15",
  number =       "9",
  pages =        "689--692",
  month =        "????",
  year =         "2008",
  doi =          "http://dx.doi.org/10.1080/13504850600735270",
  issn =         "1350-4851 (print), 1466-4291 (electronic)",
  issn-l =       "1350-4851",
  bibdate =      "Sat Jan 07 09:18:33 2012",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  url =          "http://www.tandfonline.com/doi/abs/10.1080/13504850600735270",
  acknowledgement = ack-nhfb,
  fjournal =     "Applied Economics Letters",
  onlinedate =   "04 Jul 2008",
}

@Article{Dumbgen:2008:EBA,
  author =       "Lutz D{\"u}mbgen and Christoph Leuenberger",
  title =        "Explicit bounds for the approximation error in
                 {Benford}'s law",
  journal =      j-ELECTRON-COMMUN-PROBAB,
  volume =       "13",
  pages =        "99--112",
  year =         "2008",
  coden =        "????",
  issn =         "1083-589X",
  issn-l =       "1083-589X",
  mrclass =      "60E15 (60F99)",
  mrnumber =     "2386066 (2009b:60056)",
  mrreviewer =   "Pieter C. Allaart",
  bibdate =      "Sat Nov 12 09:13:23 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  url =          "http://arxiv.org/abs/0705.4488;
                 http://weber.math.washington.edu/~ejpecp/ECP/index.php",
  abstract =     "Benford's law states that for many random variables $X
                 > 0$ its leading digit $D = D(X)$ satisfies
                 approximately the equation $P(D = d) = log_{10}(1 +
                 1/d)$ for $d = 1, 2, \ldots{}, 9$. This phenomenon
                 follows from another, maybe more intuitive fact,
                 applied to $Y:= log_{10}(X)$: For many real random
                 variables $Y$, the remainder $U:= Y - floor(Y)$ is
                 approximately uniformly distributed on $[0,1)$. The
                 present paper provides new explicit bounds for the
                 latter approximation in terms of the total variation of
                 the density of $Y$ or some derivative of it. These
                 bounds are an interesting alternative to traditional
                 Fourier methods which yield mostly qualitative results.
                 As a by-product we obtain explicit bounds for the
                 approximation error in Benford's law.",
  acknowledgement = ack-nhfb,
  fjournal =     "Electronic Communications in Probability",
}

@Article{Gauvrit:2008:PLB,
  author =       "Nicolas Gauvrit and Jean-Paul Delahaye",
  title =        "Pourquoi la loi de {Benford} n'est pas
                 myst{\'e}rieuse. ({French}) [{Why} {Benford}'s law is
                 not mysterious]",
  journal =      "Math{\'e}matiques et Sciences Humaines = Mathematics
                 and Social Sciences",
  volume =       "46",
  number =       "182",
  pages =        "7--15",
  year =         "2008",
  coden =        "????",
  issn =         "0987-6936 (print), 1950-6821 (electronic)",
  issn-l =       "0987-6936",
  mrclass =      "62A01 (91E10)",
  mrnumber =     "2433183 (2009f:62008)",
  bibdate =      "Sat Nov 12 09:13:23 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  url =          "http://www.ehess.fr/revue-msh/pdf/N182R1280.pdf",
  acknowledgement = ack-nhfb,
  ajournal =     "Math. Sci. Hum. Math. Soc. Sci.",
  fjournal =     "Math{\'e}matiques et Sciences Humaines= Mathematics
                 and Social Sciences",
  language =     "French",
}

@Article{Hefeeda:2008:TMP,
  author =       "Mohamed Hefeeda and Osama Saleh",
  title =        "Traffic modeling and proportional partial caching for
                 peer-to-peer systems",
  journal =      j-IEEE-TRANS-NETWORKING,
  volume =       "16",
  number =       "6",
  pages =        "1447--1460",
  month =        dec,
  year =         "2008",
  coden =        "IEANEP",
  doi =          "http://dx.doi.org/10.1109/TNET.2008.918081",
  issn =         "1063-6692 (print), 1558-2566 (electronic)",
  issn-l =       "1063-6692",
  bibdate =      "Fri Mar 6 16:31:04 MST 2009",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 http://www.math.utah.edu/pub/tex/bib/ieeetransnetworking.bib",
  abstract =     "Peer-to-peer (P2P) file sharing systems generate a
                 major portion of the Internet traffic, and this portion
                 is expected to increase in the future. We explore the
                 potential of deploying proxy caches in different
                 Autonomous Systems (ASes) with the goal of reducing the
                 cost incurred by Internet service providers and
                 alleviating the load on the Internet backbone. We
                 conduct an eight-month measurement study to analyze the
                 P2P traffic characteristics that are relevant to
                 caching, such as object popularity, popularity
                 dynamics, and object size. Our study shows that the
                 popularity of P2P objects can be modeled by a
                 Mandelbrot-Zipf distribution, and that several
                 workloads exist in P2P traffic. Guided by our findings,
                 we develop a novel caching algorithm for P2P traffic
                 that is based on object segmentation, and proportional
                 partial admission and eviction of objects. Our
                 trace-based simulations show that with a relatively
                 small cache size, a byte hit rate of up to 35\% can be
                 achieved by our algorithm, which is close to the byte
                 hit rate achieved by an off-line optimal algorithm with
                 complete knowledge of future requests. Our results also
                 show that our algorithm achieves a byte hit rate that
                 is at least 40\% more, and at most triple, the byte hit
                 rate of the common web caching algorithms. Furthermore,
                 our algorithm is robust in face of aborted downloads,
                 which is a common case in P2P systems.",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE\slash ACM Transactions on Networking",
  keywords =     "internet measurement; network protocols; peer-to-peer
                 systems; traffic analysis; traffic modeling",
}

@Article{Huang:2008:IZL,
  author =       "Shi-Ming Huang and David C. Yen and Luen-Wei Yang and
                 Jing-Shiuan Hua",
  title =        "An investigation of {Zipf's Law} for fraud detection
                 {(DSS\# 06-10-1826R(2))}",
  journal =      j-DEC-SUPP-SYS,
  volume =       "46",
  number =       "1",
  pages =        "70--83",
  month =        dec,
  year =         "2008",
  coden =        "DSSYDK",
  doi =          "http://dx.doi.org/10.1016/j.dss.2008.05.003",
  issn =         "0167-9236 (print), 1873-5797 (electronic)",
  issn-l =       "0167-9236",
  bibdate =      "Wed Feb 27 07:32:55 MST 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 http://www.sciencedirect.com/",
  url =          "http://www.sciencedirect.com/science/article/pii/S0167923608001073",
  acknowledgement = ack-nhfb,
  fjournal =     "Decision Support Systems",
  keywords =     "Benford's Law; Zipf's Law",
}

@Article{Humenberger:2008:EBB,
  author =       "H. Humenberger",
  title =        "{Eine elementarmathematische Begr{\"u}ndung des
                 Benford-Gesetzes}. ({German}) [{An} elementary
                 mathematical derivation of the {Benford Law}]",
  journal =      "Der Mathematikunterricht",
  volume =       "54",
  number =       "??",
  pages =        "24--34",
  month =        "????",
  year =         "2008",
  coden =        "????",
  issn =         "0025-5807",
  issn-l =       "0025-5807",
  bibdate =      "Fri Nov 18 11:59:44 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  url =          "http://www.oemg.ac.at/DK/Didaktikhefte/2008%2520Band%252041/VortragHumenberger.pdf",
  acknowledgement = ack-nhfb,
  language =     "German",
}

@Article{Ipeirotis:2008:CAH,
  author =       "Panagiotis G. Ipeirotis and Luis Gravano",
  title =        "Classification-aware hidden-web text database
                 selection",
  journal =      j-TOIS,
  volume =       "26",
  number =       "2",
  pages =        "6:1--6:??",
  month =        mar,
  year =         "2008",
  coden =        "ATISET",
  doi =          "http://doi.acm.org/10.1145/1344411.1344412",
  issn =         "1046-8188",
  issn-l =       "0734-2047",
  bibdate =      "Thu Jun 12 16:52:34 MDT 2008",
  bibsource =    "http://www.acm.org/pubs/contents/journals/tois/;
                 http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  abstract =     "Many valuable text databases on the web have
                 noncrawlable contents that are ``hidden'' behind search
                 interfaces. Metasearchers are helpful tools for
                 searching over multiple such ``hidden-web'' text
                 databases at once through a unified query interface. An
                 important step in the metasearching process is database
                 selection, or determining which databases are the most
                 relevant for a given user query. The state-of-the-art
                 database selection techniques rely on statistical
                 summaries of the database contents, generally including
                 the database vocabulary and associated word
                 frequencies. Unfortunately, hidden-web text databases
                 typically do not export such summaries, so previous
                 research has developed algorithms for constructing
                 approximate content summaries from document samples
                 extracted from the databases via querying. We present a
                 novel ``focused-probing'' sampling algorithm that
                 detects the topics covered in a database and adaptively
                 extracts documents that are representative of the topic
                 coverage of the database. Our algorithm is the first to
                 construct content summaries that include the
                 frequencies of the words in the database.
                 Unfortunately, Zipf's law practically guarantees that
                 for any relatively large database, content summaries
                 built from moderately sized document samples will fail
                 to cover many low-frequency words; in turn, incomplete
                 content summaries might negatively affect the database
                 selection process, especially for short queries with
                 infrequent words. To enhance the sparse document
                 samples and improve the database selection decisions,
                 we exploit the fact that topically similar databases
                 tend to have similar vocabularies, so samples extracted
                 from databases with a similar topical focus can
                 complement each other. We have developed two database
                 selection algorithms that exploit this observation. The
                 first algorithm proceeds hierarchically and selects the
                 best categories for a query, and then sends the query
                 to the appropriate databases in the chosen categories.
                 The second algorithm uses ``shrinkage,'' a statistical
                 technique for improving parameter estimation in the
                 face of sparse data, to enhance the database content
                 summaries with category-specific words. We describe how
                 to modify existing database selection algorithms to
                 adaptively decide (at runtime) whether shrinkage is
                 beneficial for a query. A thorough evaluation over a
                 variety of databases, including 315 real web databases
                 as well as TREC data, suggests that the proposed
                 sampling methods generate high-quality content
                 summaries and that the database selection algorithms
                 produce significantly more relevant database selection
                 decisions and overall search results than existing
                 algorithms.",
  acknowledgement = ack-nhfb,
  articleno =    "6",
  fjournal =     "ACM Transactions on Information Systems (TOIS)",
  keywords =     "database selection; Distributed information retrieval;
                 web search",
}

@Article{Jager:2008:DAD,
  author =       "Hendrik Jager and Pierre Liardet",
  title =        "Distributions arithm{\'e}tiques des d{\'e}nominateurs
                 de convergents de fractions continues. ({French})
                 [Arithmetic distributions of the denominators of
                 continued fractions]",
  journal =      "Proceedings of the Koninklijke Nederlandse Akademie
                 van Wetenschappen, Series A, Indagationes
                 mathematicae",
  volume =       "91",
  number =       "2",
  pages =        "181--197",
  day =          "20",
  month =        jun,
  year =         "2008",
  coden =        "????",
  doi =          "http://dx.doi.org/10.1016/S1385-7258(88)80026-X",
  issn =         "1385-7258 (print), 1878-5972 (electronic)",
  issn-l =       "1385-7258",
  bibdate =      "Tue Nov 22 11:28:19 MST 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 http://www.sciencedirect.com/",
  url =          "http://www.sciencedirect.com/science/article/pii/S138572588880026X",
  acknowledgement = ack-nhfb,
  fjournal =     "Indagationes Mathematicae (Proceedings)",
  keywords =     "Benford's Law",
  language =     "French",
  xxjournal =    "Indagationes Mathematicae (Proceedings)",
}

@Article{Jang:2008:CDH,
  author =       "D. Jang and J. U. Kang and A. Kruckman and J. Kudo and
                 S. J. Miller",
  title =        "Chains of distributions, hierarchical {Bayesian}
                 models and {Benford's Law}",
  journal =      "ArXiv e-prints",
  month =        may,
  year =         "2008",
  coden =        "????",
  issn =         "????",
  bibdate =      "Tue Nov 15 06:34:24 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  url =          "http://adsabs.harvard.edu/abs/2008arXiv0805.4226J;
                 http://arxiv.org/abs/0805.4226",
  abstract =     "Kossovsky recently conjectured that the distribution
                 of leading digits of a chain of probability
                 distributions converges to Benford's law as the length
                 of the chain grows. We prove his conjecture in many
                 cases, and provide an interpretation in terms of
                 products of independent random variables and a central
                 limit theorem. An interesting consequence is that in
                 hierarchical Bayesian models priors tend to satisfy
                 Benford's Law as the number of levels of the hierarchy
                 increases, which allows us to develop some simple tests
                 (based on Benford's law) to test proposed models. We
                 give explicit formulas for the error terms as sums of
                 Mellin transforms, which converges extremely rapidly as
                 the number of terms in the chain grows. We may
                 interpret our results as showing that certain Markov
                 chain Monte Carlo processes are rapidly mixing to
                 Benford's law.",
  acknowledgement = ack-nhfb,
  archiveprefix = "arXiv",
  eprint =       "0805.4226",
  keywords =     "Mathematics - Probability, Mathematics - Statistics
                 Theory, 11K06, 60A10 (Primary), 62F99 (Secondary)",
  pagecount =    "15",
  primaryclass = "math.PR",
}

@Article{Jelenkovic:2008:CMS,
  author =       "Predrag R. Jelenkovi{\'c} and Xiaozhu Kang",
  title =        "Characterizing the miss sequence of the {LRU} cache",
  journal =      j-SIGMETRICS,
  volume =       "36",
  number =       "2",
  pages =        "119--121",
  month =        sep,
  year =         "2008",
  coden =        "????",
  doi =          "http://doi.acm.org/10.1145/1453175.1453203",
  issn =         "0163-5999 (print), 1557-9484 (electronic)",
  issn-l =       "0163-5999",
  bibdate =      "Wed Aug 25 07:31:09 MDT 2010",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 http://www.math.utah.edu/pub/tex/bib/sigmetrics.bib",
  abstract =     "Renewed interest in caching systems stems from their
                 wide-spread use for reducing the document download
                 latency over the Internet. Since caches are usually
                 organized in a hierarchical manner, it is important to
                 study the performance properties of tandem caches. The
                 first step in understanding this problem is to
                 characterize the miss stream from one single cache
                 since it represents the input to the next level cache.
                 In this regard, we discover that the miss stream from
                 one single cache is approximated well by the
                 superposition of a number of asymptotically independent
                 renewal processes. Interestingly, when this weakly
                 correlated miss sequence is fed into another cache,
                 this barely observable correlation can lead to
                 measurably different caching performance when compared
                 to the independent reference model. This result is
                 likely to enable the development of a rigorous analysis
                 of the tandem cache performance.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM SIGMETRICS Performance Evaluation Review",
  keywords =     "average-case analysis; cache fault probability;
                 hierarchical caching; least-recently-used caching; web
                 caching; Zipf's law",
}

@Article{Kafri:2008:SIS,
  author =       "Oded Kafri",
  title =        "Sociological Inequality and the {Second Law}",
  journal =      "ArXiv e-prints",
  year =         "2008",
  bibdate =      "Mon Nov 21 06:41:29 2011",
  bibsource =    "http://dblp.uni-trier.de;
                 http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  url =          "http://arxiv.org/abs/0805.3206",
  abstract =     "There are two fair ways to distribute particles in
                 boxes. The first way is to divide the particles equally
                 between the boxes. The second way, which is calculated
                 here, is to score fairly the particles between the
                 boxes. The obtained power law distribution function
                 yields an uneven distribution of particles in boxes. It
                 is shown that the obtained distribution fits well to
                 sociological phenomena, such as the distribution of
                 votes in polls and the distribution of wealth and
                 Benford's law.",
  acknowledgement = ack-nhfb,
}

@InProceedings{Krakar:2008:ABL,
  author =       "Zdravko Krakar and Mario {\v{Z}}gela",
  editor =       "Boris Aurer and Miroslav Ba{\'c}a",
  booktitle =    "Proceedings of the 19th Central European Conference on
                 Information and Intelligent Systems (CECIS 2008)",
  title =        "Application of {Benford's Law} in Payment System
                 Auditing",
  publisher =    "Fakultet organizacije i informatike",
  address =      "Vara{\v{z}}din, Croatia",
  pages =        "187--193",
  year =         "2008",
  bibdate =      "Sun Nov 13 11:14:37 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Krakar:2008:EBL,
  author =       "Zdravko Krakar and Mario {\v{Z}}gela",
  editor =       "Mario Plenkovi{\'c}",
  booktitle =    "Society and Technology 2008",
  title =        "Evaluation of {Benford's Law}: application in stock
                 prices and stock turnover",
  publisher =    "Hrvatsko komunikolo{\v{s}}ko dru{\v{s}}tvo",
  address =      "Zagreb, Croatia",
  pages =        "57--71",
  year =         "2008",
  isbn =         "????",
  isbn-13 =      "????",
  lccn =         "????",
  bibdate =      "Sun Nov 13 11:18:37 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  remark =       "International Federation of Communication Studies,
                 Grafi{\v{c}}ki fakultet Sveu{\v{c}}ili{\v{s}}ta u
                 Zagrebu.",
}

@Article{Liu:2008:MNS,
  author =       "Cheng-Shi Liu",
  title =        "Maximal non-symmetric entropy leads naturally to
                 {Zipf}'s law",
  journal =      j-FRACTALS,
  volume =       "16",
  number =       "1",
  pages =        "99--101",
  year =         "2008",
  coden =        "FRACEG",
  doi =          "http://dx.doi.org/10.1142/S0218348X08003788",
  issn =         "0218-348X",
  issn-l =       "0218-348X",
  mrclass =      "94A17 (94A15)",
  mrnumber =     "2399875 (2009c:94027)",
  mrreviewer =   "Yasuichi Horibe",
  bibdate =      "Sat Nov 12 09:13:23 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Fractals. Complex Geometry, Patterns, and Scaling in
                 Nature and Society",
}

@Article{Lolbert:2008:NEG,
  author =       "Tam{\'a}s Lolbert",
  title =        "On the non-existence of a general {Benford}'s law",
  journal =      "Mathematical Social Sciences",
  volume =       "55",
  number =       "2",
  pages =        "103--106",
  month =        mar,
  year =         "2008",
  coden =        "MSOSDD",
  doi =          "http://dx.doi.org/10.1016/j.mathsocsci.2007.09.001",
  issn =         "0165-4896 (print), 1879-3118 (electronic)",
  issn-l =       "0165-4896",
  mrclass =      "60A10 (60E10)",
  mrnumber =     "2391902",
  bibdate =      "Sat Nov 12 09:13:23 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  url =          "http://www.sciencedirect.com/science/article/pii/S0165489607000935",
  abstract =     "Benford's law states that in randomly collected
                 numbers certain digits are more often leading digits
                 than others. More formally: the general law states that
                 the mantissae follow the logarithmic distribution in
                 any base. Benford's law was recognized by many
                 mathematicians so that several possible explanations
                 have been derived, but several questions are still
                 open. Applications are widespread, for example an
                 auditing technique (the so-called digital analysis),
                 which is employed around the world by internal revenue
                 services to detect tax fraud, is based on this
                 phenomenon.\par

                 In this paper it will be shown that there exists no
                 probability measure that would obey Benford's law for
                 any base, but if the set of possible bases does not
                 exceed a given upper limit, most real-life
                 distributions obey, or can be transformed to obey
                 Benford's law.",
  acknowledgement = ack-nhfb,
  fjournal =     "Mathematical Social Sciences",
}

@Article{Luque:2008:FDF,
  author =       "Bartolo Luque and Lucas Lacasa",
  title =        "The first digit frequencies of primes and {Riemann}
                 zeta zeros tend to uniformity following a
                 size-dependent generalized {Benford}'s law",
  journal =      "ArXiv e-prints",
  month =        nov,
  year =         "2008",
  coden =        "????",
  issn =         "????",
  bibdate =      "Tue Nov 15 06:34:24 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  note =         "See published paper \cite {Luque:2009:FDF}.",
  url =          "http://adsabs.harvard.edu/abs/2008arXiv0811.3302L;
                 http://arxiv.org/abs/0811.3302",
  abstract =     "Prime numbers seem to distribute among the natural
                 numbers with no other law than that of chance, however
                 its global distribution presents a quite remarkable
                 smoothness. Such interplay between randomness and
                 regularity has motivated scientists of all ages to
                 search for local and global patterns in this
                 distribution that eventually could shed light into the
                 ultimate nature of primes. In this work we show that a
                 generalization of the well known first-digit Benford's
                 law, which addresses the rate of appearance of a given
                 leading digit $d$ in data sets, describes with
                 astonishing precision the statistical distribution of
                 leading digits in the prime numbers sequence. Moreover,
                 a reciprocal version of this pattern also takes place
                 in the sequence of the nontrivial Riemann zeta zeros.
                 We prove that the prime number theorem is, in the last
                 analysis, the responsible of these patterns. Some new
                 relations concerning the prime numbers distribution are
                 also deduced, including a new approximation to the
                 counting function $ \pi (n) $. Furthermore, some
                 relations concerning the statistical conformance to
                 this generalized Benford's law are derived. Some
                 applications are finally discussed.",
  acknowledgement = ack-nhfb,
  archiveprefix = "arXiv",
  eprint =       "0811.3302",
  keywords =     "Mathematics - Number Theory, Mathematics -
                 Probability, Mathematics - Statistics",
  pagecount =    "20",
  primaryclass = "math.NT",
}

@Article{Maillart:2008:ETZ,
  author =       "T. Maillart and D. Sornette and S. Spaeth and G. von
                 Krogh",
  title =        "Empirical Tests of {Zipf's Law} Mechanism in Open
                 Source {Linux} Distribution",
  journal =      j-PHYS-REV-LET,
  volume =       "101",
  number =       "21",
  pages =        "218701",
  day =          "19",
  month =        nov,
  year =         "2008",
  coden =        "PRLTAO",
  doi =          "http://dx.doi.org/10.1103/PhysRevLett.101.218701",
  issn =         "0031-9007 (print), 1079-7114 (electronic), 1092-0145",
  issn-l =       "0031-9007",
  bibdate =      "Tue Feb 26 06:40:57 MST 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 http://www.math.utah.edu/pub/tex/bib/gnu.bib;
                 http://www.math.utah.edu/pub/tex/bib/linux.bib;
                 http://www.math.utah.edu/pub/tex/bib/unix.bib",
  url =          "http://link.aps.org/doi/10.1103/PhysRevLett.101.218701",
  acknowledgement = ack-nhfb,
  fjournal =     "Physical Review Letters",
  keywords =     "Zipf's Law",
  pagecount =    "4",
}

@Article{Manin:2008:ZLA,
  author =       "Dmitrii Y. Manin",
  title =        "{Zipf's Law} and Avoidance of Excessive Synonymy",
  journal =      j-COGN-SCI,
  volume =       "32",
  number =       "7",
  pages =        "1075--1098",
  year =         "2008",
  coden =        "COGSD5",
  doi =          "http://dx.doi.org/10.1080/03640210802020003",
  issn =         "0364-0213 (print), 1551-6709 (electronic)",
  issn-l =       "0364-0213",
  bibdate =      "Mon Feb 25 06:13:56 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Cognitive Science",
  keywords =     "Semantics; Synonymy; Word frequency; Word meaning;
                 Zipf's law",
}

@InProceedings{Mebane:2008:EFO,
  author =       "Walter R. {Mebane, Jr.}",
  editor =       "????",
  booktitle =    "{The American Electoral Process conference, Center for
                 the Study of Democratic Politics, Princeton University,
                 May 1--3, 2008}",
  title =        "Election Forensics: Outlier and Digit Tests in
                 {America} and {Russia}",
  publisher =    "????",
  address =      "????",
  pages =        "i + 26",
  year =         "2008",
  isbn =         "????",
  isbn-13 =      "????",
  lccn =         "????",
  bibdate =      "Sat Feb 16 12:08:23 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  url =          "http://www.umich.edu/~wmebane/aep2008.pdf",
  acknowledgement = ack-nhfb,
}

@InProceedings{Mebane:2008:EFS,
  author =       "Walter R. {Mebane, Jr.}",
  editor =       "R. Michael Alvarez and Thad E. Hall and Susan D.
                 Hyde",
  booktitle =    "{The Art and Science of Studying Election Fraud:
                 Detection, Prevention, and Consequences}",
  title =        "Election Forensics: The Second-digit {Benford's Law}
                 Test and Recent {American Presidential} Elections",
  publisher =    "Brookings Institution",
  address =      "Washington, DC, USA",
  pages =        "ii + 30",
  year =         "2008",
  isbn =         "????",
  isbn-13 =      "????",
  lccn =         "????",
  bibdate =      "Sat Feb 16 12:04:22 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  note =         "Preprint dated 3 November 2006.",
  url =          "http://www.umich.edu/~wmebane/fraud06.pdf",
  acknowledgement = ack-nhfb,
  remark =       "An earlier version of this paper was presented at the
                 Election Fraud Conference, Salt Lake City, Utah,
                 September 29--30, 2006.",
}

@Article{Miller:2008:MCL,
  author =       "Steven J. Miller and Mark J. Nigrini",
  title =        "The modulo $1$ central limit theorem and {Benford}'s
                 law for products",
  journal =      "International Journal of Algebra",
  volume =       "2",
  number =       "1--4",
  pages =        "119--130",
  year =         "2008",
  coden =        "????",
  issn =         "1312-8868",
  issn-l =       "1312-8868",
  mrclass =      "60F05 (11K06 42A10)",
  mrnumber =     "2417189 (2009e:60053)",
  mrreviewer =   "Gutti J. Babu",
  bibdate =      "Sat Nov 12 09:13:23 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  ajournal =     "Int. J. Algebra",
  fjournal =     "International Journal of Algebra",
}

@Article{Miller:2008:OSB,
  author =       "Steven J. Miller and Mark J. Nigrini",
  title =        "Order statistics and {Benford}'s law",
  journal =      j-INT-J-MATH-MATH-SCI,
  year =         "2008",
  coden =        "????",
  issn =         "0161-1712",
  issn-l =       "0161-1712",
  mrclass =      "62G30 (62E10)",
  mrnumber =     "2461421 (2010c:62168)",
  bibdate =      "Sat Nov 12 09:13:23 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  note =         "Article ID 382948.",
  url =          "http://arxiv.org/abs/math/0601344",
  abstract =     "Fix a base $B$ and let zeta have the standard
                 exponential distribution; the distribution of digits of
                 zeta base $B$ is known to be very close to Benford's
                 Law. If there exists a $C$ such that the distribution
                 of digits of $C$ times the elements of some set is the
                 same as that of zeta, we say that set exhibits shifted
                 exponential behavior base $B$ (with a shift of $\log_B
                 C \bmod 1$). Let $X_1, \ldots{}, X_N$ be independent
                 identically distributed random variables. If the
                 $X_i$'s are drawn from the uniform distribution on
                 $[0,L]$, then as $N \to \infty$ the distribution of the
                 digits of the differences between adjacent order
                 statistics converges to shifted exponential behavior
                 (with a shift of $\log_B L / N \bmod 1$). By
                 differentiating the cumulative distribution function of
                 the logarithms modulo 1, applying Poisson Summation and
                 then integrating the resulting expression, we derive
                 rapidly converging explicit formulas measuring the
                 deviations from Benford's Law. Fix a delta in $(0,1)$
                 and choose $N$ independent random variables from any
                 compactly supported distribution with uniformly bounded
                 first and second derivatives and a second order Taylor
                 series expansion at each point. The distribution of
                 digits of any $N^\delta$ consecutive differences {\em
                 and\/} all $N - 1$ normalized differences of the order
                 statistics exhibit shifted exponential behavior. We
                 derive conditions on the probability density which
                 determine whether or not the distribution of the digits
                 of all the un-normalized differences converges to
                 Benford's Law, shifted exponential behavior, or
                 oscillates between the two, and show that the Pareto
                 distribution leads to oscillating behavior.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Mathematics and Mathematical
                 Sciences",
  pagecount =    "19",
}

@Article{Mitchell:2008:TST,
  author =       "James G. Mitchell and Laurent Seuront",
  title =        "Towards a seascape topology {II}: {Zipf} analysis of
                 one-dimensional patterns",
  journal =      j-J-MAR-SYST,
  volume =       "69",
  number =       "3--4",
  pages =        "328--338",
  month =        feb,
  year =         "2008",
  coden =        "JMASE5",
  doi =          "http://dx.doi.org/10.1016/j.jmarsys.2006.03.026",
  issn =         "0924-7963 (print), 1879-1573 (electronic)",
  issn-l =       "0924-7963",
  bibdate =      "Wed Feb 27 07:32:55 MST 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  url =          "http://www.sciencedirect.com/science/article/pii/S0924796307000632",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Marine Systems",
  keywords =     "Zipf's Law",
}

@Article{Mizuno:2008:PLE,
  author =       "Takayuki Mizuno and Masahiro Toriyama and Takao Terano
                 and Misako Takayasu",
  title =        "{Pareto} law of the expenditure of a person in
                 convenience stores",
  journal =      j-PHYSICA-A,
  volume =       "387",
  number =       "15",
  pages =        "3931--3935",
  year =         "2008",
  coden =        "PHYADX",
  doi =          "http://dx.doi.org/10.1016/j.physa.2008.01.059",
  issn =         "0378-4371 (print), 1873-2119 (electronic)",
  issn-l =       "0378-4371",
  mrclass =      "91B82",
  mrnumber =     "2586890",
  bibdate =      "Mon Feb 18 17:05:26 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Physica A. Statistical Mechanics and its
                 Applications",
}

@Article{Ni:2008:BLH,
  author =       "D. Ni and Z. Ren",
  title =        "{Benford}'s law and half-lives of unstable nuclei",
  journal =      j-EUR-PHYS-J-A,
  volume =       "38",
  pages =        "251--255",
  month =        dec,
  year =         "2008",
  coden =        "EPJAFV",
  doi =          "http://dx.doi.org/10.1140/epja/i2008-10680-8",
  issn =         "1434-6001 (print), 1434-601X (electronic)",
  issn-l =       "1434-6001",
  bibdate =      "Tue Nov 15 06:34:24 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  url =          "http://adsabs.harvard.edu/abs/2008EPJA...38..251N",
  acknowledgement = ack-nhfb,
  fjournal =     "European Physical Journal A: Hadrons and Nuclei",
}

@Article{Pain:2008:BLC,
  author =       "Jean-Christophe Pain",
  title =        "{Benford}'s law and complex atomic spectra",
  journal =      j-PHYS-REV-E,
  volume =       "77",
  number =       "1",
  pages =        "012102",
  month =        jan,
  year =         "2008",
  coden =        "PLEEE8",
  doi =          "http://dx.doi.org/10.1103/PhysRevE.77.012102",
  issn =         "1539-3755 (print), 1550-2376 (electronic)",
  issn-l =       "1539-3755",
  bibdate =      "Tue Nov 15 06:34:24 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  url =          "http://adsabs.harvard.edu/abs/2008PhRvE..77a2102P;
                 http://pre.aps.org/abstract/PRE/v77/i1/e012102",
  abstract =     "We found that in transition arrays of complex atomic
                 spectra, the strengths of electric-dipolar lines obey
                 Benford's law, which means that their significant
                 digits follow a logarithmic distribution favoring the
                 smallest values. This indicates that atomic processes
                 result from the superposition of uncorrelated
                 probability laws and that the occurrence of digits
                 reflects the constraints induced by the selection
                 rules. Furthermore, Benford's law can be a useful test
                 of theoretical spectroscopic models. Its applicability
                 to the statistics of electric-dipolar lines can be
                 understood in the framework of random matrix theory and
                 is consistent with the Porter-Thomas law.",
  acknowledgement = ack-nhfb,
  archiveprefix = "arXiv",
  eid =          "012102",
  eprint =       "0801.0946",
  fjournal =     "Physical Review E (Statistical physics, plasmas,
                 fluids, and related interdisciplinary topics)",
  keywords =     "Probability theory, Oscillator strengths, lifetimes,
                 transition moments, Other topics in the theory of the
                 electronic structure of atoms and molecules",
  pagecount =    "3",
  primaryclass = "quant-ph",
}

@Article{Ravikumar:2008:BND,
  author =       "Bala Ravikumar",
  title =        "The {Benford--Newcomb} Distribution and Unambiguous
                 Context-Free Languages",
  journal =      j-INT-J-FOUND-COMP-SCI,
  volume =       "19",
  number =       "3",
  pages =        "717--727",
  month =        jun,
  year =         "2008",
  coden =        "IFCSEN",
  doi =          "http://dx.doi.org/10.1142/S0129054108005905",
  issn =         "0129-0541 (print), 1793-6373 (electronic)",
  issn-l =       "0129-0541",
  mrclass =      "68Q42 (68Q25 68Q45)",
  mrnumber =     "2417964 (2009h:68068)",
  bibdate =      "Sat Nov 12 09:13:23 2011",
  bibsource =    "http://ejournals.wspc.com.sg/ijfcs/mkt/archive.shtml;
                 http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Foundations of Computer
                 Science (IJFCS)",
}

@Article{Schurger:2008:EBS,
  author =       "Klaus Sch{\"u}rger",
  title =        "Extensions of {Black--Scholes} processes and
                 {Benford}'s law",
  journal =      j-STOCH-PROC-APPL,
  volume =       "118",
  number =       "7",
  pages =        "1219--1243",
  month =        jul,
  year =         "2008",
  coden =        "STOPB7",
  doi =          "http://dx.doi.org/10.1016/j.spa.2007.07.017",
  issn =         "0304-4149 (print), 1879-209X (electronic)",
  issn-l =       "0304-4149",
  mrclass =      "60F10 (60G44 91B02 91B28)",
  mrnumber =     "2428715 (2009g:60037)",
  bibdate =      "Sat Nov 12 09:13:23 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  url =          "http://www.sciencedirect.com/science/article/pii/S0304414907001391",
  acknowledgement = ack-nhfb,
  fjournal =     "Stochastic Processes and Their Applications",
}

@Article{Semboloni:2008:HCS,
  author =       "F. Semboloni",
  title =        "Hierarchy, cities size distribution and {Zipf}'s law",
  journal =      j-EUR-PHYS-J-B,
  volume =       "63",
  number =       "3",
  pages =        "295--301",
  year =         "2008",
  coden =        "EPJBFY",
  doi =          "http://dx.doi.org/10.1140/epjb/e2008-00203-1",
  issn =         "1434-6028 (print), 1434-6036 (electronic)",
  issn-l =       "1434-6028",
  mrclass =      "91D10 (82B99 91D25)",
  mrnumber =     "2421552 (2009f:91111)",
  bibdate =      "Sat Nov 12 09:13:23 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  zmnumber =     "Zbl 1189.91174",
  acknowledgement = ack-nhfb,
  fjournal =     "The European Physical Journal B. Condensed Matter and
                 Complex Systems",
}

@Article{Seuront:2008:TST,
  author =       "Laurent Seuront and James G. Mitchell",
  title =        "Towards a seascape typology. {I}. {Zipf} versus
                 {Pareto} laws",
  journal =      j-J-MAR-SYST,
  volume =       "69",
  number =       "3--4",
  pages =        "310--327",
  month =        feb,
  year =         "2008",
  coden =        "JMASE5",
  doi =          "http://dx.doi.org/10.1016/j.jmarsys.2006.03.025",
  issn =         "0924-7963 (print), 1879-1573 (electronic)",
  issn-l =       "0924-7963",
  bibdate =      "Wed Feb 27 07:32:55 MST 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  url =          "http://www.sciencedirect.com/science/article/pii/S0924796307000620",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Marine Systems",
  keywords =     "Zipf's Law",
}

@Article{Shaki:2008:RSN,
  author =       "Samuel Shaki and Martin H. Fischer",
  title =        "Reading space into numbers --- a cross-linguistic
                 comparison of the {SNARC} effect",
  journal =      j-COGNITION,
  volume =       "108",
  number =       "2",
  pages =        "590--599",
  month =        aug,
  year =         "2008",
  coden =        "CGTNAU",
  doi =          "http://dx.doi.org/10.1016/j.cognition.2008.04.001",
  issn =         "0010-0277 (print), 1873-7838 (electronic)",
  issn-l =       "0010-0277",
  bibdate =      "Tue Nov 22 11:28:19 MST 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 http://www.sciencedirect.com/",
  url =          "http://www.sciencedirect.com/science/article/pii/S0010027708000978",
  acknowledgement = ack-nhfb,
  fjournal =     "Cognition",
  keywords =     "Benford's Law; Spatial Numerical Association of
                 Response Codes (SNARC)",
}

@Article{Volchenkov:2008:SUC,
  author =       "D. Volchenkov and Ph. Blanchard",
  title =        "Scaling and universality in city space syntax: Between
                 {Zipf} and {Matthew}",
  journal =      j-PHYSICA-A,
  volume =       "387",
  number =       "10",
  pages =        "2353--2364",
  day =          "1",
  month =        apr,
  year =         "2008",
  coden =        "PHYADX",
  doi =          "http://dx.doi.org/10.1016/j.physa.2007.11.049",
  issn =         "0378-4371 (print), 1873-2119 (electronic)",
  issn-l =       "0378-4371",
  bibdate =      "Wed Feb 27 07:32:55 MST 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  url =          "http://www.sciencedirect.com/science/article/pii/S0378437107012630",
  acknowledgement = ack-nhfb,
  fjournal =     "Physica A. Statistical Mechanics and its
                 Applications",
  keywords =     "Zipf's Law",
}

@Article{Vuko:2008:UBL,
  author =       "Tina Vuko",
  title =        "Using {Benford's Law} to Detect Earnings Management
                 Practice: the Case of Listed Companies in {Croatia}",
  journal =      "Global Business \& Economics Anthology",
  volume =       "1",
  number =       "??",
  pages =        "69--74",
  month =        "????",
  year =         "2008",
  coden =        "????",
  issn =         "1553-1333",
  issn-l =       "1553-1333",
  bibdate =      "Sun Nov 13 11:10:55 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
}

@Article{Watrin:2008:BLI,
  author =       "C. Watrin and R. Struffert and R. Ullmann",
  title =        "{Benford's Law}: An Instrument for Selecting Tax Audit
                 Targets?",
  journal =      "Review of Managerial Science",
  volume =       "2",
  number =       "3",
  pages =        "219--237",
  month =        nov,
  year =         "2008",
  coden =        "????",
  doi =          "http://dx.doi.org/10.1007/s11846-008-0019-9",
  issn =         "1863-6683 (print), 1863-6691 (electronic)",
  issn-l =       "1863-6683",
  bibdate =      "Tue Nov 22 20:58:51 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
}

@Book{Ziliak:2008:CSS,
  author =       "Stephen Thomas Ziliak and Deirdre N. McCloskey",
  title =        "The Cult of Statistical Significance: How the Standard
                 Error Costs Us Jobs, Justice, and Lives",
  publisher =    "University of Michigan Press",
  address =      "Ann Arbor, MI, USA",
  pages =        "xxiii + 321",
  year =         "2008",
  isbn =         "0-472-07007-X (cloth), 0-472-05007-9 (paperback)",
  isbn-13 =      "978-0-472-07007-7 (cloth), 978-0-472-05007-9
                 (paperback)",
  lccn =         "HB137 .Z55 2008",
  bibdate =      "Tue Dec 9 15:55:11 MST 2008",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 http://www.math.utah.edu/pub/tex/bib/master.bib;
                 z3950.loc.gov:7090/Voyager",
  series =       "Economics, cognition, and society",
  url =          "http://www.loc.gov/catdir/enhancements/fy0809/2007035401-d.html",
  acknowledgement = ack-nhfb,
  remark =       "This book has important comments on the battles among
                 Sir Ronald Fisher, Jerzy Neyman, Egon Pearson, and Karl
                 Pearson, supplementing the discussion of those
                 conflicts in \cite{McGrayne:2011:TWH}.",
  subject =      "economics; statistical methods; statistics; social
                 aspects; statistical hypothesis testing",
}

@InProceedings{Altamirano:2009:GTU,
  author =       "C. Altamirano and A. Robledo",
  editor =       "J. Zhou",
  booktitle =    "Complex Sciences",
  title =        "Generalized Thermodynamics Underlying the Laws of
                 {Zipf} and {Benford}",
  volume =       "5",
  publisher =    pub-SV,
  address =      pub-SV:adr,
  pages =        "2232--??",
  year =         "2009",
  doi =          "http://dx.doi.org/10.1007/978-3-642-02469-6_100",
  isbn =         "3-642-02468-8",
  isbn-13 =      "978-3-642-02468-9",
  bibdate =      "Tue Nov 15 06:34:24 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  url =          "http://adsabs.harvard.edu/abs/2009cosc.conf.2232A",
  acknowledgement = ack-nhfb,
}

@Article{Anderson:2009:CRC,
  author =       "Thomas Anderson",
  title =        "Conference reviewing considered harmful",
  journal =      j-OPER-SYS-REV,
  volume =       "43",
  number =       "2",
  pages =        "108--116",
  month =        apr,
  year =         "2009",
  coden =        "OSRED8",
  doi =          "http://doi.acm.org/10.1145/1531793.1531815",
  issn =         "0163-5980 (print), 1943-586X (electronic)",
  issn-l =       "0163-5980",
  bibdate =      "Thu Apr 23 19:43:22 MDT 2009",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  abstract =     "This paper develops a model of computer systems
                 research to help prospective authors understand the
                 often obscure workings of conference program
                 committees. We present data to show that the
                 variability between reviewers is often the dominant
                 factor as to whether a paper is accepted. We argue that
                 paper merit is likely to be Zipf distributed, making it
                 inherently difficult for program committees to
                 distinguish between most papers. We use game theory to
                 show that with noisy reviews and Zipf merit, authors
                 have an incentive to submit papers too early and too
                 often. These factors make conference reviewing, and
                 systems research as a whole, less efficient and less
                 effective. We describe some recent changes in
                 conference design to address these issues, and we
                 suggest some further potential improvements.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM SIGOPS Operating Systems Review",
}

@Article{Battersby:2009:SAH,
  author =       "Stephen Battersby",
  title =        "Statistical analyses hint at fraud in {Iranian}
                 election",
  journal =      j-NEW-SCIENTIST,
  volume =       "202",
  number =       "2714",
  pages =        "10--??",
  day =          "24",
  month =        jun,
  year =         "2009",
  coden =        "NWSCAL",
  doi =          "http://dx.doi.org/10.1016/S0262-4079(09)61682-1",
  issn =         "0262-4079 (print), 1364-8500 (electronic)",
  issn-l =       "0262-4079",
  bibdate =      "Tue Nov 22 11:28:19 MST 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 http://www.sciencedirect.com/",
  url =          "http://www.sciencedirect.com/science/article/pii/S0262407909616821",
  acknowledgement = ack-nhfb,
  fjournal =     "The New Scientist",
  keywords =     "Benford's Law",
  xxissn =       "0262-4079, 0028-6664",
}

@TechReport{Bauer:2009:DDF,
  author =       "J. Bauer and J. Gross",
  title =        "Difficulties Detecting Fraud? {The} Use of {Benford's
                 Law} on Regression Tables",
  type =         "Report",
  number =       "??",
  institution =  "Institute of Sociology, LMU Munich",
  address =      "Munich, Germany",
  month =        "????",
  year =         "2009",
  bibdate =      "Fri Nov 18 11:46:08 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
}

@TechReport{Berger:2009:BOB,
  author =       "A. Berger and T. P. Hill",
  title =        "{Benford} Online Bibliography",
  institution =  "Department of Mathematical and Statistical Sciences,
                 University of Alberta",
  address =      "Edmonton, AB, Canada",
  year =         "2009",
  bibdate =      "Sat Nov 12 16:48:00 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  url =          "http://www.benfordonline.net",
  acknowledgement = ack-nhfb,
  remark =       "According to \cite{Berger:2011:BLS}, the authors'
                 online bibliography contains more than 600
                 references.",
}

@InProceedings{Berinde:2009:SOH,
  author =       "Radu Berinde and Graham Cormode and Piotr Indyk and
                 Martin J. Strauss",
  title =        "Space-optimal heavy hitters with strong error bounds",
  crossref =     "Paredaens:2009:PTE",
  pages =        "157--166",
  year =         "2009",
  doi =          "http://doi.acm.org/10.1145/1559795.1559819",
  bibdate =      "Thu Jul 2 14:05:34 MDT 2009",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  abstract =     "The problem of finding heavy hitters and approximating
                 the frequencies of items is at the heart of many
                 problems in data stream analysis. It has been observed
                 that several proposed solutions to this problem can
                 outperform their worst-case guarantees on real data.
                 This leads to the question of whether some stronger
                 bounds can be guaranteed. We answer this in the
                 positive by showing that a class of `counter-based
                 algorithms' (including the popular and very
                 space-efficient FREQUENT and SPACESAVING algorithms)
                 provide much stronger approximation guarantees than
                 previously known. Specifically, we show that errors in
                 the approximation of individual elements do not depend
                 on the frequencies of the most frequent elements, but
                 only on the frequency of the remaining `tail.' This
                 shows that counter-based methods are the most
                 space-efficient (in fact, space-optimal) algorithms
                 having this strong error bound.\par

                 This tail guarantee allows these algorithms to solve
                 the `sparse recovery' problem. Here, the goal is to
                 recover a faithful representation of the vector of
                 frequencies, $f$. We prove that using space $O(k)$, the
                 algorithms construct an approximation $f*$ to the
                 frequency vector $f$ so that the L1 error $||f -
                 f*||_1$ is close to the best possible error
                 $\hbox{min}_{f_2} || f_2 - f ||_1$, where $f$ 2 ranges
                 over all vectors with at most $k$ non-zero entries.
                 This improves the previously best known space bound of
                 about $O(k \log n)$ for streams without element
                 deletions (where $n$ is the size of the domain from
                 which stream elements are drawn). Other consequences of
                 the tail guarantees are results for skewed (Zipfian)
                 data, and guarantees for accuracy of merging multiple
                 summarized streams.",
  acknowledgement = ack-nhfb,
  keywords =     "frequency estimation; heavy hitters; streaming
                 algorithms",
}

@Article{Blasius:2009:ZLP,
  author =       "Bernd Blasius and Ralf T{\"o}njes",
  title =        "{Zipf's Law} in the Popularity Distribution of Chess
                 Openings",
  journal =      j-PHYS-REV-LET,
  volume =       "103",
  number =       "21",
  pages =        "218701",
  day =          "16",
  month =        nov,
  year =         "2009",
  coden =        "PRLTAO",
  doi =          "http://dx.doi.org/10.1103/PhysRevLett.103.218701",
  issn =         "0031-9007 (print), 1079-7114 (electronic), 1092-0145",
  issn-l =       "0031-9007",
  bibdate =      "Tue Feb 26 06:40:57 MST 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  url =          "http://link.aps.org/doi/10.1103/PhysRevLett.103.218701",
  acknowledgement = ack-nhfb,
  fjournal =     "Physical Review Letters",
  keywords =     "Zipf's Law",
  pagecount =    "4",
}

@Article{Bradley:2009:WBL,
  author =       "Jonathan R. Bradley and David L. Farnsworth",
  title =        "What Is {Benford's Law}?",
  journal =      "Teaching Statistics",
  volume =       "31",
  number =       "1",
  pages =        "2--6",
  month =        jan,
  year =         "2009",
  coden =        "????",
  doi =          "http://dx.doi.org/10.1111/j.1467-9639.2009.00347.x",
  issn =         "0141-982X (print), 1467-9639 (electronic)",
  issn-l =       "0141-982X",
  bibdate =      "Mon Nov 14 17:09:33 MST 2011",
  bibsource =    "http://onlinelibrary.wiley.com/;
                 http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Class activity; First significant digit; Goodness of
                 fit; Teaching",
  onlinedate =   "6 Jan 2009",
}

@InProceedings{Burns:2009:SSR,
  author =       "B. D. Burns",
  editor =       "N. Taatgen and H. van Rijn",
  booktitle =    "{Proceedings of the Thirty-First Annual Conference of
                 the Cognitive Science Society, Cognitive Science
                 Society, Austin, TX}",
  title =        "Sensitivity to Statistical Regularities: People
                 (Largely) Follow {Benford's Law}",
  publisher =    "????",
  address =      "????",
  pages =        "2872--2877",
  year =         "2009",
  isbn =         "????",
  isbn-13 =      "????",
  lccn =         "????",
  bibdate =      "Fri Nov 18 11:57:33 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
}

@Article{Chakravorty:2009:TBL,
  author =       "S. Chakravorty and V. Sridharan",
  title =        "Testing {Benford's Law} for improving supply chain
                 decision-making: a field experiment",
  journal =      j-DRUG-DISCOVERY-TODAY,
  volume =       "122",
  number =       "2",
  pages =        "606--618",
  month =        dec,
  year =         "2009",
  coden =        "DDTOFS",
  doi =          "http://dx.doi.org/10.1016/j.ijpe.2009.06.017",
  issn =         "1359-6446 (print), 1878-5832 (electronic)",
  issn-l =       "1359-6446",
  bibdate =      "Tue Nov 22 11:28:19 MST 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 http://www.sciencedirect.com/",
  url =          "http://www.sciencedirect.com/science/article/pii/S0925527309002163",
  acknowledgement = ack-nhfb,
  fjournal =     "Drug Discovery Today",
  keywords =     "Benford's Law",
}

@Article{Chou:2009:BLN,
  author =       "Mabel C. Chou and Qingxia Kong and Chung-Piaw Teo and
                 Zuozheng Wang and Huan Zheng",
  title =        "{Benford's Law} and Number Selection in Fixed-Odds
                 Numbers Game",
  journal =      j-J-GAMBL-STUD,
  volume =       "25",
  number =       "4",
  pages =        "503--521",
  month =        dec,
  year =         "2009",
  coden =        "JGSTEM",
  doi =          "http://dx.doi.org/10.1007/s10899-009-9145-9",
  issn =         "1050-5350 (print), 1573-3602 (electronic)",
  issn-l =       "1050-5350",
  bibdate =      "Sat Feb 16 15:35:14 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  url =          "http://link.springer.com/article/10.1007/s10899-009-9145-9",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Gambling Studies",
}

@Article{Chuang:2009:FPS,
  author =       "Kun-Ta Chuang and Hung-Leng Chen and Ming-Syan Chen",
  title =        "Feature-preserved sampling over streaming data",
  journal =      j-TKDD,
  volume =       "2",
  number =       "4",
  pages =        "15:1--15:??",
  month =        jan,
  year =         "2009",
  coden =        "????",
  doi =          "http://doi.acm.org/10.1145/1460797.1460798",
  issn =         "1556-4681 (print), 1556-472X (electronic)",
  issn-l =       "1556-4681",
  bibdate =      "Fri Apr 24 17:59:51 MDT 2009",
  bibsource =    "http://www.acm.org/pubs/contents/journals/tkdd/;
                 http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  abstract =     "In this article, we explore a novel sampling model,
                 called {\em feature preserved sampling\/} ({\em FPS\/})
                 that sequentially generates a high-quality sample over
                 sliding windows. The sampling quality we consider
                 refers to the degree of consistency between the sample
                 proportion and the population proportion of each
                 attribute value in a window. Due to the time-variant
                 nature of real-world datasets, users are more likely to
                 be interested in the most recent data. However,
                 previous works have not been able to generate a
                 high-quality sample over sliding windows that precisely
                 preserves up-to-date population characteristics.
                 Motivated by this shortcoming, we have developed the
                 {\em FPS\/} algorithm, which has several advantages:
                 (1) it sequentially generates a sample from a
                 time-variant data source over sliding windows; (2) the
                 execution time of {\em FPS\/} is linear with respect to
                 the database size; (3) the {\em relative\/}
                 proportional differences between the sample proportions
                 and population proportions of most distinct attribute
                 values are guaranteed to be below a specified error
                 threshold, $\epsilon$, while the {\em relative\/}
                 proportion differences of the remaining attribute
                 values are as close to $\epsilon$ as possible, which
                 ensures that the generated sample is of high quality;
                 (4) the sample rate is close to the user specified rate
                 so that a high quality sampling result can be obtained
                 without increasing the sample size; (5) by a thorough
                 analytical and empirical study, we prove that {\em
                 FPS\/} has acceptable space overheads, especially when
                 the attribute values have Zipfian distributions, and
                 {\em FPS\/} can also excellently preserve the
                 population proportion of multivariate features in the
                 sample; and (6) {\em FPS\/} can be applied to infinite
                 streams and finite datasets equally, and the generated
                 samples can be used for various applications. Our
                 experiments on both real and synthetic data validate
                 that {\em FPS\/} can effectively obtain a high quality
                 sample of the desired size. In addition, while using
                 the sample generated by {\em FPS\/} in various mining
                 applications, a significant improvement in efficiency
                 can be achieved without compromising the model's
                 precision.",
  acknowledgement = ack-nhfb,
  articleno =    "15",
  fjournal =     "ACM Transactions on Knowledge Discovery from Data
                 (TKDD)",
  keywords =     "sampling; Streaming mining",
}

@Article{Clauset:2009:PLDb,
  author =       "Aaron Clauset and Cosma Rohilla Shalizi and M. E. J.
                 Newman",
  title =        "Power-Law Distributions in Empirical Data",
  journal =      j-SIAM-REVIEW,
  volume =       "51",
  number =       "4",
  pages =        "661--703",
  month =        "????",
  year =         "2009",
  coden =        "SIREAD",
  doi =          "http://dx.doi.org/10.1137/070710111",
  issn =         "0036-1445 (print), 1095-7200 (electronic)",
  issn-l =       "0036-1445",
  bibdate =      "Mon May 17 17:56:49 MDT 2010",
  bibsource =    "http://epubs.siam.org/sam-bin/dbq/toc/SIREV/51/4;
                 http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 http://www.math.utah.edu/pub/tex/bib/siamreview.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "SIAM Review",
}

@Article{Docampo:2009:BLA,
  author =       "Silvia Docampo and Mar{\'\i}a {del Mar Trigo} and
                 Mar{\'\i}a Aira and Baltasar Cabezudo and Antonio
                 Flores-Moya",
  title =        "{Benford}'s law applied to aerobiological data and its
                 potential as a quality control tool",
  journal =      j-AEROBIOLOGIA,
  volume =       "25",
  number =       "4",
  pages =        "275--283",
  month =        dec,
  year =         "2009",
  coden =        "AROBFT",
  doi =          "http://dx.doi.org/10.1007/s10453-009-9132-8",
  issn =         "0393-5965 (print), 1573-3025 (electronic)",
  issn-l =       "0393-5965",
  bibdate =      "Fri Nov 25 10:47:33 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  url =          "http://www.ingentaconnect.com/content/klu/aero/2009/00000025/00000004/00009132",
  acknowledgement = ack-nhfb,
  fjournal =     "Aerobiologia",
}

@Article{Dorfleitner:2009:PBE,
  author =       "Gregor Dorfleitner and Christian Klein",
  title =        "Psychological barriers in {European} stock markets:
                 Where are they?",
  journal =      j-GLOB-FINANCE-J,
  volume =       "19",
  number =       "3",
  pages =        "268--285",
  month =        oct,
  year =         "2009",
  coden =        "????",
  doi =          "http://dx.doi.org/10.1016/j.gfj.2008.09.001",
  issn =         "1044-0283 (print), 1873-5665 (electronic)",
  issn-l =       "1044-0283",
  bibdate =      "Tue Nov 22 11:28:19 MST 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 http://www.sciencedirect.com/",
  url =          "http://www.sciencedirect.com/science/article/pii/S1044028308000549",
  acknowledgement = ack-nhfb,
  fjournal =     "Global Finance Journal",
  keywords =     "Benford's Law",
}

@Article{Fewster:2009:SEB,
  author =       "Rachel M. Fewster",
  title =        "A Simple Explanation of {Benford's Law}",
  journal =      j-AMER-STAT,
  volume =       "63",
  number =       "1",
  pages =        "26--32",
  month =        feb,
  year =         "2009",
  coden =        "ASTAAJ",
  doi =          "http://dx.doi.org/10.1198/tast.2009.0005",
  issn =         "0003-1305 (print), 1537-2731 (electronic)",
  issn-l =       "0003-1305",
  mrnumber =     "2655700",
  bibdate =      "Sat Nov 12 09:13:23 2011",
  bibsource =    "http://www.amstat.org/publications/tas/;
                 http://www.math.utah.edu/pub/tex/bib/amstat2000.bib;
                 http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  url =          "http://pubs.amstat.org/doi/pdfplus/10.1198/tast.2009.0005",
  acknowledgement = ack-nhfb,
  fjournal =     "The American Statistician",
}

@Article{Gauvrit:2009:LBG,
  author =       "Nicolas Gauvrit and Jean-Paul Delahaye",
  title =        "Loi de {Benford} g{\'e}n{\'e}rale. ({French})
                 [{General} {Benford}'s law]",
  journal =      "Math. Sci. Hum. Math. Soc. Sci.",
  volume =       "??",
  number =       "186",
  pages =        "5--15",
  year =         "2009",
  coden =        "????",
  issn =         "0987-6936 (print), 1950-6821 (electronic)",
  issn-l =       "0987-6936",
  mrclass =      "62E10 (11A63 37A45)",
  mrnumber =     "2562062 (2010i:62029)",
  bibdate =      "Sat Nov 12 09:13:23 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  url =          "http://msh.revues.org/document11034.html",
  acknowledgement = ack-nhfb,
  fjournal =     "Math{\'e}matiques et Sciences Humaines. Mathematics
                 and Social Sciences",
  language =     "French",
}

@Article{Gauvrit:2009:SRI,
  author =       "N. Gauvrit and J.-P. Delahaye",
  title =        "Scatter and regularity imply {Benford}'s law \ldots{}
                 and more",
  journal =      "ArXiv e-prints",
  month =        oct,
  year =         "2009",
  coden =        "????",
  issn =         "????",
  bibdate =      "Tue Nov 15 06:34:24 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  url =          "http://adsabs.harvard.edu/abs/2009arXiv0910.1359G;
                 http://arxiv.org/abs/0910.1359",
  abstract =     "A random variable (r.v.) $X$ is said to follow
                 Benford's law if $\log(X)$ is uniform $\bmod 1$. Many
                 experimental data sets prove to follow an approximate
                 version of it, and so do many mathematical series and
                 continuous random variables. This phenomenon received
                 some interest, and several explanations have been put
                 forward. Most of them focus on specific data, depending
                 on strong assumptions, often linked with the log
                 function. Some authors hinted --- implicitly --- that
                 the two most important characteristics of a random
                 variable when it comes to Benford are regularity and
                 scatter. In a first part, we prove two theorems, making
                 up a formal version of this intuition: scattered and
                 regular r.v.'s do approximately follow Benford's law.
                 The proofs only need simple mathematical tools, making
                 the analysis easy. Previous explanations thus become
                 corollaries of a more general and simpler one. These
                 results suggest that Benford's law does not depend on
                 properties linked with the log function. We thus
                 propose and test a general version of the Benford's
                 law. The success of these tests may be viewed as an a
                 posteriori validation of the analysis formulated in the
                 first part.",
  acknowledgement = ack-nhfb,
  archiveprefix = "arXiv",
  eprint =       "0910.1359",
  keywords =     "Mathematics - Probability, Statistics - Methodology,
                 G.3",
  primaryclass = "math.PR",
}

@Article{Gisin:2009:EEV,
  author =       "Vladimir Gisin and Andrey Markov and Igor Vinukov",
  title =        "Estimation of extreme values of returns using the
                 {Zipf--Mandelbrot} flow",
  journal =      j-INT-J-PURE-APPL-MATH,
  volume =       "50",
  number =       "2",
  pages =        "245--250",
  year =         "2009",
  coden =        "????",
  issn =         "1311-8080",
  issn-l =       "1314-3395",
  mrclass =      "60G70 (91B28 91B84)",
  mrnumber =     "2488836",
  bibdate =      "Sat Nov 12 09:13:23 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Pure and Applied
                 Mathematics",
}

@TechReport{Gonzales-Garcia:2009:BLM,
  author =       "J. Gonzales-Garcia and G. Pastor",
  title =        "{Benford's Law} and Macroeconomic Data Quality",
  type =         "Working Paper",
  institution =  "International Monetary Fund",
  address =      "????",
  year =         "2009",
  bibdate =      "Tue Nov 22 18:53:16 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  url =          "http://papers.ssrn.com/sol3/papers.cfm?abstract_id=1356437",
  acknowledgement = ack-nhfb,
}

@Article{Gunnel:2009:DBL,
  author =       "S. G{\"u}nnel and K.-H. T{\"o}dter",
  title =        "Does {Benford's Law} Hold in Economic Research and
                 Forecasting?",
  journal =      j-EMPIRICA,
  volume =       "36",
  number =       "3",
  pages =        "273--292",
  month =        aug,
  year =         "2009",
  coden =        "????",
  doi =          "http://dx.doi.org/10.1007/s10663-008-9084-1",
  issn =         "0340-8744 (print), 1573-6911 (electronic)",
  issn-l =       "0340-8744",
  bibdate =      "Thu Nov 17 19:16:10 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  url =          "http://www.springerlink.com/content/100261/",
  abstract =     "First and higher order digits in data sets of natural
                 and socio-economic processes often follow a
                 distribution called Benford's law. This phenomenon has
                 been used in business and scientific applications,
                 especially in fraud detection for financial data. In
                 this paper, we analyse whether Benford's law holds in
                 economic research and forecasting. First, we examine
                 the distribution of regression coefficients and
                 standard errors in research papers, published in
                 Empirica and Applied Economics Letters. Second, we
                 analyse forecasts of GDP growth and CPI inflation in
                 Germany, published in Consensus Forecasts. There are
                 two main findings: The relative frequencies of the
                 first and second digits in economic research are
                 broadly consistent with Benford's law. In sharp
                 contrast, the second digits of Consensus Forecasts
                 exhibit a massive excess of zeros and fives, raising
                 doubts on their information content.",
  acknowledgement = ack-nhfb,
  fjournal =     "Empirica",
}

@Article{Hales:2009:TBL,
  author =       "Douglas N. Hales and Satya S. Chakravorty and V.
                 Sridharan",
  title =        "Testing {Benford's Law} for improving supply chain
                 decision-making: a field experiment",
  journal =      j-INT-J-PROD-ECON,
  volume =       "122",
  number =       "2",
  pages =        "606--618",
  month =        dec,
  year =         "2009",
  coden =        "JPCEYE",
  doi =          "http://dx.doi.org/10.1016/j.ijpe.2009.06.017",
  issn =         "0925-5273 (print), 1873-7579 (electronic)",
  issn-l =       "0925-5273",
  bibdate =      "Wed Nov 23 18:41:54 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  url =          "http://www.sciencedirect.com/science/article/pii/S0925527309002163",
  acknowledgement = ack-nhfb,
  ajournal =     "Int. j. prod. econ.",
  fjournal =     "International Journal of Production Economics",
}

@Article{Hartshorn:2009:BRB,
  author =       "Kevin Hartshorn",
  title =        "Book Review: {{\booktitle{The fabulous Fibonacci
                 numbers}} by Alfred Posamentier and Ingmar Lehmann}",
  journal =      j-J-MATH-ARTS,
  volume =       "3",
  number =       "2",
  pages =        "113--116",
  month =        "????",
  year =         "2009",
  coden =        "????",
  doi =          "http://dx.doi.org/10.1080/17513470902897569",
  issn =         "1751-3472 (print), 1751-3480 (electronic)",
  issn-l =       "1751-3480",
  bibdate =      "Sat Jan 07 09:43:47 2012",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 http://www.math.utah.edu/pub/tex/bib/fibquart.bib",
  url =          "http://www.tandfonline.com/doi/abs/10.1080/17513470902897569",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Mathematics and the Arts",
  onlinedate =   "05 Jun 2009",
}

@Article{Hernando:2009:ZLF,
  author =       "A. Hernando and D. Puigdom{\`e}nech and D. Villuendas
                 and C. Vesperinas and A. Plastino",
  title =        "{Zipf}'s law from a {Fisher} variational-principle",
  journal =      j-PHYS-LET-A,
  volume =       "374",
  number =       "1",
  pages =        "18--21",
  day =          "14",
  month =        dec,
  year =         "2009",
  coden =        "PYLAAG",
  doi =          "http://dx.doi.org/10.1016/j.physleta.2009.10.027",
  issn =         "0375-9601 (print), 1873-2429 (electronic)",
  issn-l =       "0375-9601",
  bibdate =      "Wed Feb 27 07:32:55 MST 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  url =          "http://www.sciencedirect.com/science/article/pii/S0375960109012894",
  acknowledgement = ack-nhfb,
  fjournal =     "Physics Letters A",
  keywords =     "Zipf's Law",
}

@InCollection{Horgan:2009:BL,
  author =       "Jane M. Horgan",
  title =        "{Benford's Law}",
  crossref =     "Horgan:2009:PRI",
  chapter =      "9.4",
  pages =        "142--144",
  year =         "2009",
  bibdate =      "Mon Feb 18 18:46:16 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
}

@Article{Hurlimann:2009:GBL,
  author =       "Werner H{\"u}rlimann",
  title =        "Generalizing {Benford}'s law using power laws:
                 application to integer sequences",
  journal =      j-INT-J-MATH-MATH-SCI,
  pages =        "10",
  year =         "2009",
  coden =        "????",
  issn =         "0161-1712",
  issn-l =       "0161-1712",
  mrclass =      "60E05 (11B83 62E15)",
  mrnumber =     "2533550 (2010h:60043)",
  bibdate =      "Sat Nov 12 09:13:23 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  note =         "Article ID 970284.",
  url =          "http://arxiv.org/abs/math/0607166",
  abstract =     "A simple method to derive parametric analytical
                 extensions of Benford's law for first digits of
                 numerical data is proposed. Two generalized Benford
                 distributions are considered, namely the two-sided
                 power Benford distribution and the new Pareto Benford
                 distribution. The fitting capabilities of these
                 generalized Benford distributions are illustrated and
                 compared at some interesting and important integer
                 sequences.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Mathematics and Mathematical
                 Sciences",
}

@Article{Jang:2009:CDH,
  author =       "D. Jang and J. U. Kang and A. Kruckman and J. Kudo and
                 S. J. Miller",
  title =        "Chains of distributions, hierarchical {Bayesian}
                 models and {Benford's Law}",
  journal =      "Journal of Algebra, Number Theory: Advances and
                 Applications",
  volume =       "1",
  number =       "1",
  pages =        "37--60",
  month =        mar,
  year =         "2009",
  coden =        "????",
  issn =         "0972-5555",
  issn-l =       "0972-5555",
  bibdate =      "Tue Nov 15 06:34:24 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  url =          "http://adsabs.harvard.edu/abs/2008arXiv0805.4226J",
  acknowledgement = ack-nhfb,
  archiveprefix = "arXiv",
  eprint =       "0805.4226",
  keywords =     "Mathematics - Probability, Mathematics - Statistics
                 Theory, 11K06, 60A10 (Primary), 62F99 (Secondary)",
  primaryclass = "math.PR",
}

@Article{Janvresse:2009:BL,
  author =       "Elise Janvresse and Thierry de la Rue",
  title =        "{Benford}'s law",
  journal =      "Butl. Soc. Catalana Mat.",
  volume =       "24",
  number =       "1",
  pages =        "5--12",
  year =         "2009",
  coden =        "????",
  issn =         "0214-316X",
  issn-l =       "0214-316X",
  mrclass =      "62-01",
  mrnumber =     "2567485",
  bibdate =      "Sat Nov 12 09:13:23 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  note =         "Translated by Frederic Utzet",
  acknowledgement = ack-nhfb,
  fjournal =     "Butllet{\'\i}n de la Societat Catalana de
                 Matem{\`a}tiques",
}

@Article{Jin:2009:AUR,
  author =       "Jang C. Jin",
  title =        "{Asian} University Rankings in International and
                 Development Economics: An Application of {Zipf's Law}",
  journal =      j-REV-INT-ECON,
  volume =       "17",
  number =       "1",
  pages =        "137--143",
  year =         "2009",
  doi =          "http://dx.doi.org/10.1111/j.1467-9396.2008.00790.x",
  issn =         "0965-7576 (print), 1467-9396 (electronic)",
  issn-l =       "0965-7576",
  bibdate =      "Mon Feb 25 06:13:56 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Review of International Economics",
}

@Article{Jin:2009:PME,
  author =       "Jang C. Jin",
  title =        "Publications in mathematical economics and
                 econometrics: ranking of {Asian} universities and an
                 application of {Zipf's Law}",
  journal =      "{Asian-Pacific} Economic Literature",
  volume =       "23",
  number =       "2",
  pages =        "116--122",
  year =         "2009",
  doi =          "http://dx.doi.org/10.1111/j.1467-8411.2009.01233.x",
  issn =         "0818-9935 (print), 1467-8411 (electronic)",
  issn-l =       "0818-9935",
  bibdate =      "Mon Feb 25 06:13:56 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  journal-url =  "http://onlinelibrary.wiley.com/journal/10.1111/%28issn%291467-8411",
}

@Article{Jolissaint:2009:LBR,
  author =       "Paul Jolissaint",
  title =        "Loi de {Benford}, relations de r{\'e}currence et
                 suites {\'e}quidistribu{\'e}es. {II}. ({French})
                 [{Benford}'s Law, recurrence relations, and
                 equidistributed sequences. {II}]",
  journal =      j-ELEM-MATH,
  volume =       "64",
  number =       "1",
  pages =        "21--36",
  year =         "2009",
  coden =        "????",
  doi =          "http://dx.doi.org/10.4171/EM/112",
  issn =         "0013-6018 (print), 1420-8962 (electronic)",
  issn-l =       "0013-6018",
  mrclass =      "62E10 (11A63 37A45)",
  mrnumber =     "2471593 (2010f:62032)",
  mrreviewer =   "Denys Pommeret",
  bibdate =      "Sat Nov 12 09:13:23 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Elemente der Mathematik",
  language =     "French",
}

@Article{Judge:2009:DPS,
  author =       "G. Judge and L. Schechter",
  title =        "Detecting Problems in Survey Data using {Benford's
                 Law}",
  journal =      j-J-HUM-RESOUR,
  volume =       "44",
  number =       "1",
  pages =        "1--24",
  month =        "Winter",
  year =         "2009",
  coden =        "JHREA9",
  doi =          "http://dx.doi.org/10.3368/jhr.44.1.1",
  issn =         "0022-166X (print), 1548-8004 (electronic)",
  issn-l =       "0022-166X",
  bibdate =      "Tue Nov 22 18:55:52 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  url =          "http://jhr.uwpress.org/content/44/1/1.abstract;
                 http://www.ssc.wisc.edu/jhr/2009ab/judge1.htm",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Human Resources",
}

@Article{Kafri:2009:DNE,
  author =       "Oded Kafri",
  title =        "The Distributions in Nature and Entropy Principle",
  journal =      "ArXiv e-prints",
  day =          "28",
  month =        jul,
  year =         "2009",
  bibdate =      "Mon Nov 21 07:26:11 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  url =          "http://arxiv.org/abs/0907.4852",
  abstract =     "The derivation of the maximum entropy distribution of
                 particles in boxes yields two kinds of distributions: a
                 ``bell-like'' distribution and a long-tail
                 distribution. The first one is obtained when the ratio
                 between particles and boxes is low, and the second one
                 when the ratio is high. The obtained long tail
                 distribution yields correctly the empirical Zipf law,
                 Pareto's 20:80 rule and Benford's law. Therefore, it is
                 concluded that the long tail and the ``bell-like''
                 distributions are outcomes of the tendency of
                 statistical systems to maximize entropy.",
  acknowledgement = ack-nhfb,
  pagecount =    "19",
}

@Article{Kafri:2009:EPD,
  author =       "Oded Kafri",
  title =        "Entropy Principle in Direct Derivation of {Benford's
                 Law}",
  journal =      "ArXiv e-prints",
  month =        jan,
  year =         "2009",
  coden =        "????",
  issn =         "????",
  bibdate =      "Tue Nov 15 06:34:24 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  url =          "http://adsabs.harvard.edu/abs/2009arXiv0901.3047K;
                 http://arxiv.org/abs/0901.3047",
  abstract =     "The uneven distribution of digits in numerical data,
                 known as Benford's law, was discovered in 1881. Since
                 then, this law has been shown to be correct in copious
                 numerical data relating to economics, physics and even
                 prime numbers. Although it attracts considerable
                 attention, there is no a priori probabilistic criterion
                 when a data set should or should not obey the law. Here
                 a general criterion is suggested, namely that any file
                 of digits in the Shannon limit (namely, having maximum
                 entropy) has a Benford's law distribution of digits.",
  acknowledgement = ack-nhfb,
  archiveprefix = "arXiv",
  eprint =       "0901.3047",
  keywords =     "Computer Science - Discrete Mathematics, Physics -
                 Data Analysis, Statistics and Probability",
  primaryclass = "cs.DM",
}

@Article{Krakar:2009:ABL,
  author =       "Mario {\v{Z}}gela and Zdravko Krakar",
  title =        "Application of {Benford's Law} in Payment System
                 Auditing",
  journal =      j-J-INFO-ORG-SCI,
  volume =       "33",
  number =       "1",
  pages =        "39--51",
  month =        "????",
  year =         "2009",
  coden =        "????",
  issn =         "1846-3312 (print), 1846-9418 (electronic)",
  issn-l =       "1846-3312",
  bibdate =      "Sun Nov 13 11:12:19 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  url =          "http://bib.irb.hr/datoteka/457819.04_Application_of_Benford_s_Law_in_Payment_Systems_Auditing1.pdf;
                 http://jios.foi.hr/index.php/jios/article/view/108/66;
                 http://jios.foi.hr/index.php/jios/issue/view/13",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Informational and Organizational Sciences",
  journal-url =  "http://jios.foi.hr/index.php/jios/index",
  xxjournal =    "Journal of Information Ethics and Organisational
                 Science (wrong!)",
}

@Article{Lansey:2009:ISR,
  author =       "Jonathan C. Lansey and Bruce Bukiet",
  title =        "{Internet} Search Result Probabilities: {Heaps' Law}
                 and Word Associativity",
  journal =      j-J-QUANT-LINGUISTICS,
  volume =       "16",
  number =       "1",
  pages =        "40--66",
  month =        "????",
  year =         "2009",
  coden =        "????",
  doi =          "http://dx.doi.org/10.1080/09296170802514153",
  issn =         "0929-6174 (print), 1744-5035 (electronic)",
  issn-l =       "0929-6174",
  bibdate =      "Sat Jan 07 09:36:17 2012",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  url =          "http://www.tandfonline.com/doi/abs/10.1080/09296170802514153",
  abstract =     "We study the number of internet search results
                 returned from multi-word queries based on the number of
                 results returned when each word is searched for
                 individually. We derive a model to describe search
                 result values for multi-word queries using the total
                 number of pages indexed by Google and by applying the
                 Zipf power law to the words per page distribution on
                 the internet and Heaps' law for unique word counts.
                 Based on data from 351 word pairs each with exactly one
                 hit when searched for together, and a Zipf law
                 coefficient determined in other studies, we approximate
                 the Heaps' law coefficient for the indexed worldwide
                 web (about 8 billion pages) to be $\beta = 0.52$.
                 Previous studies used under 20,000 pages. We
                 demonstrate through examples how the model can be used
                 to analyse automatically the relatedness of word pairs
                 assigning each a value we call ``strength of
                 associativity''. We demonstrate the validity of our
                 method with word triplets and through two experiments
                 conducted 8 months apart. We then use our model to
                 compare the index sizes of competing search giants
                 Yahoo and Google.",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Quantitative Linguistics",
  keywords =     "Benford's Law; Heaps' Law; Zipf's Law",
  onlinedate =   "25 Feb 2009",
  remark =       "From page 65: ``We mention that tests we have
                 conducted show that internet searches for random
                 numbers return approximately log-normally distributed
                 results and sorting by first digits yields results that
                 follow Benford's law (1938).''",
}

@Article{Lipovetsky:2009:PLD,
  author =       "Stan Lipovetsky",
  title =        "{Pareto} $80/20$ law: derivation via random
                 partitioning",
  journal =      j-INT-J-MATH-EDU-SCI-TECH,
  volume =       "40",
  number =       "2",
  pages =        "271--277",
  month =        "????",
  year =         "2009",
  coden =        "IJMEBM",
  doi =          "http://dx.doi.org/10.1080/00207390802213609",
  issn =         "0020-739X (print), 1464-5211 (electronic)",
  issn-l =       "0020-739X",
  bibdate =      "Sat Jan 07 09:22:31 2012",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  url =          "http://www.tandfonline.com/doi/abs/10.1080/00207390802213609",
  abstract =     "The Pareto 80/20 Rule, also known as the Pareto
                 principle or law, states that a small number of causes
                 (20\%) is responsible for a large percentage (80\%) of
                 the effect. Although widely recognized as a heuristic
                 rule, this proportion has not been theoretically based.
                 The article considers derivation of this 80/20 rule and
                 some other standard quotients from the mean and its
                 interval estimation for the total value defined by the
                 product of two variables in the random partitioning
                 model.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Mathematical Education in
                 Science and Technology",
  onlinedate =   "19 Feb 2009",
}

@Article{Luque:2009:FDF,
  author =       "Bartolo Luque and Lucas Lacasa",
  title =        "The first digit frequencies of prime numbers and
                 {Riemann} zeta zeros",
  journal =      j-PROC-R-SOC-LOND-SER-A-MATH-PHYS-ENG-SCI,
  volume =       "465",
  number =       "2107",
  pages =        "2197--2216",
  day =          "8",
  month =        jul,
  year =         "2009",
  coden =        "PRLAAZ",
  doi =          "http://dx.doi.org/10.1098/rspa.2009.0126",
  issn =         "1364-5021 (print), 1471-2946 (electronic)",
  issn-l =       "1364-5021",
  bibdate =      "Mon Feb 25 10:44:43 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  url =          "http://rspa.royalsocietypublishing.org/content/465/2107/2197.abstract",
  acknowledgement = ack-nhfb,
  fjournal =     "Proceedings of the Royal Society A: Mathematical,
                 Physical, \& Engineering Sciences",
  keywords =     "Benford's Law",
  onlinedate =   "22 April 2009",
}

@TechReport{Moller:2009:MQA,
  author =       "M. M{\"o}ller",
  title =        "Measuring the Quality of Auditing Services with the
                 Help of {Benford's Law} -- An Empirical Analysis and
                 Discussion of this Methodical Approach",
  type =         "Report",
  number =       "??",
  institution =  "Institute for Accounting and Control, University of
                 Z{\"u}rich",
  address =      "Z{\"u}rich, Switzerland",
  pages =        "25",
  day =          "24",
  month =        apr,
  year =         "2009",
  bibdate =      "Tue Nov 22 20:40:12 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  url =          "http://ssrn.com/abstract=1529307",
  abstract =     "The so-called Benford's Law describes regularity in
                 the distribution of digits of randomly selected
                 numbers, which states that the relative frequency of
                 the leading digits reduces in a systematic manner from
                 the digit 1 to the digit 9. This distribution
                 hypothesis is being discussed in recent times as an
                 audit instrument in order to gain insights into
                 possible conscious and inadvertent errors in data
                 records. The present paper analyses the closing
                 accounts of 1,373 annual financial statements of
                 companies listed on the German DAX and compares these
                 with the Benford's distribution hypothesis. It can be
                 seen in the process that data pertaining to financial
                 accounts, which have not been audited by the so-called
                 ``Big 4'' audit firms, but by smaller external
                 auditors, deviate to a significant extent from the
                 regularity of Benford's Law, which appears to make the
                 use of Benford's Law suitable as a benchmark to assess
                 the quality of the audit.",
  acknowledgement = ack-nhfb,
}

@Article{Moret:2009:GSA,
  author =       "M. A. Moret and V. de Senna and M. C. Santana and G.
                 F. Zebende",
  title =        "Geometric Structural Aspects of Proteins and
                 {Newcomb--Benford Law}",
  journal =      j-INT-J-MOD-PHYS-C,
  volume =       "20",
  number =       "12",
  pages =        "1981--1988",
  month =        "????",
  year =         "2009",
  coden =        "IJMPEO",
  doi =          "http://dx.doi.org/10.1142/S0129183109014874",
  issn =         "0129-1831 (print), 1793-6586 (electronic)",
  issn-l =       "0129-1831",
  bibdate =      "Tue Nov 15 06:34:24 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  url =          "http://adsabs.harvard.edu/abs/2009IJMPC..20.1981M",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Modern Physics C [Physics and
                 Computers]",
  journal-url =  "http://www.worldscientific.com/loi/ijmpc",
  keywords =     "Hydrophobicity, protein packing, complex systems, Time
                 series analysis, Systems obeying scaling laws, Binary
                 and multiple stars",
}

@Article{Ni:2009:BLD,
  author =       "Dong-Dong Ni and Lai Wei and Zhong-Zhou Ren",
  title =        "{Benford's Law} and $\beta$-Decay Half-Lives",
  journal =      j-COMM-THEOR-PHYS,
  volume =       "51",
  number =       "4",
  pages =        "713--716",
  month =        apr,
  year =         "2009",
  coden =        "CTPHDI",
  doi =          "http://dx.doi.org/10.1088/0253-6102/51/4/25",
  issn =         "0253-6102",
  issn-l =       "0253-6102",
  bibdate =      "Sun Nov 13 11:01:52 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  url =          "http://adsabs.harvard.edu/abs/2009CoTPh..51..713N;
                 http://stacks.iop.org/0253-6102/51/i=4/a=25",
  abstract =     "The experimental values of 2059 $\beta$-decay
                 half-lives are systematically analyzed and
                 investigated. We have found that they are in
                 satisfactory agreement with Benford's law, which states
                 that the frequency of occurrence of each figure, 1--9,
                 as the first significant digit in a surprisingly large
                 number of different data sets follows a logarithmic
                 distribution favoring the smaller ones. Benford's
                 logarithmic distribution of $\beta$-decay half-lives
                 can be explained in terms of Newcomb's justification of
                 Benford's law and empirical exponential law of
                 $\beta$-decay half-lives. Moreover, we test the
                 calculated values of 6721 $\beta$-decay half-lives with
                 the aid of Benford's law. This indicates that Benford's
                 law is useful for theoretical physicists to test their
                 methods for calculating $\beta$-decay half-lives.",
  acknowledgement = ack-nhfb,
  fjournal =     "Communications in theoretical physics",
}

@Article{Nigrini:2009:DDU,
  author =       "Mark J. Nigrini and Steven J. Miller",
  title =        "Data Diagnostics Using Second-Order Tests of
                 {Benford's Law}",
  journal =      j-AUDITING,
  volume =       "28",
  number =       "2",
  pages =        "305--324",
  month =        nov,
  year =         "2009",
  coden =        "????",
  doi =          "http://dx.doi.org/10.2308/aud.2009.28.2.305",
  issn =         "0278-0380 (print), 1558-7991 (electronic)",
  issn-l =       "0278-0380",
  bibdate =      "Tue Nov 15 09:11:56 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  url =          "http://aaapubs.org/loi/ajpt;
                 http://link.aip.org/link/AJPTXX/v28/i2/p305/s1",
  abstract =     "Auditors are required to use analytical procedures to
                 identify the existence of unusual transactions, events,
                 and trends. Benford's Law gives the expected patterns
                 of the digits in numerical data, and has been advocated
                 as a test for the authenticity and reliability of
                 transaction level accounting data. This paper describes
                 a new second-order test that calculates the digit
                 frequencies of the differences between the ordered
                 (ranked) values in a data set. These digit frequencies
                 approximate the frequencies of Benford's Law for most
                 data sets. The second-order test is applied to four
                 sets of transactional data. The second-order test
                 detected errors in data downloads, rounded data, data
                 generated by statistical procedures, and the inaccurate
                 ordering of data. The test can be applied to any data
                 set and nonconformity usually signals an unusual issue
                 related to data integrity that might not have been
                 easily detectable using traditional analytical
                 procedures",
  acknowledgement = ack-nhfb,
  fjournal =     "Auditing: A Journal of Practice \& Theory",
}

@Article{Rajabpour:2009:SRC,
  author =       "M. A. Rajabpour and S. M. {Vaez Allaei}",
  title =        "Scaling relations for contour lines of rough
                 surfaces",
  journal =      j-PHYS-REV-E,
  volume =       "80",
  number =       "1",
  pages =        "011115",
  day =          "13",
  month =        jul,
  year =         "2009",
  coden =        "PLEEE8",
  doi =          "http://dx.doi.org/10.1103/PhysRevE.80.011115",
  issn =         "1539-3755 (print), 1550-2376 (electronic)",
  issn-l =       "1539-3755",
  bibdate =      "Tue Feb 26 06:40:57 MST 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  url =          "http://link.aps.org/doi/10.1103/PhysRevE.80.011115",
  acknowledgement = ack-nhfb,
  fjournal =     "Physical Review E (Statistical physics, plasmas,
                 fluids, and related interdisciplinary topics)",
  keywords =     "Zipf's Law",
}

@Article{Romero-Rochin:2009:DBL,
  author =       "V. Romero-Rochin",
  title =        "A derivation of {Benford's Law} \ldots{} and a
                 vindication of {Newcomb}",
  journal =      "ArXiv e-prints",
  month =        sep,
  year =         "2009",
  coden =        "????",
  issn =         "????",
  bibdate =      "Tue Nov 15 06:34:24 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  url =          "http://adsabs.harvard.edu/abs/2009arXiv0909.3822R;
                 http://arxiv.org/abs/0909.3822",
  abstract =     "We show how Benford's Law (BL) for first, second,
                 \ldots{}, digits, emerges from the distribution of
                 digits of numbers of the type $a^{R}$, with $a$ any
                 real positive number and $R$ a set of real numbers
                 uniformly distributed in an interval $[P\log_a(10), (P
                 + 1) \log_a(10))$ for any integer $P$. The result is
                 shown to be number base and scale invariant. A rule
                 based on the mantissas of the logarithms allows for a
                 determination of whether a set of numbers obeys BL or
                 not. We show that BL applies to numbers obtained from
                 the {\it multiplication\/} or {\it division\/} of
                 numbers drawn from any distribution. We also argue that
                 (most of) the real-life sets that obey BL are because
                 they are obtained from such basic arithmetic
                 operations. We exhibit that all these arguments were
                 discussed in the original paper by Simon Newcomb in
                 1881, where he presented Benford's Law.",
  acknowledgement = ack-nhfb,
  archiveprefix = "arXiv",
  eprint =       "0909.3822",
  keywords =     "Mathematics - Probability, Mathematics - History and
                 Overview",
  pagecount =    "12",
  primaryclass = "math.PR",
}

@Article{Roukema:2009:BLA,
  author =       "B. F. Roukema",
  title =        "{Benford's Law} anomalies in the 2009 {Iranian}
                 presidential election",
  journal =      "ArXiv e-prints",
  month =        jun,
  year =         "2009",
  coden =        "????",
  issn =         "????",
  bibdate =      "Tue Nov 15 06:34:24 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  url =          "http://adsabs.harvard.edu/abs/2009arXiv0906.2789R;
                 http://arxiv.org/abs/0906.2789",
  abstract =     "The vote count first digit frequencies of the 2009
                 Iranian presidential election are analysed assuming
                 proportionality of candidates' votes to the total vote
                 per voting area. This method is closely related to
                 Benford's Law. A highly significant ($p \approx
                 0.0007$) excess of vote counts for candidate $K$ that
                 start with the digit 7 is found (41 observed, 21.2--22
                 expected). Using this property as a selection criterion
                 leads to the following coincidences. (i) Among the six
                 most populous voting areas, this criterion selects
                 those three that have greater proportions of votes for
                 A than the other three. The probability that the two
                 sub-groups are drawn from the same distribution is $p
                 \approx 0.1$. (ii) $K$'s vote counts for these same
                 three voting areas all have the same second digit. The
                 probability of this is $p \approx 0.01$. (iii) Most
                 (75\%) of the vote counts for $K$ in voting areas with
                 70 to 79 votes for $K$ are odd, and every even number
                 occurs exactly once. The probability of the latter is
                 $p \approx 0.0005$. Interpreting the big city effect
                 (i) +( ii) as an overestimate of the true vote, assumed
                 to be roughly 50\% to match other data, while retaining
                 constant total vote numbers and increasing votes for
                 the other three candidates in proportion to their
                 average voting percentages, would imply that the
                 difference between A's and M's vote totals would drop
                 by about one million votes. These results do not
                 exclude other anomalies.",
  acknowledgement = ack-nhfb,
  archiveprefix = "arXiv",
  eprint =       "0906.2789",
  keywords =     "Statistics - Applications",
  primaryclass = "stat.AP",
}

@Article{Sambridge:2009:ABL,
  author =       "M. Sambridge and H. Tkalcic and A. Jackson",
  title =        "On the applicability of {Benford's Law} in the
                 Geosciences",
  journal =      "AGU Fall Meeting Abstracts",
  pages =        "A1756--??",
  month =        dec,
  year =         "2009",
  coden =        "????",
  issn =         "????",
  bibdate =      "Tue Nov 15 06:32:38 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  url =          "http://adsabs.harvard.edu/abs/2009AGUFM.S33A1756S",
  acknowledgement = ack-nhfb,
  keywords =     "[1294] GEODESY AND GRAVITY / Instruments and
                 techniques, [1594] GEOMAGNETISM AND PALEOMAGNETISM /
                 Instruments and techniques, [3294] MATHEMATICAL
                 GEOPHYSICS / Instruments and techniques, [7299]
                 SEISMOLOGY / General or miscellaneous",
}

@Article{Shao:2009:FDD,
  author =       "Lijing Shao and Bo-Qiang Ma",
  title =        "First digit distribution of hadron full width",
  journal =      j-MOD-PHYS-LETT-A,
  volume =       "24",
  number =       "40",
  pages =        "3275--3282",
  month =        "????",
  year =         "2009",
  coden =        "MPLAEQ",
  doi =          "http://dx.doi.org/10.1142/S0217732309031223",
  issn =         "0217-7323 (print), 1793-6632 (electronic)",
  issn-l =       "0217-7323",
  bibdate =      "Mon Nov 14 16:26:06 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  abstract =     "A phenomenological law, called Benford's law, states
                 that the occurrence of the first digit, i.e.,
                 $1,2,\ldots{},9$, of numbers from many real world
                 sources is not uniformly distributed, but instead
                 favors smaller ones according to a logarithmic
                 distribution. We investigate, for the first time, the
                 first digit distribution of the full widths of mesons
                 and baryons in the well defined science domain of
                 particle physics systematically, and find that they
                 agree excellently with the Benford distribution. We
                 also discuss several general properties of Benford's
                 law, i.e., the law is scale-invariant, base-invariant,
                 and power-invariant. This means that the lifetimes of
                 hadrons follow also Benford's law.",
  acknowledgement = ack-nhfb,
  archiveprefix = "arXiv",
  eprint =       "1004.3077",
  fjournal =     "Modern Physics Letters A (MPLA)",
  primaryclass = "hep-ph",
}

@Article{Shi:2009:FDL,
  author =       "Yun Q. Shi",
  title =        "{First Digit Law} and Its Application to Digital
                 Forensics",
  journal =      j-LECT-NOTES-COMP-SCI,
  volume =       "5450",
  pages =        "448--453",
  year =         "2009",
  coden =        "LNCSD9",
  doi =          "http://dx.doi.org/10.1007/978-3-642-04438-0_37",
  issn =         "0302-9743 (print), 1611-3349 (electronic)",
  issn-l =       "0302-9743",
  bibdate =      "Mon Jan 21 17:32:48 MST 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 http://www.math.utah.edu/pub/tex/bib/lncs.bib",
  url =          "http://link.springer.com/content/pdf/10.1007/978-3-642-04438-0_37",
  acknowledgement = ack-nhfb,
  book-doi =     "http://dx.doi.org/10.1007/978-3-642-04438-0",
  book-url =     "http://www.springerlink.com/content/978-3-642-04438-0",
  fjournal =     "Lecture Notes in Computer Science",
}

@Article{Speed:2009:YWP,
  author =       "T. Speed",
  title =        "You want proof?",
  journal =      j-BULL-INST-MATH-STAT,
  volume =       "38",
  number =       "??",
  pages =        "11--??",
  month =        "????",
  year =         "2009",
  coden =        "SMBCVA",
  issn =         "0146-3942",
  issn-l =       "0146-3942",
  bibdate =      "Wed Nov 16 07:00:01 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  url =          "http://bulletin.imstat.org/archive/",
  acknowledgement = ack-nhfb,
  fjournal =     "Bulletin --- Institute of Mathematical Statistics",
  keywords =     "Benford's Law",
  remark =       "As of 16 November 2011, volume 38 is not yet online at
                 the publisher Web site, although there are (broken)
                 links for volumes 31 (2002) to date.",
}

@Article{Stosic:2009:CSM,
  author =       "Borko D. Stosi{\'c} and Tatijana Stosi{\'c}",
  title =        "Comment on {``Ising model on the scale-free network
                 with a Cayley-tree-like structure''}",
  journal =      j-PHYS-REV-E,
  volume =       "79",
  number =       apr,
  pages =        "048101",
  day =          "24",
  month =        apr,
  year =         "2009",
  coden =        "PLEEE8",
  doi =          "http://dx.doi.org/10.1103/PhysRevE.79.048101",
  issn =         "1539-3755 (print), 1550-2376 (electronic)",
  issn-l =       "1539-3755",
  bibdate =      "Tue Feb 26 06:40:57 MST 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  url =          "http://link.aps.org/doi/10.1103/PhysRevE.79.048101",
  acknowledgement = ack-nhfb,
  fjournal =     "Physical Review E (Statistical physics, plasmas,
                 fluids, and related interdisciplinary topics)",
  keywords =     "Zipf's Law",
  pagecount =    "2",
}

@Misc{Tao:2009:BLZ,
  author =       "Terrence Tao",
  title =        "{Benford}'s law, {Zipf}'s law, and the {Pareto}
                 distribution",
  howpublished = "Web document.",
  year =         "2009",
  bibdate =      "Mon Nov 14 16:59:19 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  url =          "http://terrytao.wordpress.com/2009/07/03/benfords-law-zipfs-law-and-the-pareto-distribution/",
  acknowledgement = ack-nhfb,
}

@Article{Todter:2009:BLI,
  author =       "Karl-Heinz T{\"o}dter",
  title =        "{Benford's Law} as an Indicator of Fraud in
                 Economics",
  journal =      j-GER-ECON-REV,
  volume =       "10",
  number =       "3",
  pages =        "339--351",
  month =        aug,
  year =         "2009",
  coden =        "????",
  doi =          "http://dx.doi.org/10.1111/j.1468-0475.2009.00475.x",
  issn =         "1465-6485 (print), 1468-0475 (electronic)",
  issn-l =       "1465-6485",
  bibdate =      "Mon Nov 14 17:09:33 MST 2011",
  bibsource =    "http://onlinelibrary.wiley.com/;
                 http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "German Economic Review",
  onlinedate =   "16 Jun 2009",
}

@Article{Xie:2009:FAS,
  author =       "Tao Xie and Yao Sun",
  title =        "A file assignment strategy independent of workload
                 characteristic assumptions",
  journal =      j-TOS,
  volume =       "5",
  number =       "3",
  pages =        "10:1--10:??",
  month =        nov,
  year =         "2009",
  coden =        "????",
  doi =          "http://doi.acm.org/10.1145/1629075.1629079",
  issn =         "1553-3077 (print), 1553-3093 (electronic)",
  issn-l =       "1553-3077",
  bibdate =      "Tue Mar 16 15:33:57 MDT 2010",
  bibsource =    "http://www.acm.org/pubs/contents/journals/tos/;
                 http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 http://www.math.utah.edu/pub/tex/bib/tos.bib",
  abstract =     "The problem of statically assigning nonpartitioned
                 files in a parallel I/O system has been extensively
                 investigated. A basic workload characteristic
                 assumption of most existing solutions to the problem is
                 that there exists a strong inverse correlation between
                 file access frequency and file size. In other words,
                 the most popular files are typically small in size,
                 while the large files are relatively unpopular. Recent
                 studies on the characteristics of Web proxy traces
                 suggested, however, the correlation, if any, is so weak
                 that it can be ignored. Hence, the following two
                 questions arise naturally. First, can existing
                 algorithms still perform well when the workload
                 assumption does not hold? Second, if not, can one
                 develop a new file assignment strategy that is immune
                 to the workload assumption? To answer these questions,
                 we first evaluate the performance of three well-known
                 file assignment algorithms with and without the
                 workload assumption, respectively. Next, we develop a
                 novel static nonpartitioned file assignment strategy
                 for parallel I/O systems, called static round-robin
                 (SOR), which is immune to the workload assumption.
                 Comprehensive experimental results show that SOR
                 consistently improves the performance in terms of mean
                 response time over the existing schemes.",
  acknowledgement = ack-nhfb,
  articleno =    "10",
  fjournal =     "ACM Transactions on Storage",
  keywords =     "File assignment; load balancing; parallel I/O;
                 workload characteristics; Zipfian distribution",
}

@Article{Zhang:2009:ZDT,
  author =       "Jianhua Zhang and Qinghua Chen and Yougui Wang",
  title =        "{Zipf} distribution in top {Chinese} firms and an
                 economic explanation",
  journal =      j-PHYSICA-A,
  volume =       "388",
  number =       "10",
  pages =        "2020--2024",
  day =          "15",
  month =        may,
  year =         "2009",
  coden =        "PHYADX",
  doi =          "http://dx.doi.org/10.1016/j.physa.2009.01.027",
  issn =         "0378-4371 (print), 1873-2119 (electronic)",
  issn-l =       "0378-4371",
  bibdate =      "Wed Feb 27 07:32:55 MST 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  url =          "http://www.sciencedirect.com/science/article/pii/S0378437109000806",
  acknowledgement = ack-nhfb,
  fjournal =     "Physica A. Statistical Mechanics and its
                 Applications",
  keywords =     "Zipf's Law",
}

@Article{Abourbih:2010:SSD,
  author =       "Jonathan A. Abourbih and Luke Blaney and Alan Bundy
                 and Fiona McNeill",
  title =        "A Single-Significant-Digit Calculus for Semi-Automated
                 Guesstimation",
  journal =      j-LECT-NOTES-COMP-SCI,
  volume =       "6173",
  pages =        "354--368",
  year =         "2010",
  coden =        "LNCSD9",
  doi =          "http://dx.doi.org/10.1007/978-3-642-14203-1_31",
  issn =         "0302-9743 (print), 1611-3349 (electronic)",
  issn-l =       "0302-9743",
  bibdate =      "Mon Jan 21 17:43:23 MST 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 http://www.math.utah.edu/pub/tex/bib/lncs.bib",
  url =          "http://link.springer.com/content/pdf/10.1007/978-3-642-14203-1_31",
  acknowledgement = ack-nhfb,
  book-doi =     "http://dx.doi.org/10.1007/978-3-642-14203-1",
  book-url =     "http://www.springerlink.com/content/978-3-642-14203-1",
  fjournal =     "Lecture Notes in Computer Science",
}

@Misc{Alagoz:2010:MDB,
  author =       "Ali Alag{\"o}z and Mustafa Ay",
  title =        "Muhasebe Denetiminde {Benford} Kanunu Temelli Dijital
                 Analiz. ({Turkish}) [{Benford Law}-Based Digital
                 Analysis of Accounting Oversight]",
  pages =        "17",
  day =          "8",
  month =        jan,
  year =         "2010",
  bibdate =      "Mon Feb 18 09:19:01 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  url =          "www.alialagoz.com.tr/doc-dr-alialagoz-makaleleri/muhasebe_denetiminde_benfrod_kanunu_temelli_dijital_analiz.pdf",
  acknowledgement = ack-nhfb,
  language =     "Turkish",
}

@Article{Aldous:2010:WCO,
  author =       "David Aldous and Tung Phan",
  title =        "When Can One Test an Explanation? {Compare} and
                 Contrast {Benford's Law} and the Fuzzy {CLT}",
  journal =      j-AMER-STAT,
  volume =       "64",
  number =       "3",
  pages =        "221--227",
  month =        aug,
  year =         "2010",
  coden =        "ASTAAJ",
  doi =          "http://dx.doi.org/10.1198/tast.2010.09098",
  issn =         "0003-1305 (print), 1537-2731 (electronic)",
  issn-l =       "0003-1305",
  mrnumber =     "2757166",
  bibdate =      "Sat Nov 12 09:13:23 2011",
  bibsource =    "http://www.amstat.org/publications/tas/;
                 http://www.math.utah.edu/pub/tex/bib/amstat.bib;
                 http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  url =          "http://www.tandfonline.com/doi/abs/10.1198/tast.2010.09098",
  acknowledgement = ack-nhfb,
  fjournal =     "The American Statistician",
}

@Article{Altamirano:2010:PTS,
  author =       "Carlo Altamirano and Alberto Robledo",
  title =        "Possible thermodynamic structure underlying the laws
                 of {Zipf} and {Benford}",
  journal =      "ArXiv e-prints",
  day =          "10",
  month =        aug,
  year =         "2010",
  bibdate =      "Mon Nov 21 07:12:08 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  url =          "http://arxiv.org/abs/1008.1614",
  abstract =     "We show that the laws of Zipf and Benford, obeyed by
                 scores of numerical data generated by many and diverse
                 kinds of natural phenomena and human activity are
                 related to the focal expression of a generalized
                 thermodynamic structure. This structure is obtained
                 from a deformed type of statistical mechanics that
                 arises when configurational phase space is incompletely
                 visited in a severe way. Specifically, the restriction
                 is that the accessible fraction of this space has
                 fractal properties. The focal expression is an
                 (incomplete) Legendre transform between two entropy (or
                 Massieu) potentials that when particularized to first
                 digits leads to a previously existing generalization of
                 Benford's law. The inverse functional of this
                 expression leads to Zipf's law; but it naturally
                 includes the bends or tails observed in real data for
                 small and large rank. Remarkably, we find that the
                 entire problem is analogous to the transition to chaos
                 via intermittency exhibited by low-dimensional
                 nonlinear maps. Our results also explain the generic
                 form of the degree distribution of scale-free
                 networks.",
  acknowledgement = ack-nhfb,
  remark =       "To be published in European Physical Journal B.",
}

@Article{Anderson:2010:BLC,
  author =       "Theresa Anderson and Larry Rolen and Ruth Stoehr",
  title =        "{Benford's} Law For Coefficients of Modular Forms and
                 Partition Functions",
  journal =      "ArXiv e-prints",
  day =          "3",
  month =        sep,
  year =         "2010",
  bibdate =      "Mon Nov 21 07:10:51 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  url =          "http://arxiv.org/abs/1009.0780",
  abstract =     "Here we prove that Benford's law holds for
                 coefficients of an infinite class of modular forms.
                 Expanding the work of Bringmann and Ono on exact
                 formulas for harmonic Maass forms, we derive the
                 necessary asymptotics. This implies that the
                 unrestricted partition function $p(n)$, as well as
                 other natural partition functions, satisfy Benford's
                 law.",
  acknowledgement = ack-nhfb,
  pagecount =    "10",
}

@Article{Bachmann:2010:APC,
  author =       "Val{\'e}rie Bachmann and Martin H. Fischer and
                 Hans-Peter Landolt and Peter Brugger",
  title =        "Asymmetric prefrontal cortex functions predict
                 asymmetries in number space",
  journal =      j-BRAIN-COGN,
  volume =       "74",
  number =       "3",
  pages =        "306--311",
  month =        dec,
  year =         "2010",
  coden =        "????",
  doi =          "http://dx.doi.org/10.1016/j.bandc.2010.08.011",
  issn =         "0278-2626 (print), 1090-2147 (electronic)",
  issn-l =       "0278-2626",
  bibdate =      "Tue Nov 22 11:28:19 MST 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 http://www.sciencedirect.com/",
  url =          "http://www.sciencedirect.com/science/article/pii/S0278262610001272",
  acknowledgement = ack-nhfb,
  fjournal =     "Brain and Cognition",
  keywords =     "Benford's Law; small-number bias (SNB); Spatial
                 Numerical Association of Response Codes (SNARC)
                 effect",
}

@Article{Balanzario:2010:SCB,
  author =       "Eugenio P. Balanzario and Jorge S{\'a}nchez-Ortiz",
  title =        "Sufficient conditions for {Benford}'s law",
  journal =      j-STAT-PROB-LETT,
  volume =       "80",
  number =       "23--24",
  pages =        "1713--1719",
  day =          "1--15",
  month =        dec,
  year =         "2010",
  coden =        "SPLTDC",
  doi =          "http://dx.doi.org/10.1016/j.spl.2010.07.014",
  issn =         "0167-7152 (print), 1879-2103 (electronic)",
  issn-l =       "0167-7152",
  mrclass =      "62E10 (62E17)",
  mrnumber =     "2734233 (2011i:62019)",
  bibdate =      "Tue Nov 22 11:28:19 MST 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 http://www.sciencedirect.com/",
  url =          "http://www.sciencedirect.com/science/article/pii/S0167715210002087",
  acknowledgement = ack-nhfb,
  fjournal =     "Statistics \& Probability Letters",
  keywords =     "Benford's Law",
}

@Article{Balaz:2010:BLD,
  author =       "V. Bal{\'a}{\v{z}} and K. Nagasaka and O. Strauch",
  title =        "{Benford}'s law and distribution functions of
                 sequences in $ (0, 1) $",
  journal =      j-MATH-NOTES-ACAD-SCI-USSR,
  volume =       "88",
  number =       "3--4",
  pages =        "449--463",
  month =        oct,
  year =         "2010",
  coden =        "MTHNB2",
  doi =          "http://dx.doi.org/10.1134/S0001434610090178",
  issn =         "0001-4346 (print), 1573-8876 (electronic)",
  issn-l =       "0001-4346",
  bibdate =      "Fri Nov 25 10:52:53 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  url =          "http://link.springer.com/article/10.1134%2FS0001434610090178",
  acknowledgement = ack-nhfb,
  fjournal =     "Mathematical Notes of the {Academy of Sciences of the
                 USSR = Matematicheskie Zametki}",
}

@Article{Balazh:2010:BLD,
  author =       "V. Balazh and K. Nagasaka and O. Shtraukh",
  title =        "{Benford}'s law and distribution functions of
                 sequences in {$(0, 1)$}",
  journal =      j-MAT-ZAMETKI,
  volume =       "88",
  number =       "4",
  pages =        "485--501",
  year =         "2010",
  doi =          "http://dx.doi.org/10.1134/S0001434610090178",
  issn =         "0025-567X",
  issn-l =       "0025-567X",
  mrclass =      "11K06 (60E05)",
  mrnumber =     "2882211",
  mrreviewer =   "Michael Drmota",
  bibdate =      "Thu Feb 14 07:02:03 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Rossi{\u\i}skaya Akademiya Nauk. Matematicheskie
                 Zametki",
}

@TechReport{Bauer:2010:DDF,
  author =       "J. Bauer and J. Gross",
  title =        "Difficulties Detecting Fraud? {The} Use of {Benford's
                 Law} on Regression Tables",
  type =         "Report",
  institution =  "Institute of Sociology,
                 Ludwig-Maximilians-Universit{\"a}t",
  address =      "M{\"u}nchen, Germany",
  pages =        "????",
  year =         "2010",
  bibdate =      "Tue Nov 22 21:15:18 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
}

@Article{Beber:2010:WNS,
  author =       "Bernd Beber and Alexandria Scacco",
  title =        "What the Numbers Say: a Digit-Based Test for Election
                 Fraud",
  journal =      j-POLIT-ANAL,
  volume =       "20",
  number =       "2",
  pages =        "211--234",
  month =        "Spring",
  year =         "2010",
  doi =          "http://dx.doi.org/10.1093/pan/mps003",
  issn =         "1047-1987 (print), 1476-4989 (electronic)",
  issn-l =       "1047-1987",
  bibdate =      "Mon Feb 18 17:29:42 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  url =          "http://pan.oxfordjournals.org/content/20/2/211.abstract",
  acknowledgement = ack-nhfb,
  fjournal =     "Political Analysis",
  keywords =     "Benford's Law",
}

@TechReport{Berger:2010:FFFa,
  author =       "A. Berger and T. P. Hill",
  title =        "Fundamental Flaws in {Feller}'s Classical Derivation
                 of {Benford's Law}",
  type =         "Preprint",
  institution =  "Department of Mathematical and Statistical Sciences,
                 University of Alberta",
  address =      "Edmonton, AB, Canada",
  pages =        "8",
  year =         "2010",
  bibdate =      "Mon Feb 18 17:31:57 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  url =          "http://www.benfordonline.net/ARTICLES/BergerHill2010.pdf",
  abstract =     "Feller's classic text \booktitle{An Introduction to
                 Probability Theory and its Applications}
                 \cite{Feller:1968:IPT} contains a derivation of the
                 well known significant-digit law called Benford's law.
                 More specifically, Feller gives a sufficient condition
                 (`large spread') for a random variable $X$ to be
                 approximately Benford distributed, that is, for $
                 \log_{10} X$ to be approximately uniformly distributed
                 modulo one. This note shows that the large-spread
                 derivation, which continues to be widely cited and
                 used, contains serious basic errors. Concrete examples
                 and a new inequality clearly demonstrate that large
                 spread (or large spread on a logarithmic scale) does
                 not imply that a random variable is approximately
                 Benford distributed, for any reasonable definition of
                 `spread' or measure of dispersion.",
  acknowledgement = ack-nhfb,
}

@Article{Berger:2010:FFFb,
  author =       "Arno Berger and Theodore P. Hill",
  title =        "Fundamental Flaws in {Feller}'s Classical Derivation
                 of {Benford's Law}",
  journal =      "ArXiv e-prints",
  month =        may,
  year =         "2010",
  coden =        "????",
  issn =         "????",
  bibdate =      "Mon Nov 14 18:23:13 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  url =          "http://adsabs.harvard.edu/abs/2010arXiv1005.2598B;
                 http://arxiv.org/abs/1005.2598",
  abstract =     "Feller's classic text \booktitle{An Introduction to
                 Probability Theory and its Applications}
                 \cite{Feller:1968:IPT} contains a derivation of the
                 well known significant-digit law called Benford's law.
                 More specifically, Feller gives a sufficient condition
                 (`large spread') for a random variable $X$ to be
                 approximately Benford distributed, that is, for
                 $\log_{10}X$ to be approximately uniformly distributed
                 modulo one. This note shows that the large-spread
                 derivation, which continues to be widely cited and
                 used, contains serious basic errors. Concrete examples
                 and a new inequality clearly demonstrate that large
                 spread (or large spread on a logarithmic scale) does
                 not imply that a random variable is approximately
                 Benford distributed, for any reasonable definition of
                 `spread' or measure of dispersion",
  acknowledgement = ack-nhfb,
  archiveprefix = "arXiv",
  eprint =       "1005.2598",
  keywords =     "Mathematics - Probability, Mathematics - Statistics,
                 62Axx",
  primaryclass = "math.PR",
}

@TechReport{Berger:2010:LSD,
  author =       "A. Berger",
  title =        "Large Spread Does Not Imply {Benford's Law}",
  type =         "Preprint",
  institution =  "Department of Mathematical and Statistical Sciences,
                 University of Alberta",
  address =      "Edmonton, AB, Canada",
  year =         "2010",
  bibdate =      "Sat Nov 12 16:46:10 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  url =          "http://www.math.ualberta.ca/~aberger/Publications.html",
  acknowledgement = ack-nhfb,
}

@Article{Block:2010:GEB,
  author =       "Henry W. Block and Thomas H. Savits",
  title =        "A General Example for {Benford} Data",
  journal =      j-AMER-STAT,
  volume =       "64",
  number =       "4",
  pages =        "335--339",
  month =        nov,
  year =         "2010",
  coden =        "ASTAAJ",
  doi =          "http://dx.doi.org/10.1198/tast.2010.09169",
  issn =         "0003-1305 (print), 1537-2731 (electronic)",
  issn-l =       "0003-1305",
  mrnumber =     "2758565",
  bibdate =      "Sat Nov 12 09:13:23 2011",
  bibsource =    "http://www.amstat.org/publications/tas/;
                 http://www.math.utah.edu/pub/tex/bib/amstat.bib;
                 http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  abstract =     "Benford's Law deals, among other things, with the
                 proportion of numbers whose first significant digit is
                 a $1$ (e.g., $0.00131$ and $19668$ both have first
                 significant digit $1$) in a variety of datasets. In
                 these datasets, which arise in various compendiums or
                 as mixtures of various sets of numbers, the proportion
                 of numbers with first significant digit one is $0.3010$
                 which is much higher than the commonsense value of $1 /
                 9$. The reasons for this occurrence have been elusive.
                 Mathematical attempts to explain this phenomenon have
                 been relatively fruitless. Methods involving
                 probability have been somewhat more successful. In this
                 article we give some simple reasons for this occurrence
                 and also give an example of a general mixture of
                 distributions which exactly satisfies this Law. Various
                 other examples and counterexamples are also given.",
  acknowledgement = ack-nhfb,
  fjournal =     "The American Statistician",
}

@Article{Bonache:2010:DFL,
  author =       "A. B. Bonache and K. Moris and J. Maurice",
  title =        "{D}{\'e}tection de fraudes et loi de {Benford}:
                 Quelques risques associ{\'e}s. ({French}) [{Fraud}
                 detection and {Benford}'s law: Some risks]",
  journal =      "Revue Fran{\c{c}}aise de Comptabilit{\'e}",
  volume =       "??",
  number =       "431",
  pages =        "24--27",
  month =        apr,
  year =         "2010",
  coden =        "????",
  doi =          "????",
  issn =         "0484-8764",
  issn-l =       "0484-8764",
  bibdate =      "Mon Feb 18 17:33:12 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  url =          "????",
  acknowledgement = ack-nhfb,
  journal-url =  "http://www.experts-comptables.fr/csoec/Publications/RFC",
  language =     "French",
}

@InCollection{Brahler:2010:EMS,
  author =       "Gernot Br{\"a}hler and Markus Bensmann and Anna-Lena
                 Emke",
  booktitle =    "{Ilmenauer Schriften zur Betriebswirtschaftslehre}.
                 ({German}) [{Illmenauer} writings on economics]",
  title =        "{Der Einsatz mathematisch-statistischer Methoden in
                 der digitalen Betriebspr{\"u}fung}. ({German}) [{The}
                 use of mathematical and statistical methods in the
                 digital audit]",
  volume =       "4/2010",
  publisher =    "Verlag proWiWi e.V.",
  address =      "Ilmenau, Germany",
  pages =        "48",
  month =        apr,
  year =         "2010",
  isbn =         "3-940882-23-2",
  isbn-13 =      "978-3-940882-23-3",
  issn =         "1866-2145 (print), 2192-4643 (electronic)",
  lccn =         "????",
  bibdate =      "Mon Feb 18 17:35:58 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  url =          "https://www.econstor.eu/dspace/bitstream/10419/55680/1/665348576.pdf",
  acknowledgement = ack-nhfb,
  language =     "German",
}

@Article{Bravo-Marquez:2010:HLM,
  author =       "Felipe Bravo-Marquez and Gaston L'Huillier and
                 Sebasti{\'a}n A. R{\'\i}os and Juan D. Vel{\'a}squez",
  title =        "Hypergeometric Language Model and {Zipf}-Like Scoring
                 Function for {Web} Document Similarity Retrieval",
  journal =      j-LECT-NOTES-COMP-SCI,
  volume =       "6393",
  pages =        "303--308",
  year =         "2010",
  coden =        "LNCSD9",
  doi =          "http://dx.doi.org/10.1007/978-3-642-16321-0_32",
  issn =         "0302-9743 (print), 1611-3349 (electronic)",
  issn-l =       "0302-9743",
  bibdate =      "Mon Jan 21 17:49:42 MST 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 http://www.math.utah.edu/pub/tex/bib/lncs.bib",
  url =          "http://link.springer.com/content/pdf/10.1007/978-3-642-16321-0_32",
  acknowledgement = ack-nhfb,
  book-doi =     "http://dx.doi.org/10.1007/978-3-642-16321-0",
  book-url =     "http://www.springerlink.com/content/978-3-642-16321-0",
  fjournal =     "Lecture Notes in Computer Science",
}

@Article{Cartlidge:2010:NNO,
  author =       "Edwin Cartlidge",
  title =        "In nature, number one dominates",
  journal =      "Institute of Physics, Environmental Research Letters",
  volume =       "??",
  number =       "??",
  pages =        "??--??",
  day =          "25",
  month =        oct,
  year =         "2010",
  doi =          "????",
  bibdate =      "Mon Feb 18 17:38:16 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  url =          "http://environmentalresearchweb.org/cws/article/news/44124",
  acknowledgement = ack-nhfb,
  keywords =     "Benford's Law",
}

@Misc{Conway:2010:CFM,
  author =       "D. Conway",
  title =        "{Benford's Law} Tests for {Wikileaks} Data",
  howpublished = "Zero Intelligence Agents website.",
  day =          "1",
  month =        aug,
  year =         "2010",
  bibdate =      "Mon Feb 18 17:39:45 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  url =          "http://www.drewconway.com/zia/?p=2234",
  acknowledgement = ack-nhfb,
}

@InCollection{Corazza:2010:CFM,
  author =       "Marco Corazza and Andrea Ellero and Alberto Zorzi",
  booktitle =    "Mathematical and statistical methods for actuarial
                 sciences and finance",
  title =        "Checking financial markets via {Benford}'s law: the
                 {S\&P 500} case",
  publisher =    "Springer Italia",
  address =      "Milan, Italy",
  pages =        "93--102",
  year =         "2010",
  doi =          "http://dx.doi.org/10.1007/978-88-470-1481-7_10",
  mrclass =      "62P05",
  mrnumber =     "2676191",
  bibdate =      "Sat Nov 12 09:13:23 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
}

@Article{Corominas-Murtra:2010:UZL,
  author =       "Bernat Corominas-Murtra and Ricard V. Sol{\'e}",
  title =        "Universality of {Zipf}'s law",
  journal =      j-PHYS-REV-E,
  volume =       "82",
  number =       "1",
  pages =        "011102",
  day =          "1",
  month =        jul,
  year =         "2010",
  coden =        "PLEEE8",
  doi =          "http://dx.doi.org/10.1103/PhysRevE.82.011102",
  issn =         "1539-3755 (print), 1550-2376 (electronic)",
  issn-l =       "1539-3755",
  mrclass =      "82B03 (62B10)",
  mrnumber =     "2736361 (2011j:82002)",
  mrreviewer =   "N. N. Ganikhodjaev",
  bibdate =      "Tue Feb 26 06:40:57 MST 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  url =          "http://link.aps.org/doi/10.1103/PhysRevE.82.011102",
  acknowledgement = ack-nhfb,
  fjournal =     "Physical Review E (Statistical physics, plasmas,
                 fluids, and related interdisciplinary topics)",
  keywords =     "Zipf's Law",
  pagecount =    "9",
}

@Article{Courtland:2010:CML,
  author =       "Rachel Courtland",
  title =        "Curious mathematical law is rife in nature",
  journal =      j-NEW-SCIENTIST,
  volume =       "208",
  number =       "2782",
  pages =        "10--10",
  day =          "16",
  month =        oct,
  year =         "2010",
  coden =        "NWSCAL",
  doi =          "http://dx.doi.org/10.1016/S0262-4079(10)62497-9",
  issn =         "0262-4079 (print), 1364-8500 (electronic)",
  issn-l =       "0262-4079",
  bibdate =      "Tue Nov 22 11:28:19 MST 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 http://www.sciencedirect.com/",
  url =          "http://www.sciencedirect.com/science/article/pii/S0262407910624979",
  acknowledgement = ack-nhfb,
  fjournal =     "The New Scientist",
  keywords =     "Benford's Law; earthquake detection",
  xxissn =       "0262-4079, 0028-6664",
}

@Article{Debreceny:2010:DMJ,
  author =       "S. Debreceny and Glen L. Gray",
  title =        "Data mining journal entries for fraud detection: An
                 exploratory study",
  journal =      j-INT-J-ACCOUNT-INFO-SYS,
  volume =       "11",
  number =       "3",
  pages =        "157--181",
  month =        sep,
  year =         "2010",
  coden =        "IJAIA7",
  doi =          "http://dx.doi.org/10.1016/j.accinf.2010.08.001",
  issn =         "1467-0895 (print), 1873-4723 (electronic)",
  issn-l =       "1467-0895",
  bibdate =      "Tue Nov 22 11:28:19 MST 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 http://www.sciencedirect.com/",
  note =         "See discussion
                 \cite{Grabski:2010:DDM,Kriel:2010:DDM}.",
  url =          "http://www.sciencedirect.com/science/article/pii/S1467089510000540;
                 http://www.sciencedirect.com/science/journal/14670895",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Accounting Information
                 Systems",
  keywords =     "Benford's Law",
}

@TechReport{Deckert:2010:IBL,
  author =       "Joseph Deckert and Mikhail Myagkov and Peter C.
                 Ordeshook",
  title =        "The Irrelevance of {Benford's Law} for Detecting Fraud
                 in Elections",
  type =         "{CALTECH} working paper",
  number =       "9",
  institution =  "California Institute of Technology",
  address =      "Pasadena, CA, USA",
  pages =        "27",
  day =          "9",
  month =        mar,
  year =         "2010",
  bibdate =      "Mon Feb 18 17:40:53 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  url =          "http://vote.caltech.edu/drupal/node/327",
  acknowledgement = ack-nhfb,
  remark =       "From the abstract: ``..., we argue here that Benford's
                 Law is essentially useless as a forensic indicator of
                 fraud.''",
}

@Article{Deligny:2010:RRL,
  author =       "H. Deligny and P. Jolissaint",
  title =        "Relations de r{\'e}currence lin{\'e}aires,
                 primitivit{\'e} et loi de {Benford}. ({French})
                 [{Linear} recurrence relations, primitivity, and
                 {Benford's Law}]",
  journal =      "ArXiv e-prints",
  day =          "23",
  month =        jul,
  year =         "2010",
  coden =        "????",
  issn =         "????",
  bibdate =      "Mon Nov 14 18:14:51 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  url =          "http://adsabs.harvard.edu/abs/2010arXiv1007.5349D;
                 http://arxiv.org/abs/1007.5349",
  abstract =     "We prove that many sequences of positive numbers
                 $(a_n)$ defined by finite linear difference equations
                 $a_{n+k} = c_{k-1} a_{n+k-1} + \ldots{} + c_0 a_n$ with
                 suitable nonnegative reals coefficients $c_i$ satisfy
                 Benford's Law on the first digit in many bases $b > 2$.
                 Our techniques rely on Perron--Frobenius theory via the
                 companion matrix of the characteristic polynomial of
                 the defining equation.",
  acknowledgement = ack-nhfb,
  archiveprefix = "arXiv",
  eprint =       "1007.5349",
  keywords =     "Mathematics - Dynamical Systems, Mathematics - Rings
                 and Algebras, 11A99",
  language =     "French",
  primaryclass = "math.DS",
}

@Article{Diekmann:2010:BLF,
  author =       "Andreas Diekmann and Ben Jann",
  title =        "{Benford's Law} and Fraud Detection: Facts and
                 Legends",
  journal =      j-GER-ECON-REV,
  volume =       "11",
  number =       "3",
  pages =        "397--401",
  month =        aug,
  year =         "2010",
  coden =        "????",
  doi =          "http://dx.doi.org/10.1111/j.1468-0475.2010.00510.x",
  issn =         "1465-6485 (print), 1468-0475 (electronic)",
  issn-l =       "1465-6485",
  bibdate =      "Mon Nov 14 17:09:33 MST 2011",
  bibsource =    "http://onlinelibrary.wiley.com/;
                 http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "German Economic Review",
  keywords =     "Benford's law; false negative; false positive; fraud
                 detection; regression coefficients",
  onlinedate =   "6 Apr 2010",
}

@Article{Egghe:2010:NSP,
  author =       "Leo Egghe",
  title =        "A new short proof of {Naranan}'s theorem, explaining
                 {Lotka's Law} and {Zipf's Law}",
  journal =      j-J-AM-SOC-INF-SCI-TECHNOL,
  volume =       "61",
  number =       "12",
  pages =        "2581--2583",
  year =         "2010",
  coden =        "JASIEF",
  doi =          "http://dx.doi.org/10.1002/asi.21431",
  issn =         "1532-2882 (print), 1532-2890 (electronic)",
  issn-l =       "1532-2882",
  bibdate =      "Mon Feb 25 06:13:56 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of the American Society for Information
                 Science and Technology",
}

@Article{Farkas:2010:SUN,
  author =       "Janos Farkas and Gy{\"o}rgy Gyurky",
  title =        "The significance of using the {Newcomb--Benford} law
                 as a test of nuclear half-life calculations",
  journal =      "Acta Physica Polonica, B",
  volume =       "41",
  pages =        "1213--1221",
  year =         "2010",
  coden =        "APOBBB",
  issn =         "0587-4254 (print), 1509-5770 (electronic)",
  issn-l =       "0587-4254",
  bibdate =      "Mon Nov 14 16:21:42 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  url =          "http://adsabs.harvard.edu/abs/2010arXiv1006.3615F;
                 http://arxiv.org/abs/1006.3615",
  abstract =     "Half-life number sequences collected from nuclear data
                 charts are found to obey the Newcomb--Benford law.
                 Based on this fact, it has been suggested recently,
                 that this law should be used to test the quality of
                 nuclear decay models. In this paper we briefly recall
                 how, when and why the Newcomb--Benford law can be
                 observed in a set of numbers with a given probability
                 distribution. We investigate the special case of
                 nuclear half-lives, and show that the law provides no
                 additional clue in understanding decay half-lives.
                 Thus, it can play no significant role in testing
                 nuclear decay theories.",
  acknowledgement = ack-nhfb,
  ajournal =     "Acta Phys. Pol. B",
  ajournal-2 =   "Acta Phys. Polon. B",
  archiveprefix = "arXiv",
  eprint =       "1006.3615",
  primaryclass = "math-ph",
}

@Article{Fischer:2010:HCS,
  author =       "Martin H. Fischer and Richard A. Mills and Samuel
                 Shaki",
  title =        "How to cook a {SNARC}: Number placement in text
                 rapidly changes spatial-numerical associations",
  journal =      j-BRAIN-COGN,
  volume =       "72",
  number =       "3",
  pages =        "333--336",
  month =        apr,
  year =         "2010",
  coden =        "????",
  doi =          "http://dx.doi.org/10.1016/j.bandc.2009.10.010",
  issn =         "0278-2626 (print), 1090-2147 (electronic)",
  issn-l =       "0278-2626",
  bibdate =      "Tue Nov 22 11:28:19 MST 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 http://www.sciencedirect.com/",
  url =          "http://www.sciencedirect.com/science/article/pii/S0278262609002024",
  acknowledgement = ack-nhfb,
  fjournal =     "Brain and Cognition",
  keywords =     "Benford's Law; Spatial Numerical Association of
                 Response Codes (SNARC)",
}

@Article{Formann:2010:NBL,
  author =       "A. K. Formann and R. J. Morris",
  title =        "The {Newcomb--Benford Law} in Its Relation to Some
                 Common Distributions",
  journal =      j-PLOS-ONE,
  volume =       "51",
  month =        may,
  year =         "2010",
  coden =        "POLNCL",
  doi =          "http://dx.doi.org/10.1371/journal.pone.0010541",
  issn =         "1932-6203",
  issn-l =       "1932-6203",
  bibdate =      "Mon Nov 14 18:19:09 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  url =          "http://adsabs.harvard.edu/abs/2010PLoSO...510541F",
  acknowledgement = ack-nhfb,
  ages =         "10541",
  fjournal =     "PLoS One",
}

@Article{Genolini:2010:EIP,
  author =       "Christophe Genolini and Tarak Driss",
  title =        "Eveiller l'int{\'e}r{\^e}t pour la statistique par
                 l'exemple. ({French}) [{Raising} interest in statistics
                 by example]",
  journal =      "Statistique et Enseignement",
  volume =       "1",
  number =       "2",
  pages =        "49--57",
  month =        "????",
  year =         "2010",
  coden =        "????",
  doi =          "????",
  issn =         "2108-6745",
  issn-l =       "2108-6745",
  bibdate =      "Mon Feb 18 17:43:03 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  url =          "http://publications-sfds.math.cnrs.fr/index.php/StatEns/article/view/16",
  acknowledgement = ack-nhfb,
  journal-url =  "http://www.statistique-et-enseignement.fr/",
  keywords =     "Benford's Law",
  language =     "French",
}

@Article{Giuliano:2010:UPI,
  author =       "Rita Giuliano and {\'E}lise Janvresse",
  title =        "A unifying probabilistic interpretation of {Benford}'s
                 law",
  journal =      "Uniform Distribution Theory",
  volume =       "5",
  number =       "2",
  pages =        "169--182",
  year =         "2010",
  coden =        "????",
  issn =         "1336-913X",
  issn-l =       "1336-913X",
  mrclass =      "60J10 (11K99 60A99)",
  mrnumber =     "2781415",
  bibdate =      "Sat Nov 12 09:13:23 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  url =          "http://www.boku.ac.at/MATH/udt/vol05/no2/91GiulJan10-2.pdf",
  acknowledgement = ack-nhfb,
  ajournal =     "Unif. Distrib. Theory",
  fjournal =     "Uniform Distribution Theory",
}

@Article{Grabski:2010:DDM,
  author =       "Severin Grabski",
  title =        "Discussion of {``Data mining journal entries for fraud
                 detection: An exploratory study''}",
  journal =      j-INT-J-ACCOUNT-INFO-SYS,
  volume =       "11",
  number =       "3",
  pages =        "182--185",
  month =        sep,
  year =         "2010",
  coden =        "IJAIA7",
  doi =          "http://dx.doi.org/10.1016/j.accinf.2010.07.008",
  issn =         "1467-0895 (print), 1873-4723 (electronic)",
  issn-l =       "1467-0895",
  bibdate =      "Tue Nov 22 11:28:19 MST 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 http://www.sciencedirect.com/",
  note =         "See \cite{Debreceny:2010:DMJ,Kriel:2010:DDM}.",
  url =          "http://www.sciencedirect.com/science/article/pii/S1467089510000394",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Accounting Information
                 Systems",
  keywords =     "Benford's Law",
}

@Article{Hickman:2010:DAC,
  author =       "Matthew Hickman and Stephen Rice",
  title =        "Digital Analysis of Crime Statistics: Does Crime
                 Conform to {Benford's Law}?",
  journal =      j-J-QUANT-CRIMINOL,
  volume =       "26",
  number =       "3",
  pages =        "333--349",
  month =        sep,
  year =         "2010",
  coden =        "JQCRE6",
  doi =          "http://dx.doi.org/10.1007/s10940-010-9094-6",
  issn =         "0748-4518 (print), 1573-7799 (electronic)",
  issn-l =       "0748-4518",
  bibdate =      "Fri Nov 25 10:30:30 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Quantitative Criminology",
  keywords =     "Benford distribution; Benford's law; Crime data; Crime
                 statistics; Data errors; Digital analysis; Fabricated
                 data; First digit; Fraud detection; Uniform crime
                 reports",
}

@MastersThesis{Jasak:2010:BZR,
  author =       "Zoran Jasak",
  title =        "Benfordov zakon i reinforcement u{\v{c}}enje.
                 ({Bosnian}) [{Benford's Law} and reinforcement
                 learning]",
  type =         "{Magistarski Rad} ({M.Sc.} Thesis)",
  school =       "Prirodno-Matematicki Fakultet, Odsjek za matematiku,
                 Ju Univerzitet u Tuzla",
  address =      "Tuzla, Bosnia and Herzegovina",
  pages =        "124",
  month =        dec,
  year =         "2010",
  bibdate =      "Mon Feb 18 17:48:33 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  url =          "http://www.math.ualberta.ca/~aberger/benford_bibliography/jasak_10.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "action; Adaptive Benford's method; Adaptivna
                 Benfordova metoda; akcija; Benford's law; Benfordov
                 zakon; confidence intervals; contamination level;
                 intervali povjerenja; koli{\v{c}}nik; nivo
                 kontaminacije; Q learning; Q u{\v{c}}enje; quotient;
                 reinforcement learning; reinforcement u{\v{c}}enje;
                 Sarsa; stanje; state",
  language =     "Bosnian",
}

@Article{Jiang:2010:NMS,
  author =       "Weina Jiang and Anthony T. S. Ho and Helen Treharne
                 and Yun Q. Shi",
  title =        "A Novel Multi-size Block {Benford's Law} Scheme for
                 Printer Identification",
  journal =      j-LECT-NOTES-COMP-SCI,
  volume =       "6297",
  pages =        "643--652",
  year =         "2010",
  coden =        "LNCSD9",
  doi =          "http://dx.doi.org/10.1007/978-3-642-15702-8_59",
  issn =         "0302-9743 (print), 1611-3349 (electronic)",
  issn-l =       "0302-9743",
  bibdate =      "Mon Jan 21 17:47:23 MST 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 http://www.math.utah.edu/pub/tex/bib/lncs.bib",
  url =          "http://link.springer.com/content/pdf/10.1007/978-3-642-15702-8_59",
  acknowledgement = ack-nhfb,
  book-doi =     "http://dx.doi.org/10.1007/978-3-642-15702-8",
  book-url =     "http://www.springerlink.com/content/978-3-642-15702-8",
  fjournal =     "Lecture Notes in Computer Science",
}

@Article{Kaynar:2010:FSM,
  author =       "B. Kaynar and A. Berger and T. P. Hill and A. Ridder",
  title =        "Finite-state {Markov} Chains obey {Benford's Law}",
  journal =      "ArXiv e-prints",
  month =        mar,
  year =         "2010",
  coden =        "????",
  issn =         "????",
  mrclass =      "60J22, 11K06, 15B51",
  bibdate =      "Tue Nov 15 06:30:53 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  url =          "http://adsabs.harvard.edu/abs/2010arXiv1003.0562K;
                 http://arxiv.org/abs/1003.0562",
  acknowledgement = ack-nhfb,
  archiveprefix = "arXiv",
  eprint =       "1003.0562",
  keywords =     "Mathematics - Probability",
  primaryclass = "math.PR",
}

@Article{Klar:2010:ZLL,
  author =       "B. Klar and P. R. Parthasarathy and N. Henze",
  title =        "{Zipf} and {Lerch} limit of birth and death
                 processes",
  journal =      "Probability in the Engineering and Informational
                 Sciences",
  volume =       "24",
  number =       "1",
  pages =        "129--144",
  year =         "2010",
  coden =        "????",
  doi =          "http://dx.doi.org/10.1017/S0269964809990179",
  issn =         "0269-9648",
  issn-l =       "0269-9648",
  mrclass =      "60J27 (91F20)",
  mrnumber =     "2575846 (2010m:60254)",
  bibdate =      "Sat Nov 12 09:13:23 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  ajournal =     "Probab. Engrg. Inform. Sci.",
  fjournal =     "Probability in the Engineering and Informational
                 Sciences",
}

@Article{Kriel:2010:DDM,
  author =       "Eckhardt Kriel",
  title =        "Discussion of {``Data mining journal entries for fraud
                 detection: An exploratory study''}",
  journal =      j-INT-J-ACCOUNT-INFO-SYS,
  volume =       "11",
  number =       "3",
  pages =        "186--188",
  month =        sep,
  year =         "2010",
  coden =        "IJAIA7",
  doi =          "http://dx.doi.org/10.1016/j.accinf.2010.07.009",
  issn =         "1467-0895 (print), 1873-4723 (electronic)",
  issn-l =       "1467-0895",
  bibdate =      "Tue Nov 22 11:28:19 MST 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 http://www.sciencedirect.com/",
  note =         "See \cite{Debreceny:2010:DMJ,Grabski:2010:DDM}.",
  url =          "http://www.sciencedirect.com/science/article/pii/S1467089510000400",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Accounting Information
                 Systems",
  keywords =     "Benford's Law",
}

@Article{Lee:2010:SAR,
  author =       "Joanne Lee and Wendy K. Tam Cho and George G. Judge",
  title =        "{Stigler}'s approach to recovering the distribution of
                 first significant digits in natural data sets",
  journal =      j-STAT-PROB-LETT,
  volume =       "80",
  number =       "2",
  pages =        "82--88",
  day =          "15",
  month =        jan,
  year =         "2010",
  coden =        "SPLTDC",
  doi =          "http://dx.doi.org/10.1016/j.spl.2009.09.015",
  issn =         "0167-7152 (print), 1879-2103 (electronic)",
  issn-l =       "0167-7152",
  bibdate =      "Tue Nov 22 11:28:19 MST 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 http://www.sciencedirect.com/",
  url =          "http://www.sciencedirect.com/science/article/pii/S0167715209003563",
  acknowledgement = ack-nhfb,
  fjournal =     "Statistics \& Probability Letters",
  keywords =     "Benford's Law",
}

@Article{Liu:2010:CIE,
  author =       "Hongyan Liu and Xiaoyu Wang and Yinghui Yang",
  title =        "Comments on {``An integrated efficient solution for
                 computing frequent and top-$k$ elements in data
                 streams''}",
  journal =      j-TODS,
  volume =       "35",
  number =       "2",
  pages =        "15:1--15:??",
  month =        apr,
  year =         "2010",
  coden =        "ATDSD3",
  doi =          "http://doi.acm.org/10.1145/1735886.1735894",
  issn =         "0362-5915 (print), 1557-4644 (electronic)",
  issn-l =       "0362-5915",
  bibdate =      "Wed Apr 28 13:44:08 MDT 2010",
  bibsource =    "http://www.acm.org/pubs/contents/journals/tods/;
                 http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  note =         "See \cite{Metwally:2006:IES}.",
  abstract =     "We investigate a well-known algorithm, {\em
                 Space-Saving\/} [Metwally et al. 2006], which has been
                 proven efficient and effective at mining frequent
                 elements in data streams. We discovered an error in one
                 of the theorems in Metwally et al. [2006]. Experiments
                 are conducted to illustrate the error.",
  acknowledgement = ack-nhfb,
  articleno =    "15",
  fjournal =     "ACM Transactions on Database Systems",
  keywords =     "approximate queries; data streams; frequent elements;
                 top-$k$ elements; Zipfian distributions",
}

@Article{Lu:2010:BLP,
  author =       "Ocean Fan Lu and David E. Giles",
  title =        "{Benford's Law} and psychological barriers in certain
                 {eBay} auctions",
  journal =      j-APPL-ECON-LETT,
  volume =       "17",
  number =       "10",
  pages =        "1005--1008",
  month =        "????",
  year =         "2010",
  coden =        "????",
  doi =          "http://dx.doi.org/10.1080/13504850802631814",
  issn =         "1350-4851 (print), 1466-4291 (electronic)",
  issn-l =       "1350-4851",
  bibdate =      "Sat Jan 07 09:10:23 2012",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  url =          "http://www.tandfonline.com/doi/abs/10.1080/13504850802631814",
  abstract =     "Using generalizations of Benford's Law we test for the
                 absence of psychological barriers at various price
                 levels in eBay auctions for professional football
                 tickets. Our empirical results indicate that this
                 hypothesis cannot be rejected.",
  acknowledgement = ack-nhfb,
  fjournal =     "Applied Economics Letters",
  onlinedate =   "16 Jun 2009",
}

@Article{Mahdian:2010:BBM,
  author =       "Babak Mahdian and Stanislav Saic",
  title =        "A bibliography on blind methods for identifying image
                 forgery",
  journal =      j-SIGNAL-PROCESS-IMAGE-COMMUN,
  volume =       "25",
  number =       "6",
  pages =        "389--399",
  month =        jul,
  year =         "2010",
  coden =        "SPICEF",
  doi =          "http://dx.doi.org/10.1016/j.image.2010.05.003",
  issn =         "0923-5965 (print), 1879-2677 (electronic)",
  issn-l =       "0923-5965",
  bibdate =      "Tue Nov 22 11:28:19 MST 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 http://www.sciencedirect.com/",
  url =          "http://www.sciencedirect.com/science/article/pii/S0923596510000536",
  acknowledgement = ack-nhfb,
  fjournal =     "Signal Processing: Image Communication",
  keywords =     "Benford's Law",
}

@Article{Manoochehrnia:2010:BLA,
  author =       "P. Manoochehrnia and F. Rachidi and M. Rubinstein and
                 W. Schulz and G. Diendorfer",
  title =        "{Benford's Law} and Its Application to Lightning
                 Data",
  journal =      j-IEEE-TRANS-ELECTROMAGN-COMPAT,
  volume =       "52",
  number =       "4",
  pages =        "956--961",
  month =        nov,
  year =         "2010",
  coden =        "IEMCAE",
  doi =          "http://dx.doi.org/10.1109/TEMC.2010.2067218",
  issn =         "0018-9375 (print), 1558-187X (electronic)",
  issn-l =       "0018-9375",
  bibdate =      "Mon Nov 21 22:24:43 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Electromagnetic Compatibility",
}

@InProceedings{Mebane:2010:EFS,
  author =       "Walter R. {Mebane, Jr.}",
  editor =       "????",
  booktitle =    "{2010 Summer Meeting of the Political Methodology
                 Society, University of Iowa, July 22--24, 2010}",
  title =        "Election Fraud or Strategic Voting? {Can} Second-digit
                 Tests Tell the Difference?",
  publisher =    "????",
  address =      "????",
  pages =        "1--49",
  year =         "2010",
  isbn =         "????",
  isbn-13 =      "????",
  bibdate =      "Sat Feb 16 11:56:47 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  url =          "http://www.umich.edu/~wmebane/pm10.pdf",
  acknowledgement = ack-nhfb,
}

@Article{Mebane:2010:FPE,
  author =       "Walter R. {Mebane, Jr.}",
  title =        "Fraud in the 2009 presidential election in {Iran}?",
  journal =      j-CHANCE,
  volume =       "23",
  number =       "1",
  pages =        "6--15",
  month =        mar,
  year =         "2010",
  coden =        "CNDCE4",
  doi =          "http://dx.doi.org/10.1007/s00144-010-0003-4",
  issn =         "0933-2480 (print), 1867-2280 (electronic)",
  issn-l =       "0933-2480",
  bibdate =      "Mon Feb 18 17:50:18 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  url =          "http://www.springerlink.com/content/0337v415563q0753/abstract/",
  acknowledgement = ack-nhfb,
  fjournal =     "Chance: a magazine for people interested in the
                 analysis of data",
  xxnote =       "Publisher archive at
                 \path=http://amstat.tandfonline.com/loi/ucha20= is
                 missing volumes 18 (2005)--24 (2011). Those volumes are
                 available at
                 \path=http://link.springer.com/journal/144=",
}

@TechReport{Mebane:2010:MSD,
  author =       "Walter R. {Mebane, Jr.}",
  title =        "Memo on second-digit tests done on precinct counts for
                 {Democratic Senate} primary in {South Carolina}, 2010",
  type =         "Report",
  institution =  "University of Michigan",
  address =      "Ann Arbor, MI, USA",
  day =          "12",
  month =        jun,
  year =         "2010",
  bibdate =      "Sat Feb 16 12:06:16 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  url =          "http://www.umich.edu/~wmebane/SCmemo12jun2010.pdf",
  acknowledgement = ack-nhfb,
}

@Article{Morrison:2010:MG,
  author =       "Kent E. Morrison",
  title =        "The Multiplication Game",
  journal =      j-MATH-MAG,
  volume =       "83",
  number =       "??",
  pages =        "100--110",
  month =        apr,
  year =         "2010",
  coden =        "MAMGA8",
  doi =          "????",
  issn =         "0025-570X",
  issn-l =       "0025-570X",
  bibdate =      "Mon Feb 18 17:51:50 2013",
  bibsource =    "http://www.maa.org/pubs/mag_apr10_toc.html;
                 http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  url =          "http://www.calpoly.edu/~kmorriso/Research/multgameMMfinal.pdf",
  acknowledgement = ack-nhfb,
  fjournal =     "Mathematics Magazine",
  journal-url =  "http://www.maa.org/pubs/mathmag.html",
}

@Book{Nillsen:2010:RRD,
  author =       "Rodney Victor Nillsen",
  title =        "Randomness and recurrence in dynamical systems: a real
                 analysis approach",
  volume =       "31",
  publisher =    pub-MATH-ASSOC-AMER,
  address =      pub-MATH-ASSOC-AMER:adr,
  pages =        "xviii + 357",
  year =         "2010",
  isbn =         "0-88385-043-5",
  isbn-13 =      "978-0-88385-043-5",
  lccn =         "QA614.8 .N55 2010",
  bibdate =      "Mon Feb 18 17:53:28 MST 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                z3950.loc.gov:7090/Voyager",
  series =       "The Carus mathematical monographs",
  acknowledgement = ack-nhfb,
  subject =      "Differentiable dynamical systems; Measure theory",
  tableofcontents = "Background ideas and knowledge \\
                 Irrational numbers and dynamical systems \\
                 Probability and randomness \\
                 Recurrence \\
                 Averaging in time and space",
}

@Article{Novikov:2010:APB,
  author =       "V. P. Novikov",
  title =        "Aspectual Principle, {Benford's Law} and {Russell's
                 Paradox}",
  journal =      "ArXiv e-prints",
  month =        dec,
  year =         "2010",
  coden =        "????",
  issn =         "????",
  bibdate =      "Mon Nov 14 18:11:57 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  url =          "http://adsabs.harvard.edu/abs/2010arXiv1012.5537N;
                 http://arxiv.org/abs/1012.5537",
  acknowledgement = ack-nhfb,
  archiveprefix = "arXiv",
  eprint =       "1012.5537",
  keywords =     "Mathematics - Classical Analysis and ODEs",
  pagecount =    "5",
  primaryclass = "math.CA",
}

@Book{Oleksy:2010:DMB,
  author =       "Marius Oleksy",
  title =        "{Data Mining und Benford's Law als
                 Controllinginstrumente}. ({German}) [{Data} Mining and
                 {Benford's Law} as controlling instruments]",
  volume =       "45",
  publisher =    "Europ{\"a}ischer Hochschulverlag",
  address =      "Bremen, Germany",
  pages =        "181 (est.)",
  year =         "2010",
  isbn =         "3-86741-405-X",
  isbn-13 =      "978-3-86741-405-0",
  lccn =         "????",
  bibdate =      "Mon Feb 18 17:54:59 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  series =       "{Wismarer Schriften zu Management und Recht}",
  url =          "http://www.amazon.de/Data-Mining-Benfords-Law-Controllinginstrumente/dp/386741405X",
  acknowledgement = ack-nhfb,
  language =     "German",
}

@Article{Orita:2010:UBL,
  author =       "Masaya Orita and Ayako Moritomo and Tatsuya Niimi and
                 Kazuki Ohno",
  title =        "Use of {Benford}'s law in drug discovery data",
  journal =      j-DRUG-DISCOVERY-TODAY,
  volume =       "15",
  number =       "9--10",
  pages =        "328--331",
  month =        may,
  year =         "2010",
  coden =        "DDTOFS",
  doi =          "http://dx.doi.org/10.1016/j.drudis.2010.03.003",
  issn =         "1359-6446 (print), 1878-5832 (electronic)",
  issn-l =       "1359-6446",
  bibdate =      "Wed Nov 23 18:48:37 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  url =          "http://www.sciencedirect.com/science/article/pii/S1359644610000796",
  acknowledgement = ack-nhfb,
  fjournal =     "Drug Discovery Today",
}

@Misc{Pan:2010:EJC,
  author =       "Da Pan and Lijing Shao and Bo-Qiang Ma",
  title =        "{Benford's Law} in Statistical Physics",
  howpublished = "Wolfram Online Demonstrations Projects.",
  year =         "2010",
  bibdate =      "Mon Feb 18 18:00:17 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  url =          "http://demonstrations.wolfram.com/BenfordsLawInStatisticalPhysics/",
  acknowledgement = ack-nhfb,
}

@Article{Peng:2010:ZLC,
  author =       "Guohua Peng",
  title =        "{Zipf}'s law for {Chinese} cities: {Rolling} sample
                 regressions",
  journal =      j-PHYSICA-A,
  volume =       "389",
  number =       "18",
  pages =        "3804--3813",
  day =          "15",
  month =        sep,
  year =         "2010",
  coden =        "PHYADX",
  doi =          "http://dx.doi.org/10.1016/j.physa.2010.05.004",
  issn =         "0378-4371 (print), 1873-2119 (electronic)",
  issn-l =       "0378-4371",
  bibdate =      "Wed Feb 27 07:32:55 MST 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  url =          "http://www.sciencedirect.com/science/article/pii/S037843711000381X",
  acknowledgement = ack-nhfb,
  fjournal =     "Physica A. Statistical Mechanics and its
                 Applications",
  keywords =     "Zipf's Law",
}

@Article{Perc:2010:ZLL,
  author =       "Matja{\v{z}} Perc",
  title =        "{Zipf}'s law and log-normal distributions in measures
                 of scientific output across fields and institutions: 40
                 years of {Slovenia's} research as an example",
  journal =      j-J-INFORMETRICS,
  volume =       "4",
  number =       "3",
  pages =        "358--364",
  day =          "1",
  month =        jul,
  year =         "2010",
  coden =        "????",
  doi =          "http://dx.doi.org/10.1016/j.joi.2010.03.001",
  issn =         "1751-1577 (print), 1875-5879 (electronic)",
  issn-l =       "1751-1577",
  bibdate =      "Wed Feb 27 07:32:55 MST 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  url =          "http://www.sciencedirect.com/science/article/pii/S1751157710000234",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Informetrics",
  journal-url =  "http://www.sciencedirect.com/science/journal/17511577",
  keywords =     "Zipf's Law",
}

@Book{Posch:2010:ZNB,
  author =       "Peter N. Posch",
  title =        "{Ziffernanalyse mit dem Newcomb--Benford Gesetz in
                 Theorie und Praxis}. ({German}) [{Digit} analysis with
                 the {Newcomb--Benford} law in theory and practice]",
  publisher =    "Verlag Europ{\"a}ische Wirtschaft",
  address =      "Munich, Germany",
  edition =      "Second",
  pages =        "105 (est.)",
  year =         "2010",
  isbn =         "????",
  isbn-13 =      "????",
  lccn =         "????",
  bibdate =      "Mon Feb 18 18:01:16 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  language =     "German",
}

@InProceedings{Qadir:2010:EJC,
  author =       "G. Qadir and X. Zhao and A. T. S. Ho",
  booktitle =    "{Society of Photo-Optical Instrumentation Engineers
                 (SPIE)} Conference Series",
  title =        "Estimating {JPEG2000} compression for image forensics
                 using {Benford's Law}",
  volume =       "7723",
  publisher =    pub-SPIE,
  address =      pub-SPIE:adr,
  month =        apr,
  year =         "2010",
  doi =          "http://dx.doi.org/10.1117/12.855085",
  bibdate =      "Mon Nov 14 18:25:16 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  series =       "Society of Photo-Optical Instrumentation Engineers
                 (SPIE) Conference Series",
  url =          "http://adsabs.harvard.edu/abs/2010SPIE.7723E..14Q",
  acknowledgement = ack-nhfb,
}

@Article{Rousseau:2010:AFO,
  author =       "Christiane Rousseau",
  title =        "Apprendre {\`a} frauder ou {\`a} d{\'e}tecter les
                 fraudes. ({French}) [{Learning} to defraud or to detect
                 fraud]",
  journal =      "Accrom$\alpha$th",
  volume =       "5",
  pages =        "2--7",
  month =        "{\'E}t{\'e}--automne",
  year =         "2010",
  issn =         "1911-0197",
  bibdate =      "Mon Feb 18 18:07:49 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  url =          "http://accromath.uqam.ca/contents/pdf/Benford.pdf",
  acknowledgement = ack-nhfb,
  journal-url =  "http://www.accromath.ca/",
  language =     "French",
}

@Book{Saichev:2010:TZL,
  author =       "Alexander Saichev and Yannick Malevergne and Didier
                 Sornette",
  title =        "Theory of {Zipf}'s law and beyond",
  volume =       "632",
  publisher =    pub-SV,
  address =      pub-SV:adr,
  pages =        "xii + 171",
  year =         "2010",
  doi =          "http://dx.doi.org/10.1007/978-3-642-02946-2",
  isbn =         "3-642-02945-0",
  isbn-13 =      "978-3-642-02945-5",
  mrclass =      "91-02 (91B70 91B82)",
  mrnumber =     "2569206 (2011b:91008)",
  bibdate =      "Sat Nov 12 09:13:23 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  series =       "Lecture Notes in Economics and Mathematical Systems",
  zmnumber =     "Zbl 1189.91009",
  acknowledgement = ack-nhfb,
}

@Article{Sambridge:2010:BLN,
  author =       "M. Sambridge and Hrvoje Tkal{\v{c}}i{\'c} and A.
                 Jackson",
  title =        "{Benford}'s law in the natural sciences",
  journal =      "Geophysical Research Letters",
  volume =       "37",
  number =       "22",
  pages =        "L22301--L22306",
  month =        "????",
  year =         "2010",
  coden =        "GPRLAJ",
  doi =          "http://dx.doi.org/10.1029/2010GL044830",
  issn =         "0094-8276 (print), 1944-8007 (electronic)",
  issn-l =       "0094-8276",
  bibdate =      "Sun Nov 13 11:03:47 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  url =          "http://adsabs.harvard.edu/abs/2010GeoRL..3722301S;
                 http://www.agu.org/pubs/crossref/2010/2010GL044830.shtml",
  abstract =     "More than 100 years ago it was predicted that the
                 distribution of first digits of real world observations
                 would not be uniform, but instead follow a trend where
                 measurements with lower first digit (1, 2, \ldots {})
                 occur more frequently than those with higher first
                 digits (\ldots {}, 8, 9). This result has long been
                 known but regarded largely as a mathematical curiosity
                 and received little attention in the natural sciences.
                 Here we show that the first digit rule is likely to be
                 a widespread phenomenon and may provide new ways to
                 detect anomalous signals in data. We test 15 sets of
                 modern observations drawn from the fields of physics,
                 astronomy, geophysics, chemistry, engineering and
                 mathematics, and show that Benford's law holds for them
                 all. These include geophysical observables such as the
                 length of time between geomagnetic reversals, depths of
                 earthquakes, models of Earth's gravity, geomagnetic and
                 seismic structure. In addition we find it also holds
                 for other natural science observables such as the
                 rotation frequencies of pulsars; green-house gas
                 emissions, the masses of exoplanets as well as numbers
                 of infectious diseases reported to the World Health
                 Organization. The wide range of areas where it is
                 manifested opens up new possibilities for exploitation.
                 An illustration is given of how seismic energy from an
                 earthquake can be detected from just the first digit
                 distribution of displacement counts on a seismometer,
                 i.e., without actually looking at the details of a
                 seismogram at all. This led to the first ever detection
                 of an earthquake using first digit information alone.",
  acknowledgement = ack-nhfb,
  ajournal =     "Geophys. Res. Lett.",
  fjournal =     "Geophysical research letters",
  keywords =     "earthquakes; large data sets; observational
                 seismology; statistics",
}

@TechReport{Schraepler:2010:BLI,
  author =       "J{\"o}rg-Peter Schraepler",
  title =        "{Benford's Law} as an instrument for fraud detection
                 in surveys using the data of the {Socio-Economic Panel
                 (SOEP)}",
  type =         "{SOEP} paper",
  number =       "273",
  institution =  "Socio-Economic Panel, Deutsches Institut f{\"u}r
                 Wirtschaftsforschung",
  address =      "Berlin, Germany",
  pages =        "ii + 56",
  day =          "2",
  month =        mar,
  year =         "2010",
  issn =         "1864-6689",
  issn-l =       "1864-6689",
  bibdate =      "Mon Feb 18 18:10:18 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  url =          "http://www.diw.de/documents/publikationen/73/diw_01.c.349061.de/diw_sp0273.pdf",
  acknowledgement = ack-nhfb,
}

@Article{Shao:2010:EMD,
  author =       "Lijing Shao and Bo-Qiang Ma",
  title =        "Empirical Mantissa Distributions of Pulsars",
  journal =      j-ASTROPART-PHYS,
  volume =       "33",
  number =       "4",
  pages =        "255--262",
  month =        may,
  year =         "2010",
  coden =        "APHYEE",
  doi =          "http://dx.doi.org/10.1016/j.astropartphys.2010.02.003",
  issn =         "0927-6505 (print), 1873-2852 (electronic)",
  issn-l =       "0927-6505",
  bibdate =      "Mon Nov 14 16:24:03 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  url =          "http://arxiv.org/abs/1005.1702;
                 http://www.sciencedirect.com/science/article/pii/S0927650510000447",
  abstract =     "The occurrence of digits one through nine as the
                 leftmost nonzero digit of numbers from real world
                 sources is often not uniformly distributed, but
                 instead, is distributed according to a logarithmic law,
                 known as Benford's law. Here, we investigate
                 systematically the mantissa distributions of some
                 pulsar quantities, and find that for most quantities
                 their first digits conform to this law. However, the
                 barycentric period shows significant deviation from the
                 usual distribution, but satisfies a generalized
                 Benford's law roughly. Therefore pulsars can serve as
                 an ideal assemblage to study the first digit
                 distributions of real world data, and the observations
                 can be used to constrain theoretical models of pulsar
                 behavior.",
  acknowledgement = ack-nhfb,
  archiveprefix = "arXiv",
  eprint =       "1005.1702",
  fjournal =     "Astroparticle Physics",
  primaryclass = "astro-ph.IM",
}

@Article{Shao:2010:FDD,
  author =       "Lijing Shao and Bo-Qiang Ma",
  title =        "First Digit Distribution of Hadron Full Width",
  journal =      "ArXiv e-prints",
  day =          "19",
  month =        apr,
  year =         "2010",
  bibdate =      "Mon Nov 21 07:21:00 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  url =          "http://arxiv.org/abs/1004.3077",
  abstract =     "A phenomenological law, called Benford's law, states
                 that the occurrence of the first digit, i.e., $1, 2,
                 \ldots{}, 9$, of numbers from many real world sources
                 is not uniformly distributed, but instead favors
                 smaller ones according to a logarithmic distribution.
                 We investigate, for the first time, the first digit
                 distribution of the full widths of mesons and baryons
                 in the well defined science domain of particle physics
                 systematically, and find that they agree excellently
                 with the Benford distribution. We also discuss several
                 general properties of Benford's law, i.e., the law is
                 scale-invariant, base-invariant, and power-invariant.
                 This means that the lifetimes of hadrons follow also
                 Benford's law.",
  acknowledgement = ack-nhfb,
  pagecount =    "8",
}

@Article{Shao:2010:FDLa,
  author =       "Lijing Shao and Bo-Qiang Ma",
  title =        "First-Digit Law in Nonextensive Statistics",
  journal =      "ArXiv e-prints",
  year =         "2010",
  bibdate =      "Mon Nov 21 07:09:52 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  url =          "http://arxiv.org/abs/1010.2699",
  abstract =     "Nonextensive statistics, characterized by a
                 nonextensive parameter $q$, is a promising and
                 practically useful generalization of the Boltzmann
                 statistics to describe power-law behaviors from
                 physical and social observations. We here explore the
                 unevenness of the first digit distribution of
                 nonextensive statistics analytically and numerically.
                 We find that the first-digit distribution follows
                 Benford's law and fluctuates slightly in a periodical
                 manner with respect to the logarithm of the
                 temperature. The fluctuation decreases when $q$
                 increases, and the result converges to Benford's law
                 exactly as $q$ approaches 2. The relevant regularities
                 between nonextensive statistics and Benford's law are
                 also presented and discussed.",
  acknowledgement = ack-nhfb,
}

@Article{Shao:2010:FDLb,
  author =       "Lijing Shao and Bo-Qiang Ma",
  title =        "First-digit law in nonextensive statistics",
  journal =      j-PHYS-REV-E,
  volume =       "82",
  number =       "4",
  pages =        "041110",
  month =        oct,
  year =         "2010",
  coden =        "PLEEE8",
  doi =          "http://dx.doi.org/10.1103/PhysRevE.82.041110",
  issn =         "1539-3755 (print), 1550-2376 (electronic)",
  issn-l =       "1539-3755",
  bibdate =      "Mon Feb 18 18:11:37 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  url =          "http://link.aps.org/doi/10.1103/PhysRevE.82.041110;
                 http://pre.aps.org/abstract/PRE/v82/i4/e041110",
  acknowledgement = ack-nhfb,
  fjournal =     "Physical Review E (Statistical physics, plasmas,
                 fluids, and related interdisciplinary topics)",
}

@Article{Shao:2010:SDL,
  author =       "Lijing Shao and Bo-Qiang Ma",
  title =        "The significant digit law in statistical physics",
  journal =      j-PHYSICA-A,
  volume =       "389",
  number =       "16",
  pages =        "3109--3116",
  month =        may,
  year =         "2010",
  coden =        "PHYADX",
  doi =          "http://dx.doi.org/10.1016/j.physa.2010.04.021",
  issn =         "0378-4371 (print), 1873-2119 (electronic)",
  issn-l =       "0378-4371",
  mrclass =      "82B03",
  mrnumber =     "2652860 (2011d:82007)",
  bibdate =      "Sat Nov 12 10:09:22 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  url =          "http://arxiv.org/abs/1005.0660;
                 http://inspirehep.net/record/855898;
                 http://inspirehep.net/record/873155;
                 http://www.sciencedirect.com/science/article/pii/S0378437110003596",
  abstract =     "The occurrence of the nonzero leftmost digit, i.e.,
                 $1, 2, \ldots{}, 9$, of numbers from many real world
                 sources is not uniformly distributed as one might
                 naively expect, but instead, the nature favors smaller
                 ones according to a logarithmic distribution, named
                 Benford's law. We investigate three kinds of widely
                 used physical statistics, i.e., the Boltzmann--Gibbs
                 (BG) distribution, the Fermi--Dirac (FD) distribution,
                 and the Bose--Einstein (BE) distribution, and find that
                 the BG and FD distributions both fluctuate slightly in
                 a periodic manner around the Benford distribution with
                 respect to the temperature of the system, while the BE
                 distribution conforms to it exactly whatever the
                 temperature is. Thus the Benford's law seems to present
                 a general pattern for physical statistics and might be
                 even more fundamental and profound in nature.
                 Furthermore, various elegant properties of Benford's
                 law, especially the mantissa distribution of data sets,
                 are discussed.",
  acknowledgement = ack-nhfb,
  fjournal =     "Physica A. Statistical Mechanics and its
                 Applications",
}

@InProceedings{Shengmin:2010:DSC,
  author =       "Z. Shengmin and W. Wenchao",
  editor =       "{IEEE}",
  booktitle =    "{2010 International Conference on Management and
                 Service Science (MASS), 24--26 Aug. 2010, Wuhan,
                 China}",
  title =        "Does [sic] {Chinese} Stock Indices Agree with
                 {Benford's Law}?",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "1--3",
  year =         "2010",
  doi =          "http://dx.doi.org/10.1109/ICMSS.2010.5575999",
  isbn =         "1-4244-5325-9, 1-4244-5326-7",
  isbn-13 =      "978-1-4244-5325-2, 978-1-4244-5326-9",
  lccn =         "????",
  bibdate =      "Mon Feb 18 18:12:46 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
}

@Book{Singleton:2010:FAF,
  author =       "Tommie Singleton and Aaron J. Singleton",
  title =        "Fraud auditing and forensic accounting",
  publisher =    pub-WILEY,
  address =      pub-WILEY:adr,
  edition =      "Fourth",
  pages =        "xiv + 317",
  year =         "2010",
  isbn =         "0-470-56413-X",
  isbn-13 =      "978-0-470-56413-4",
  lccn =         "HV8079.W47 B65 2010",
  bibdate =      "Tue Nov 22 10:31:33 MST 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 z3950.loc.gov:7090/Voyager",
  series =       "Wiley corporate F and A",
  url =          "http://catalogimages.wiley.com/images/db/jimages/9780470564134.jpg;
                 http://catdir.loc.gov/catdir/enhancements/fy1007/2010013504-d.html;
                 http://catdir.loc.gov/catdir/enhancements/fy1007/2010013504-t.html;
                 http://catdir.loc.gov/catdir/enhancements/fy1011/2010013504-b.html",
  abstract =     "Completely revised and updated, Fraud Auditing and
                 Forensic Accounting, Fourth Edition reveals how to
                 develop an investigative eye toward both internal and
                 external fraud and provides crucial information on how
                 to deal with it when discovered. With new chapters on
                 the physiological aspects of the fraudster and on fraud
                 response, as well as new material on non-financial
                 aspects of fraud investigation, body language,
                 discourse analysis, and interviewing techniques, this
                 authoritative, timely book equips auditors,
                 investigators, corporate attorneys, and accountants to
                 identify the signs of financial fraud and successfully
                 investigate it",
  acknowledgement = ack-nhfb,
  remark =       "Derived from third edition (2006). This book does not
                 discuss Benford's Law, but may be helpful background
                 for application of that law to the detection of
                 fraud.",
  subject =      "White collar crime investigation; United States;
                 Forensic accounting; Fraud investigation",
  tableofcontents = "Background of Fraud Auditing and Forensic
                 Accounting \\
                 Fraud Principles \\
                 Fraud Schemes \\
                 Red Flags \\
                 Fraud Risk Assessment \\
                 Fraud Prevention \\
                 Fraud Detection \\
                 Fraud Response \\
                 Computer Crime \\
                 Fraud and the Accounting Information System \\
                 Gathering Evidence \\
                 Cyber Forensics \\
                 Obtaining and Evaluating Nonfinancial Evidence in a
                 Fraud Examination \\
                 General Criteria and Standards for Establishing an
                 Expert Witness's Qualifications \\
                 The Legal Role and Qualifications of an Expert Witness
                 \\
                 Effective Tactics and Procedures for the Expert Witness
                 in Court \\
                 Fraud and the Public Accounting Profession",
}

@Article{Stalcup:2010:BLH,
  author =       "Ken Stalcup",
  title =        "{Benford's Law}: How a Simple Misconception can Trip
                 up a Fraudster and How a Savvy {CFE} Can Spot It",
  journal =      "Fraud Magazine",
  volume =       "??",
  number =       "??",
  pages =        "??--??",
  month =        jan # "\slash " # feb,
  year =         "2010",
  issn =         "1553-6645",
  issn-l =       "1553-6645",
  bibdate =      "Sun Feb 17 07:57:24 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  url =          "http://www.fraud-magazine.com/article.aspx?id=203",
  acknowledgement = ack-nhfb,
  fjournal =     "Fraud Magazine. {A} Publication of the Association of
                 Certified Fraud Examiners",
}

@Article{Strzalka:2010:SPB,
  author =       "Dominik Strza{\l}ka",
  title =        "On some properties of {Benford}'s law",
  journal =      "Journal of the {Korean Mathematical Society}",
  volume =       "47",
  number =       "5",
  pages =        "1055--1075",
  year =         "2010",
  coden =        "JKMSDG",
  doi =          "http://dx.doi.org/10.4134/JKMS.2010.47.5.1055",
  issn =         "0304-9914",
  issn-l =       "0304-9914",
  mrclass =      "11A63",
  mrnumber =     "2723008",
  bibdate =      "Sat Nov 12 09:13:23 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  ajournal =     "J. {Korean Math. Soc.}",
  fjournal =     "Journal of the {Korean Mathematical Society}",
}

@Article{Suh:2010:CAB,
  author =       "Ikseon Suh and T. Christopher Headrick",
  title =        "A comparative analysis of the bootstrap versus
                 traditional statistical procedures applied to digital
                 analysis based on {Benford's Law}",
  journal =      "Journal of Forensic and Investigative Accounting",
  volume =       "2",
  number =       "2",
  pages =        "144--175",
  month =        jul # "\slash " # dec,
  year =         "2010",
  coden =        "????",
  doi =          "????",
  issn =         "2165-3755",
  bibdate =      "Mon Feb 18 18:16:07 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  url =          "http://epublications.marquette.edu/account_fac/31;
                 http://www.bus.lsu.edu/accounting/faculty/lcrumbley/jfia/Articles/FullText/2010v2n2a7.pdf;
                 http://www.bus.lsu.edu/accounting/faculty/lcrumbley/jfia/Articles/v2n2.htm",
  acknowledgement = ack-nhfb,
  journal-url =  "http://www.bus.lsu.edu/accounting/faculty/lcrumbley/jfia/articles.htm",
}

@Article{Szewczak:2010:LTR,
  author =       "S. Szewczak",
  title =        "A limit theorem for random sums modulo $1$",
  journal =      j-STAT-PROB-LETT,
  volume =       "80",
  number =       "9--10",
  pages =        "747--751",
  month =        may,
  year =         "2010",
  coden =        "SPLTDC",
  doi =          "http://dx.doi.org/10.1016/j.spl.2010.01.005",
  issn =         "0167-7152 (print), 1879-2103 (electronic)",
  issn-l =       "0167-7152",
  bibdate =      "Tue Nov 22 11:28:19 MST 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 http://www.sciencedirect.com/",
  url =          "http://www.sciencedirect.com/science/article/pii/S0167715210000106",
  acknowledgement = ack-nhfb,
  fjournal =     "Statistics \& Probability Letters",
  keywords =     "Benford's Law",
}

@Article{Uzer:2010:MTC,
  author =       "Ali Uzer",
  title =        "Multiplicative type complex calculus as an alternative
                 to the classical calculus",
  journal =      j-COMP-MATH-APPL,
  volume =       "60",
  number =       "10",
  pages =        "2725--2737",
  month =        nov,
  year =         "2010",
  coden =        "CMAPDK",
  doi =          "http://dx.doi.org/10.1016/j.camwa.2010.08.089",
  issn =         "0898-1221 (print), 1873-7668 (electronic)",
  issn-l =       "0898-1221",
  bibdate =      "Thu Feb 14 05:56:39 MST 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  url =          "http://www.sciencedirect.com/science/article/pii/S0898122110006747",
  acknowledgement = ack-nhfb,
  fjournal =     "Computers and Mathematics with Applications",
  remark =       "From the paper: ``\ldots{} an important work of
                 Benford that was published 70 years ago implies many
                 physical quantities in the nature are of exponentially
                 varying type.''.",
}

@Misc{Wagon:2010:BLD,
  author =       "S. Wagon",
  title =        "{Benford's Law} and Data Spread",
  year =         "2010",
  bibdate =      "Sat Nov 12 16:59:25 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  note =         "Web site.",
  url =          "http://demonstrations.wolfram.com/BenfordsLawAndDataSpread",
  acknowledgement = ack-nhfb,
}

@Article{Abrantes-Metz:2011:TLR,
  author =       "R. M. Abrantes-Metz and S. B. Villas-Boas and G.
                 Judge",
  title =        "Tracking the {Libor} rate",
  journal =      j-APPL-ECON-LETT,
  volume =       "18",
  number =       "10",
  pages =        "893--899",
  month =        "????",
  year =         "2011",
  doi =          "http://dx.doi.org/10.1080/13504851.2010.515197",
  issn =         "1350-4851 (print), 1466-4291 (electronic)",
  issn-l =       "1350-4851",
  bibdate =      "Mon Feb 18 18:17:20 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  url =          "http://www.tandfonline.com/doi/abs/10.1080/13504851.2010.515197",
  acknowledgement = ack-nhfb,
  fjournal =     "Applied Economics Letters",
  keywords =     "Benford's Second-Digit Law",
  remark =       "From the abstract: ``Libor rates depart significantly
                 from the expected Benford reference distribution. This
                 raises potential concerns relative to the unbiased
                 nature of the signals coming from the 16 banks from
                 which the Libor is computed and the usefulness of the
                 Libor as a major economic indicator.''",
}

@Article{Adamic:2011:CSU,
  author =       "Lada Adamic",
  title =        "Complex systems: Unzipping {Zipf}'s law",
  journal =      j-NATURE,
  volume =       "474",
  number =       "7350",
  pages =        "164--165",
  month =        jun,
  year =         "2011",
  coden =        "NATUAS",
  doi =          "http://dx.doi.org/10.1038/474164a",
  issn =         "0028-0836 (print), 1476-4687 (electronic)",
  issn-l =       "0028-0836",
  bibdate =      "Tue Nov 15 09:29:15 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  url =          "http://www.nature.com/nature/journal/v474/n7350/full/474164a.html",
  acknowledgement = ack-nhfb,
  fjournal =     "Nature",
  onlinedate =   "09 June 2011",
}

@Article{Altamirano:2011:PTS,
  author =       "C. Altamirano and A. Robledo",
  title =        "Possible thermodynamic structure underlying the laws
                 of {Zipf} and {Benford}",
  journal =      j-EUR-PHYS-J-B,
  volume =       "81",
  number =       "3",
  pages =        "345--351",
  month =        jun,
  year =         "2011",
  coden =        "EPJBFY",
  doi =          "http://dx.doi.org/10.1140/epjb/e2011-10968-5",
  issn =         "1434-6028 (print), 1434-6036 (electronic)",
  issn-l =       "1434-6028",
  bibdate =      "Mon Nov 14 17:53:47 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  url =          "http://adsabs.harvard.edu/abs/2011EPJB...81..345A",
  acknowledgement = ack-nhfb,
  archiveprefix = "arXiv",
  eprint =       "1008.1614",
  fjournal =     "European Physical Journal B: Condensed Matter and
                 Complex Systems",
  primaryclass = "cond-mat.stat-mech",
}

@Article{Anderson:2011:BLC,
  author =       "Theresa C. Anderson and Larry Rolen and Ruth Stoehr",
  title =        "{Benford}'s law for coefficients of modular forms and
                 partition functions",
  journal =      j-PROC-AM-MATH-SOC,
  volume =       "139",
  number =       "5",
  pages =        "1533--1541",
  year =         "2011",
  coden =        "PAMYAR",
  doi =          "http://dx.doi.org/10.1090/S0002-9939-2010-10577-4",
  issn =         "0002-9939 (print), 1088-6826 (electronic)",
  issn-l =       "0002-9939",
  mrclass =      "11F12 (11F20 11P83)",
  mrnumber =     "2763743",
  bibdate =      "Sat Nov 12 09:13:23 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  url =          "http://adsabs.harvard.edu/abs/2010arXiv1009.0780A",
  acknowledgement = ack-nhfb,
  fjournal =     "Proceedings of the American Mathematical Society",
}

@Article{Andrew:2011:OBM,
  author =       "Alex M. Andrew",
  title =        "Obituary: {Beno{\^\i}t Mandelbrot: 20 November
                 1924--14 October 2010}",
  journal =      "Kybernetes",
  volume =       "40",
  number =       "1--2",
  pages =        "??--??",
  month =        "????",
  year =         "2011",
  coden =        "KBNTA3",
  issn =         "0368-492X (print), 1758-7883 (electronic)",
  issn-l =       "0368-492X",
  bibdate =      "Fri Nov 25 07:32:54 2011",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/m/mandelbrot-benoit.bib;
                 http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  url =          "http://en.wikipedia.org/wiki/ernst_von_glasersfeld;
                 http://www.boston.com/news/world/europe/articles/2010/11/12/intellectual_ernst_von_glasersf;
                 http://www.emeraldinsight.com/journals.htm?issn=0368-492X&volume=40&issue=1/2&articleid=1921825;
                 http://www.guardian.co.uk/science/2010/oct/17/benoit-mandelbrot-obituary;
                 http://www.math.yale.edu/mandelbrot/;
                 http://www.telegraph.co.uk/news/obituaries/science-obituaries/8069558/benoit-mandelbrot.html",
  acknowledgement = ack-nhfb,
}

@Article{Archambault:2011:EMA,
  author =       "J. Archambault and M. Archambault",
  title =        "Earnings management among firms during the pre-{SEC}
                 era: a {Benford}'s law analysis",
  journal =      j-ACCOUNT-HIST-J,
  volume =       "38",
  number =       "2",
  pages =        "145--170",
  month =        "????",
  year =         "2011",
  issn =         "0148-4184",
  issn-l =       "0148-4184",
  bibdate =      "Mon Feb 18 11:32:23 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Accounting Historians Journal",
  journal-url =  "http://www.jstor.org/action/showPublication?journalCode=accohistjour;
                 http://www.aahhq.org/",
  remark =       "JSTOR has a 3-year moving wall, so this article is not
                 yet in that archive; the publisher's Web site is poor,
                 and I cannot find the article there.",
}

@Article{Baek:2011:ZLU,
  author =       "Seung Ki Baek and Sebastian Bernhardsson and Petter
                 Minnhagen",
  title =        "{Zipf}'s law unzipped",
  journal =      j-NEW-J-PHYS,
  volume =       "13",
  number =       "4",
  pages =        "043004",
  month =        "????",
  year =         "2011",
  coden =        "NJOPFM",
  doi =          "http://dx.doi.org/10.1088/1367-2630/13/4/043004",
  issn =         "1367-2630",
  issn-l =       "1367-2630",
  bibdate =      "Tue Nov 15 09:32:45 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  url =          "http://iopscience.iop.org/1367-2630/13/4/043004",
  abstract =     "Why does Zipf's law give a good description of data
                 from seemingly completely unrelated phenomena? Here it
                 is argued that the reason is that they can all be
                 described as outcomes of a ubiquitous random group
                 division: the elements can be citizens of a country and
                 the groups family names, or the elements can be all the
                 words making up a novel and the groups the unique
                 words, or the elements could be inhabitants and the
                 groups the cities in a country and so on. A random
                 group formation (RGF) is presented from which a
                 Bayesian estimate is obtained based on minimal
                 information: it provides the best prediction for the
                 number of groups with $k$ elements, given the total
                 number of elements, groups and the number of elements
                 in the largest group. For each specification of these
                 three values, the RGF predicts a unique group
                 distribution $N(k) \propto \exp(-b k) / k^\gamma$,
                 where the power-law index $\gamma$ is a unique function
                 of the same three values. The universality of the
                 result is made possible by the fact that no
                 system-specific assumptions are made about the
                 mechanism responsible for the group division. The
                 direct relation between $\gamma$ and the total number
                 of elements, groups and the number of elements in the
                 largest group is calculated. The predictive power of
                 the RGF model is demonstrated by direct comparison with
                 data from a variety of systems. It is shown that
                 $\gamma$ usually takes values in the interval $1 \leq
                 \gamma \leq 2$ and that the value for a given
                 phenomenon depends in a systematic way on the total
                 size of the dataset. The results are put in the context
                 of earlier discussions on Zipf's and Gibrat's laws,
                 $N(k) \propto k^{-2}$ and the connection between growth
                 models and RGF is elucidated.",
  acknowledgement = ack-nhfb,
  fjournal =     "New Journal of Physics",
  pagecount =    "21",
}

@Article{Bauer:2011:DDF,
  author =       "Johannes Bauer and Jochen Gross",
  title =        "Difficulties Detecting Fraud? {The} Use of {Benford?s
                 Law} on Regression Tables",
  journal =      "Journal of Economics and Statistics (Jahrb{\"u}cher
                 f{\"u}r National{\"o}konomie und Statistik)",
  volume =       "231",
  number =       "5--6",
  pages =        "733--748",
  month =        nov,
  year =         "2011",
  doi =          "????",
  bibdate =      "Mon Feb 18 18:18:45 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  url =          "http://ideas.repec.org/a/jns/jbstat/v231y2011i5-6p733-748.html",
  acknowledgement = ack-nhfb,
  journal-url =  "http://wiwi.uni-giessen.de/home/oekonometrie/Jahrbuecher/",
}

@Article{Bawden:2011:BMS,
  author =       "David Bawden",
  title =        "{Beno{\^\i}t Mandelbrot} and the self-similarity of
                 information",
  journal =      j-J-DOC,
  volume =       "67",
  number =       "2",
  pages =        "??--??",
  month =        "????",
  year =         "2011",
  coden =        "JDOCAS",
  issn =         "0022-0418 (print), 1758-7379 (electronic)",
  issn-l =       "0022-0418",
  bibdate =      "Fri Nov 25 07:40:34 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  url =          "http://www.emeraldinsight.com/journals.htm?issn=0022-0418&volume=67&issue=2&articleid=1911717",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Documentation",
}

@Article{Becker:2011:BLC,
  author =       "T. Becker and A. Greaves-Tunnell and S. J. Miller and
                 R. Ronan and F. W. Strauch",
  title =        "{Benford's Law} and Continuous Dependent Random
                 Variables",
  journal =      "ArXiv e-prints",
  month =        nov,
  year =         "2011",
  coden =        "????",
  issn =         "????",
  bibdate =      "Mon Nov 14 17:50:20 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  url =          "http://adsabs.harvard.edu/abs/2011arXiv1111.0568B;
                 http://arxiv.org/abs/1111.0568",
  abstract =     "Many systems exhibit a digit bias. For example, the
                 first digit base 10 of the Fibonacci numbers, or of
                 $2^n$, equals 1 not 10\% or 11\% of the time, as one
                 would expect if all digits were equally likely, but
                 about 30\% of the time. This phenomenon, known as
                 Benford's Law, has many applications, ranging from
                 detecting tax fraud for the IRS to analyzing round-off
                 errors in computer science.\par

                 The central question is determining which data sets
                 follow Benford's law. Inspired by natural processes
                 such as particle decay, our work examines models for
                 the decomposition of conserved quantities. We prove
                 that in many instances the distribution of lengths of
                 the resulting pieces converges to Benford behavior as
                 the number of divisions grow. The main difficulty is
                 that the resulting random variables are dependent,
                 which we handle by a careful analysis of the
                 dependencies and tools from Fourier analysis to obtain
                 quantified convergence rates.",
  acknowledgement = ack-nhfb,
  archiveprefix = "arXiv",
  eprint =       "1111.0568",
  keywords =     "Mathematics - Probability, 11K06, 60A10 (primary),
                 60E10 (secondary)",
  primaryclass = "math.PR",
}

@Article{Berger:2011:BLS,
  author =       "Arno Berger and Theodore P. Hill",
  title =        "{Benford}'s law strikes back: no simple explanation in
                 sight for mathematical gem",
  journal =      j-MATH-INTEL,
  volume =       "33",
  number =       "1",
  pages =        "85--91",
  month =        mar,
  year =         "2011",
  coden =        "MAINDC",
  doi =          "http://dx.doi.org/10.1007/s00283-010-9182-3",
  issn =         "0343-6993 (print), 1866-7414 (electronic)",
  issn-l =       "0343-6993",
  mrclass =      "62A99 (60E05)",
  mrnumber =     "2774458",
  bibdate =      "Sat Nov 12 09:13:23 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/amstat2010.bib;
                 http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  note =         "See letter \cite{Hill:2011:LEB}.",
  acknowledgement = ack-nhfb,
  fjournal =     "The Mathematical Intelligencer",
}

@Article{Berger:2011:BTB,
  author =       "Arno Berger and Theodore P. Hill",
  title =        "A basic theory of {Benford's Law}",
  journal =      j-PROBAB-SURV,
  volume =       "8",
  pages =        "1--126",
  year =         "2011",
  coden =        "????",
  doi =          "http://dx.doi.org/10.1214/11-PS175",
  issn =         "1549-5787",
  issn-l =       "1549-5787",
  bibdate =      "Tue Nov 15 11:07:49 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  url =          "http://projecteuclid.org/euclid.ps/1311860830",
  abstract =     "Drawing from a large, diverse body of work, this
                 survey presents a comprehensive and unified
                 introduction to the mathematics underlying the
                 prevalent logarithmic distribution of significant
                 digits and significands, often referred to as {\em
                 Benford's Law\/} (BL) or, in a special case, as the
                 {\em First Digit Law}. The invariance properties that
                 characterize BL are developed in detail. Special
                 attention is given to the emergence of BL in a wide
                 variety of deterministic and random processes. Though
                 mainly expository in nature, the article also provides
                 strengthened versions of, and simplified proofs for,
                 many key results in the literature. Numerous intriguing
                 problems for future research arise naturally.",
  acknowledgement = ack-nhfb,
  fjournal =     "Probabability Surveys",
  keywords =     "base-invariance; Benford's Law; difference equation;
                 mixture of distributions; random probability measure;
                 scale-invariance; shadowing; significant digits;
                 sum-invariance; uniform distribution mod 1",
}

@Article{Berger:2011:FSM,
  author =       "Arno Berger and Theodore P. Hill and Bahar Kaynar and
                 Ad Ridder",
  title =        "Finite-state {Markov} Chains Obey {Benford's Law}",
  journal =      j-SIAM-J-MAT-ANA-APPL,
  volume =       "32",
  number =       "3",
  pages =        "665--684",
  month =        "????",
  year =         "2011",
  coden =        "SJMAEL",
  doi =          "http://dx.doi.org/10.1137/100789890",
  issn =         "0895-4798 (print), 1095-7162 (electronic)",
  issn-l =       "0895-4798",
  bibdate =      "Wed Aug 24 11:18:18 MDT 2011",
  bibsource =    "http://epubs.siam.org/sam-bin/dbq/toc/SIMAX/32/3;
                 http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 http://www.math.utah.edu/pub/tex/bib/siamjmatanaappl.bib",
  url =          "http://epubs.siam.org/simax/resource/1/sjmael/v32/i3/p665_s1",
  acknowledgement = ack-nhfb,
  fjournal =     "SIAM Journal on Matrix Analysis and Applications",
  onlinedate =   "July 21, 2011",
}

@Article{Berger:2011:SDP,
  author =       "Arno Berger",
  title =        "Some dynamical properties of {Benford} sequences",
  journal =      j-J-DIFFERENCE-EQU-APPL,
  volume =       "17",
  number =       "2",
  pages =        "137--159",
  year =         "2011",
  coden =        "????",
  doi =          "http://dx.doi.org/10.1080/10236198.2010.549012",
  issn =         "1023-6198 (print), 1563-5120 (electronic)",
  issn-l =       "1023-6198",
  mrclass =      "37A45 (11K06 37Bxx)",
  mrnumber =     "2783341",
  bibdate =      "Sat Nov 12 09:13:23 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  url =          "http://www.tandfonline.com/doi/abs/10.1080/10236198.2010.549012",
  acknowledgement = ack-nhfb,
  ajournal =     "J. Difference Equ. Appl.",
  fjournal =     "Journal of Difference Equations and Applications",
}

@Article{Bernhardsson:2011:PPM,
  author =       "Sebastian Bernhardsson and Seung Ki Baek and Petter
                 Minnhagen",
  title =        "A paradoxical property of the monkey book",
  journal =      j-J-STAT-MECH-THEORY-EXP,
  volume =       "2011",
  number =       "??",
  pages =        "P07013",
  month =        jul,
  year =         "2011",
  coden =        "JSMTC6",
  doi =          "http://dx.doi.org/10.1088/1742-5468/2011/07/P07013",
  issn =         "1742-5468",
  issn-l =       "1742-5468",
  bibdate =      "Mon Nov 21 21:57:13 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  url =          "http://arxiv.org/abs/1103.2681;
                 http://iopscience.iop.org/1742-5468/2011/07/P07013/",
  abstract =     "A `monkey book' is a book consisting of a random
                 sequence of letters and blanks, where a group of
                 letters surrounded by two blanks is defined as a word.
                 We compare the statistics of the word distribution for
                 a monkey book to real books. It is shown that the word
                 distribution statistics for the monkey book is
                 different and quite distinct from a typical real book.
                 In particular, the monkey book obeys Heaps' power law
                 to an extraordinarily good approximation, in contrast
                 to the word distributions for real books, which deviate
                 from Heaps' law in a characteristic way. This
                 discrepancy is traced to the different properties of a
                 `spiked' distribution and its smooth envelope. The
                 somewhat counter-intuitive conclusion is that a `monkey
                 book' obeys Heaps' power law precisely because its
                 word-frequency distribution is not a smooth power law,
                 contrary to the expectation based on simple
                 mathematical arguments that if one is a power law, so
                 is the other.",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Statistical Mechanics: Theory and
                 Experiment",
  keywords =     "Heaps' Law",
}

@Article{Bhattacharya:2011:ABA,
  author =       "Sukanto Bhattacharya and Dongming Xu and Kuldeep
                 Kumar",
  title =        "An {ANN}-based auditor decision support system using
                 {Benford}'s law",
  journal =      j-DEC-SUPP-SYS,
  volume =       "50",
  number =       "3",
  pages =        "576--584",
  month =        feb,
  year =         "2011",
  coden =        "DSSYDK",
  doi =          "http://dx.doi.org/10.1016/j.dss.2010.08.011",
  issn =         "0167-9236 (print), 1873-5797 (electronic)",
  issn-l =       "0167-9236",
  bibdate =      "Tue Nov 22 11:28:19 MST 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 http://www.sciencedirect.com/",
  url =          "http://www.sciencedirect.com/science/article/pii/S0167923610001351",
  acknowledgement = ack-nhfb,
  fjournal =     "Decision Support Systems",
  keywords =     "Benford's Law",
}

@Article{Bose:2011:QMD,
  author =       "Indranil Bose and Selwyn Piramuthu and Michael J.
                 Shaw",
  title =        "Quantitative methods for Detection of Financial
                 Fraud",
  journal =      j-DEC-SUPP-SYS,
  volume =       "50",
  number =       "3",
  pages =        "557--558",
  month =        feb,
  year =         "2011",
  coden =        "DSSYDK",
  doi =          "http://dx.doi.org/10.1016/j.dss.2010.08.005",
  issn =         "0167-9236 (print), 1873-5797 (electronic)",
  issn-l =       "0167-9236",
  bibdate =      "Tue Nov 22 11:28:19 MST 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 http://www.sciencedirect.com/",
  url =          "http://www.sciencedirect.com/science/article/pii/S0167923610001296",
  acknowledgement = ack-nhfb,
  fjournal =     "Decision Support Systems",
  keywords =     "Benford's Law",
}

@InCollection{Brahler:2011:BGS,
  author =       "Gernot Br{\"a}hler and Markus Bensmann and Hans-Ralph
                 Jakobi",
  editor =       "????",
  booktitle =    "Ilmenauer Schriften zur Betriebswirtschaftslehre",
  title =        "{Das Benfordsche Gesetz und seine Anwendbarkeit bei
                 der digitalen Pr{\"u}fung von Fahrtenb{\"u}chern}.
                 ({German}) [{The} {Benford} law and its applicability
                 in the digital examination of logbooks]",
  volume =       "3/2011",
  publisher =    "Verlag proWiWi e.V.",
  address =      "Ilmenau, Germany",
  pages =        "??--??",
  month =        mar,
  year =         "2011",
  isbn =         "3-940882-28-3",
  isbn-13 =      "978-3-940882-28-8",
  issn =         "1866-2145 (print), 2192-4643 (electronic)",
  lccn =         "????",
  bibdate =      "Mon Feb 18 18:21:29 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  url =          "https://www.econstor.eu/dspace/bitstream/10419/55703/1/662518055.pdf",
  acknowledgement = ack-nhfb,
  language =     "German",
}

@Article{Breunig:2011:SEI,
  author =       "Christian Breunig and Achim Goerres",
  title =        "Searching for electoral irregularities in an
                 established democracy: Applying {Benford's Law} tests
                 to {Bundestag} elections in {Unified Germany}",
  journal =      j-ELECT-STUDIES,
  volume =       "30",
  number =       "3",
  pages =        "534--545",
  month =        sep,
  year =         "2011",
  coden =        "????",
  doi =          "http://dx.doi.org/10.1016/j.electstud.2011.03.005",
  issn =         "0261-3794 (print), 1873-6890 (electronic)",
  issn-l =       "0261-3794",
  bibdate =      "Tue Nov 22 11:28:19 MST 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 http://www.sciencedirect.com/",
  url =          "http://www.sciencedirect.com/science/article/pii/S0261379411000370",
  acknowledgement = ack-nhfb,
  fjournal =     "Electoral Studies",
  keywords =     "Benford's Law",
}

@Article{Campanario:2011:BLC,
  author =       "Juan Campanario and Mar{\'\i}a Coslado",
  title =        "{Benford}'s law and citations, articles and impact
                 factors of scientific journals",
  journal =      j-SCIENTOMETRICS,
  volume =       "88",
  number =       "2",
  pages =        "421--432",
  month =        aug,
  year =         "2011",
  coden =        "SCNTDX",
  doi =          "http://dx.doi.org/10.1007/s11192-011-0387-9",
  issn =         "0138-9130 (print), 1588-2861 (electronic)",
  issn-l =       "0138-9130",
  bibdate =      "Fri Nov 25 10:43:36 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Scientometrics",
}

@Article{Cantu:2011:FDA,
  author =       "F. Cantu and S. M. Saiegh",
  title =        "Fraudulent Democracy? {An} Analysis of {Argentina}'s
                 Infamous Decade Using Supervised Machine Learning",
  journal =      j-POLIT-ANAL,
  volume =       "19",
  number =       "4",
  pages =        "409--433",
  month =        "Autumn",
  year =         "2011",
  doi =          "http://dx.doi.org/10.1093/pan/mpr033",
  issn =         "1047-1987 (print), 1476-4989 (electronic)",
  issn-l =       "1047-1987",
  bibdate =      "Mon Feb 18 18:24:47 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  url =          "http://pan.oxfordjournals.org/content/19/4/409.abstract",
  acknowledgement = ack-nhfb,
  fjournal =     "Political Analysis",
  keywords =     "Benford's Law",
}

@Article{Chang:2011:CGR,
  author =       "Harry M. Chang",
  title =        "Constructing $n$-gram rules for natural language
                 models through exploring the limitation of the
                 {Zipf--Mandelbrot} law",
  journal =      j-COMPUTING,
  volume =       "91",
  number =       "3",
  pages =        "241--264",
  month =        mar,
  year =         "2011",
  coden =        "CMPTA2",
  doi =          "http://dx.doi.org/10.1007/s00607-010-0116-x",
  issn =         "0010-485X (print), 1436-5057 (electronic)",
  issn-l =       "0010-485X",
  mrclass =      "68T50",
  mrnumber =     "2776088",
  bibdate =      "Sat Nov 12 09:13:23 2011",
  bibsource =    "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0010-485X&volume=91&issue=3;
                 http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  url =          "http://www.springerlink.com/openurl.asp?genre=article&issn=0010-485X&volume=91&issue=3&spage=241",
  acknowledgement = ack-nhfb,
  fjournal =     "Computing. Archives for Scientific Computing",
}

@Article{Chida:2011:LSI,
  author =       "Satoshi Chida and Naoto Miyoshi",
  title =        "Limiting size index distributions for ball-bin models
                 with {Zipf}-type frequencies",
  journal =      j-ANN-INST-STAT-MATH-TOKYO,
  volume =       "63",
  number =       "4",
  pages =        "745--768",
  year =         "2011",
  coden =        "AISXAD",
  doi =          "http://dx.doi.org/10.1007/s10463-010-0276-7",
  issn =         "0020-3157 (print), 1572-9052 (electronic)",
  issn-l =       "0020-3157",
  mrclass =      "60C05 (60F15 60J27)",
  mrnumber =     "2805906 (2012f:60035)",
  mrreviewer =   "Elvira Di Nardo",
  bibdate =      "Mon Feb 18 16:48:12 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Annals of the Institute of Statistical Mathematics
                 (Tokyo)",
}

@Article{Corominas-Murtra:2011:EZL,
  author =       "Bernat Corominas-Murtra and Jordi Fortuny and Ricard
                 V. Sol{\'e}",
  title =        "Emergence of {Zipf}'s law in the evolution of
                 communication",
  journal =      j-PHYS-REV-E,
  volume =       "83",
  number =       "1",
  pages =        "036115",
  day =          "28",
  month =        mar,
  year =         "2011",
  coden =        "PLEEE8",
  doi =          "http://dx.doi.org/10.1103/PhysRevE.83.036115",
  issn =         "1539-3755 (print), 1550-2376 (electronic)",
  issn-l =       "1539-3755",
  bibdate =      "Tue Feb 26 06:40:57 MST 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  url =          "http://link.aps.org/doi/10.1103/PhysRevE.83.036115",
  acknowledgement = ack-nhfb,
  fjournal =     "Physical Review E (Statistical physics, plasmas,
                 fluids, and related interdisciplinary topics)",
  keywords =     "Zipf's Law",
  pagecount =    "9",
}

@Article{Deckert:2011:BLD,
  author =       "Joseph Deckert and Mikhail Myagkov and Peter C.
                 Ordeshook",
  title =        "{Benford's Law} and the Detection of Election Fraud",
  journal =      j-POLIT-ANAL,
  volume =       "19",
  number =       "3",
  pages =        "245--268",
  month =        "Summer",
  year =         "2011",
  doi =          "http://dx.doi.org/10.1093/pan/mpr014",
  issn =         "1047-1987 (print), 1476-4989 (electronic)",
  issn-l =       "1047-1987",
  bibdate =      "Mon Feb 18 18:26:03 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  note =         "See \cite{Mebane:2011:CBL} for a rebuttal.",
  url =          "http://pan.oxfordjournals.org/content/19/3/245.abstract",
  acknowledgement = ack-nhfb,
  fjournal =     "Political Analysis",
  remark =       "The authors argue that application of Benford's Law
                 tests to election results to detect fraud is
                 inconclusive and ``essentially equivalent to a toss of
                 a coin''.",
}

@Article{Doyle:2011:ITA,
  author =       "Laurance R. Doyle and Brenda McCowan and Simon
                 Johnston and Sean F. Hanser",
  title =        "Information theory, animal communication, and the
                 search for extraterrestrial intelligence",
  journal =      j-ACTA-ASTRONAUT,
  volume =       "68",
  number =       "3--4",
  pages =        "406--417",
  month =        feb # "\slash " # mar,
  year =         "2011",
  coden =        "AASTCF",
  doi =          "http://dx.doi.org/10.1016/j.actaastro.2009.11.018",
  issn =         "0094-5765 (print), 1879-2030 (electronic)",
  issn-l =       "0094-5765",
  bibdate =      "Tue Nov 22 11:28:19 MST 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 http://www.sciencedirect.com/",
  url =          "http://www.sciencedirect.com/science/article/pii/S0094576509005682",
  acknowledgement = ack-nhfb,
  fjournal =     "Acta Astronautica",
  keywords =     "Benford's Law; Zipf's Law",
}

@Article{Edwards:2011:LFP,
  author =       "Roderick Edwards and Laura Collins",
  title =        "Lexical Frequency Profiles and {Zipf's Law}",
  journal =      "Language Learning",
  volume =       "61",
  number =       "1",
  pages =        "1--30",
  year =         "2011",
  doi =          "http://dx.doi.org/10.1111/j.1467-9922.2010.00616.x",
  issn =         "0023-8333 (print), 1467-9922 (electronic)",
  issn-l =       "0023-8333",
  bibdate =      "Mon Feb 25 06:13:56 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  keywords =     "L2 vocabulary learning; L2 vocabulary size; modeling
                 vocabulary learning; Zipf's law",
}

@Article{Egghe:2011:BLS,
  author =       "Leo Egghe",
  title =        "{Benford}'s law is a simple consequence of {Zipf}'s
                 law",
  journal =      "ISSI Newsletter",
  volume =       "7",
  number =       "3",
  pages =        "55--56",
  month =        sep,
  year =         "2011",
  doi =          "????",
  bibdate =      "Mon Feb 18 18:27:01 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  url =          "http://www.issi-society.info/archives/newsletter27.pdf",
  abstract =     "We show that benford's law (describing the logarithmic
                 distribution of the numbers 1, 2, \ldots{}, 9 as first
                 digits of data in decimal form) can be deduced from the
                 classical law of zipf. this explains Bensford's law as
                 a scientometric or informetric law.",
  acknowledgement = ack-nhfb,
}

@TechReport{Eliahou:2011:MDP,
  author =       "Shalom Eliahou and Bruno Mass{\'e} and Dominique
                 Schneider",
  title =        "On the mantissa distribution of powers of natural and
                 prime numbers",
  type =         "Preprint",
  institution =  "Universit{\'e} du Littoral C{\^o}te d'Opale",
  address =      "Nord-Pas-de-Calais, France",
  pages =        "14",
  day =          "15",
  month =        nov,
  year =         "2011",
  bibdate =      "Mon Feb 18 18:27:51 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  url =          "http://fr.wikipedia.org/wiki/Universit%C3%A9_du_Littoral_C%C3%B4te_d%27Opale;
                 http://www-lmpa.univ-littoral.fr/publications/articles/lmpa447.pdf",
  acknowledgement = ack-nhfb,
}

@Article{Eliazar:2011:LLZ,
  author =       "Iddo Eliazar",
  title =        "Limit laws for {Zipf}'s law",
  journal =      j-J-PHYS-A,
  volume =       "44",
  number =       "2",
  pages =        "022001",
  year =         "2011",
  coden =        "JPHAC5",
  doi =          "http://dx.doi.org/10.1088/1751-8113/44/2/022001",
  issn =         "1751-8113",
  issn-l =       "0305-4470",
  mrclass =      "62G30 (91D20)",
  mrnumber =     "2749082 (2011i:62083)",
  bibdate =      "Sat Nov 12 09:13:23 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  zmnumber =     "Zbl 1204.62196",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Physics. A. Mathematical and Theoretical",
  pagecount =    "6",
}

@Misc{Farbaniec:2011:AFD,
  author =       "Marzena Farbaniec and Tadeusz Grabi{\'n}ski and
                 Bart{\l}omiej Zab{\l}ocki and Wac{\l}aw Zaj{\k{a}}c",
  title =        "Application of the first digit law in credibility
                 evaluation of the financial accounting data based on
                 particular cases",
  howpublished = "Lecture slides for 10th International Congress on
                 Internal Control, Internal Audit, Fraud and
                 Anti-Corruption Issues, Krak{\'o}w, September 14--16,
                 2011.",
  pages =        "27",
  year =         "2011",
  bibdate =      "Thu Dec 01 21:27:25 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  url =          "http://benford.pl/documents/benford_pikw.pdf",
  acknowledgement = ack-nhfb,
}

@InProceedings{Farbaniec:2011:UBL,
  author =       "Marzena Farbaniec and Tadeusz Grabi{\'n}ski and
                 Bart{\l}omiej Zab{\l}ocki and Wac{\l}aw Zaj{\k{a}}c",
  editor =       "????",
  booktitle =    "10th International Congress on Internal Control,
                 Internal Audit, Fraud and Anti-Corruption Issues,
                 Krak{\'o}w, September 14--16, 2011",
  title =        "Using {Benford}'s law to detect irregularities in the
                 collection of data",
  publisher =    "????",
  address =      "????",
  pages =        "??--??",
  year =         "2011",
  isbn =         "????",
  isbn-13 =      "????",
  lccn =         "????",
  bibdate =      "Thu Dec 01 21:32:03 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
}

@Article{Garcia:2011:FPA,
  author =       "Juan Manuel Garcia Garcia",
  title =        "A fixed-point algorithm to estimate the {Yule-Simon}
                 distribution parameter",
  journal =      j-APPL-MATH-COMP,
  volume =       "217",
  number =       "21",
  pages =        "8560--8566",
  day =          "1",
  month =        jul,
  year =         "2011",
  coden =        "AMHCBQ",
  doi =          "http://dx.doi.org/10.1016/j.amc.2011.03.092",
  issn =         "0096-3003 (print), 1873-5649 (electronic)",
  issn-l =       "0096-3003",
  bibdate =      "Tue Oct 25 12:05:30 MDT 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/applmathcomput2010.bib;
                 http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 http://www.sciencedirect.com/science/journal/00963003",
  url =          "http://www.sciencedirect.com/science/article/pii/S0096300311004607",
  acknowledgement = ack-nhfb,
  fjournal =     "Applied Mathematics and Computation",
}

@InCollection{Gauvrit:2011:SRI,
  author =       "N. Gauvrit and J-P. Delahaye",
  title =        "Scatter and Regularity Implies {Benford's Law}\ldots{}
                 and More",
  crossref =     "Zenil:2011:RTC",
  pages =        "53--69",
  year =         "2011",
  bibdate =      "Mon Feb 18 18:29:00 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
}

@Article{Giuliano:2011:WCS,
  author =       "Rita Giuliano",
  title =        "Weak convergence of sequences from fractional parts of
                 random variables and applications",
  journal =      j-THEORY-PROBAB-MATH-STAT,
  volume =       "83",
  number =       "??",
  pages =        "49--58",
  month =        "????",
  year =         "2011",
  coden =        "TPMSCO",
  doi =          "????",
  issn =         "0094-9000 (print), 1547-7363 (electronic)",
  issn-l =       "0094-9000",
  mrclass =      "60F05, 60G52, 60G70, 11K06 (62G07, 42A10, 42A61)",
  mrnumber =     "http://www.ams.org/mathscinet-getitem?mr=2768848",
  bibdate =      "Mon Feb 18 17:47:02 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  url =          "http://www.ams.org/journals/tpms/2011-83-00/S0094-9000-2012-00841-7/S0094-9000-2012-00841-7.pdf",
  acknowledgement = ack-nhfb,
  fjournal =     "Theory of Probability and Mathematical Statistics",
  journal-url =  "http://www.ams.org/publications/journals/journalsframework/tpms",
  keywords =     "Benford's Law",
}

@Article{Hill:2011:LEB,
  author =       "Theodore P. Hill",
  title =        "Letter to the Editor: {Benford's Law} Blunders",
  journal =      j-AMER-STAT,
  volume =       "65",
  number =       "2",
  pages =        "141--141",
  month =        may,
  year =         "2011",
  coden =        "ASTAAJ",
  doi =          "http://dx.doi.org/10.1198/tast.2011.10179",
  issn =         "0003-1305 (print), 1537-2731 (electronic)",
  issn-l =       "0003-1305",
  bibdate =      "Mon Feb 18 18:34:43 2013",
  bibsource =    "http://www.amstat.org/publications/tas/;
                 http://www.math.utah.edu/pub/tex/bib/amstat2010.bib;
                 http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  url =          "http://www.tandfonline.com/doi/pdf/10.1198/tast.2011.11011",
  acknowledgement = ack-nhfb,
  fjournal =     "The American Statistician",
  remark =       "Brief comment on a error in Feller's derivation of
                 Benford's Law, with pointer to a corrected proof in
                 \cite{Berger:2011:BLS}.",
}

@Article{Hisano:2011:PVD,
  author =       "Ryohei Hisano and Didier Sornette and Takayuki
                 Mizuno",
  title =        "Predicted and verified deviations from {Zipf}'s law in
                 ecology of competing products",
  journal =      j-PHYS-REV-E,
  volume =       "84",
  number =       "2",
  pages =        "026117",
  day =          "24",
  month =        aug,
  year =         "2011",
  coden =        "PLEEE8",
  doi =          "http://dx.doi.org/10.1103/PhysRevE.84.026117",
  issn =         "1539-3755 (print), 1550-2376 (electronic)",
  issn-l =       "1539-3755",
  bibdate =      "Tue Feb 26 06:40:57 MST 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  url =          "http://link.aps.org/doi/10.1103/PhysRevE.84.026117",
  acknowledgement = ack-nhfb,
  fjournal =     "Physical Review E (Statistical physics, plasmas,
                 fluids, and related interdisciplinary topics)",
  keywords =     "Zipf's Law",
  pagecount =    "8",
}

@Article{Hui:2011:BLN,
  author =       "Jiang Hui and Shen Jia-Jie and Zhao Yu-Min",
  title =        "{Benford's Law} in Nuclear Structure Physics",
  journal =      j-CHIN-PHYS-LETT,
  volume =       "28",
  number =       "3",
  pages =        "32101--32104",
  month =        mar,
  year =         "2011",
  coden =        "CPLEEU",
  doi =          "http://dx.doi.org/10.1088/0256-307X/28/3/032101",
  issn =         "0256-307X (print), 1741-3540 (electronic)",
  issn-l =       "0256-307X",
  bibdate =      "Fri Nov 25 10:37:25 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Chinese Physics Letters",
}

@Article{Janvresse:2011:AAU,
  author =       "{\'E}lise Janvresse and Thierry {De La Rue}",
  title =        "Averaging along Uniform Random Integers",
  journal =      "ArXiv e-prints",
  year =         "2011",
  bibdate =      "Mon Nov 21 07:06:41 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  url =          "http://arxiv.org/abs/1103.1719",
  abstract =     "Motivated by giving a meaning to ``The probability
                 that a random integer has initial digit d'', we define
                 a URI-set as a random set E of natural integers such
                 that each n>0 belongs to E with probability 1/n,
                 independently of other integers. This enables us to
                 introduce two notions of densities on natural numbers:
                 The URI-density, obtained by averaging along the
                 elements of $E$, and the local URI-density, which we
                 get by considering the $k$-th element of $E$ and
                 letting $k$ go to infinity. We prove that the elements
                 of $E$ satisfy Benford's law, both in the sense of
                 URI-density and in the sense of local URI-density.
                 Moreover, if $b_1$ and $b_2$ are two multiplicatively
                 independent integers, then the mantissae of a natural
                 number in base $b_1$ and in base $b_2$ are independent.
                 Connections of URI-density and local URI-density with
                 other well-known notions of densities are established:
                 Both are stronger than the natural density, and
                 URI-density is equivalent to log-density. We also give
                 a stochastic interpretation, in terms of URI-set, of
                 the $H_\infty$-density.",
  acknowledgement = ack-nhfb,
}

@Article{Jiang:2011:BLN,
  author =       "Hui Jiang and Jia-Jie Shen and Yu-Min Zhao",
  title =        "{Benford}'s law in nuclear structure physics",
  journal =      j-CHIN-PHYS-LETT,
  volume =       "28",
  number =       "3",
  pages =        "032101",
  month =        "????",
  year =         "2011",
  coden =        "CPLEEU",
  doi =          "http://dx.doi.org/10.1088/0256-307X/28/3/032101",
  issn =         "0256-307X (print), 1741-3540 (electronic)",
  issn-l =       "0256-307X",
  bibdate =      "Mon Nov 14 16:16:10 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  ajournal =     "Chin. Phys. Lett.",
  fjournal =     "Chinese Physics Letters",
  pagecount =    "4",
}

@Article{Kim:2011:ZAS,
  author =       "SeongKi Kim and HaYoon Song and SangYong Han",
  title =        "{ZipfAllocation}: an algorithm for static allocation
                 of movies in a cluster of video servers",
  journal =      j-SPE,
  volume =       "41",
  number =       "6",
  pages =        "695--716",
  month =        may,
  year =         "2011",
  coden =        "SPEXBL",
  doi =          "http://dx.doi.org/10.1002/spe.1027",
  issn =         "0038-0644 (print), 1097-024X (electronic)",
  issn-l =       "0038-0644",
  bibdate =      "Tue Jun 21 17:09:57 MDT 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Soft{\-}ware\emdash Prac{\-}tice and Experience",
  onlinedate =   "25 Nov 2010",
}

@Misc{Li:2011:ZLB,
  author =       "Wentian Li",
  title =        "{Zipf's Law} bibliography",
  howpublished = "Web site.",
  month =        aug,
  year =         "2011",
  bibdate =      "Fri Nov 25 08:58:21 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  note =         "The site holds 870 references (in untagged
                 reference-list form) up to 11 August 2011.",
  url =          "http://www.nslij-genetics.org/wli/zipf/",
  acknowledgement = ack-nhfb,
  lastaccess =   "25 November 2011",
}

@Article{Liu:2011:BLC,
  author =       "X. J. Liu and X. P. Zhang and D. D. Ni and Z. Z. Ren",
  title =        "{Benford}'s law and cross-sections of {$A(n, \alpha)
                 B$} reactions",
  journal =      j-EUR-PHYS-J-A,
  volume =       "47",
  pages =        "78",
  month =        jun,
  year =         "2011",
  coden =        "EPJAFV",
  doi =          "http://dx.doi.org/10.1140/epja/i2011-11078-3",
  issn =         "1434-6001 (print), 1434-601X (electronic)",
  issn-l =       "1434-6001",
  bibdate =      "Mon Nov 14 18:00:32 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  url =          "http://adsabs.harvard.edu/abs/2011EPJA...47...78L",
  acknowledgement = ack-nhfb,
  fjournal =     "European Physical Journal A: Hadrons and Nuclei",
}

@InProceedings{Lyons:2011:NSF,
  author =       "M. Lyons and E. Carl-Ludwig Siegel",
  booktitle =    "APS March Meeting Abstracts",
  title =        "{NON-Shor} Factorization via {BEQS BEC}: {Watkins}
                 Number-Theory ``Pure''-Mathematics $\cup$ with
                 Statistical-Physics: {Benford} Log-Law Inversion to
                 {ONLY} {BEQS} digit $d = 0$ {BEC}!!!",
  publisher =    "American Physical Society",
  address =      "????",
  pages =        "K1142",
  month =        mar,
  year =         "2011",
  bibdate =      "Mon Nov 14 18:08:39 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  url =          "http://adsabs.harvard.edu/abs/2011APS..MAR.K1142L",
  acknowledgement = ack-nhfb,
}

@Article{Malevergne:2011:TPA,
  author =       "Yannick Malevergne and Vladilen Pisarenko and Didier
                 Sornette",
  title =        "Testing the {Pareto} against the lognormal
                 distributions with the uniformly most powerful unbiased
                 test applied to the distribution of cities",
  journal =      j-PHYS-REV-E,
  volume =       "83",
  number =       "3",
  pages =        "036111",
  day =          "22",
  month =        mar,
  year =         "2011",
  coden =        "PLEEE8",
  doi =          "http://dx.doi.org/10.1103/PhysRevE.83.036111",
  issn =         "1539-3755 (print), 1550-2376 (electronic)",
  issn-l =       "1539-3755",
  bibdate =      "Tue Feb 26 06:40:57 MST 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  url =          "http://link.aps.org/doi/10.1103/PhysRevE.83.036111",
  acknowledgement = ack-nhfb,
  fjournal =     "Physical Review E (Statistical physics, plasmas,
                 fluids, and related interdisciplinary topics)",
  keywords =     "Pareto distribution; Zipf's Law",
  pagecount =    "11",
}

@Article{Masse:2011:SWD,
  author =       "B. Mass{\'e} and D. Schneider",
  title =        "A survey on weighted densities and their connection
                 with the first digit phenomenon",
  journal =      j-ROCKY-MOUNTAIN-J-MATH,
  volume =       "41",
  number =       "5",
  pages =        "1395--1415",
  month =        "????",
  year =         "2011",
  coden =        "RMJMAE",
  doi =          "http://dx.doi.org/10.1216/RMJ-2011-41-5-1395",
  issn =         "0035-7596 (print), 1945-3795 (electronic)",
  issn-l =       "0035-7596",
  bibdate =      "Mon Feb 18 18:47:30 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  url =          "http://rmmc.asu.edu/abstracts/rmj/vol41-5/surv-masspag1.pdf",
  acknowledgement = ack-nhfb,
  fjournal =     "Rocky Mountain Journal of Mathematics",
  keywords =     "Benford's law; first digit phenomenon; hierarchy;
                 mantissa; weighted density",
}

@Book{McGrayne:2011:TWH,
  author =       "Sharon Bertsch McGrayne",
  title =        "The theory that would not die: how {Bayes}' rule
                 cracked the {Enigma} code, hunted down {Russian}
                 submarines, and emerged triumphant from two centuries
                 of controversy",
  publisher =    pub-YALE,
  address =      pub-YALE:adr,
  pages =        "xiii + 320",
  year =         "2011",
  isbn =         "0-300-16969-8",
  isbn-13 =      "978-0-300-16969-0",
  lccn =         "QA279.5 .M415 2011",
  bibdate =      "Wed May 11 14:42:54 MDT 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 http://www.math.utah.edu/pub/tex/bib/master.bib;
                 z3950.loc.gov:7090/Voyager",
  abstract =     "Bayes' rule appears to be a straightforward, one-line
                 theorem: by updating our initial beliefs with objective
                 new information, we get a new and improved belief. To
                 its adherents, it is an elegant statement about
                 learning from experience. To its opponents, it is
                 subjectivity run amok. In the first-ever account of
                 Bayes' rule for general readers, Sharon Bertsch
                 McGrayne explores this controversial theorem and the
                 human obsessions surrounding it. She traces its
                 discovery by an amateur mathematician in the 1740s
                 through its development into roughly its modern form by
                 French scientist Pierre Simon Laplace. She reveals why
                 respected statisticians rendered it professionally
                 taboo for 150 years --- at the same time that
                 practitioners relied on it to solve crises involving
                 great uncertainty and scanty information, even breaking
                 Germany's Enigma code during World War II, and explains
                 how the advent of off-the-shelf computer technology in
                 the 1980s proved to be a game-changer. Today, Bayes'
                 rule is used everywhere from DNA de-coding to Homeland
                 Security. Drawing on primary source material and
                 interviews with statisticians and other scientists, The
                 Theory That Would Not Die is the riveting account of
                 how a seemingly simple theorem ignited one of the
                 greatest controversies of all time.",
  acknowledgement = ack-nhfb,
  remark =       "This book has important comments on the battles among
                 Sir Ronald Fisher, Jerzy Neyman, Egon Pearson, and Karl
                 Pearson, supplementing the extensive discussion of
                 those conflicts in \cite{Ziliak:2008:CSS}.",
  subject =      "Bayesian statistical decision theory; history; science
                 / history; mathematics / history and philosophy",
}

@Article{Mebane:2011:CBL,
  author =       "Walter R. {Mebane, Jr.}",
  title =        "Comment on {Benford's Law} and the Detection of
                 Election Fraud",
  journal =      j-POLIT-ANAL,
  volume =       "19",
  number =       "3",
  pages =        "269--272",
  day =          "18",
  month =        "Summer",
  year =         "2011",
  coden =        "????",
  doi =          "http://dx.doi.org/10.1093/pan/mpr024",
  issn =         "1047-1987 (print), 1476-4989 (electronic)",
  issn-l =       "1047-1987",
  bibdate =      "Fri Nov 25 11:00:46 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  note =         "See \cite{Deckert:2011:BLD}.",
  url =          "http://pan.oxfordjournals.org/content/19/3/269.abstract",
  acknowledgement = ack-nhfb,
  fjournal =     "Political Analysis",
}

@Article{Michel:2011:QAC,
  author =       "Jean-Baptiste Michel and Yuan Kui Shen and Aviva
                 Presser Aiden and Adrian Veres and Matthew K. Gray and
                 {The Google Books Team} and Joseph P. Pickett and Dale
                 Hoiberg and Dan Clancy and Peter Norvig and Jon Orwant
                 and Steven Pinker and Martin A. Nowak and Erez
                 Lieberman Aiden",
  title =        "Quantitative Analysis of Culture Using Millions of
                 Digitized Books",
  journal =      j-SCIENCE,
  volume =       "331",
  number =       "6014",
  pages =        "176--182",
  day =          "14",
  month =        jan,
  year =         "2011",
  coden =        "SCIEAS",
  doi =          "http://dx.doi.org/10.1126/science.1199644",
  issn =         "0036-8075 (print), 1095-9203 (electronic)",
  issn-l =       "0036-8075",
  bibdate =      "Fri Dec 09 11:06:28 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  url =          "http://www.sciencemag.org/content/331/6014/176.abstract",
  acknowledgement = ack-nhfb,
  fjournal =     "Science",
  keywords =     "Zipf's law",
  remark =       "This papers reports results from a large study of
                 cultural phenomena, fame, and word usage from 4\% of
                 all books ever printed. Among the findings is this
                 quote from the first page: ``we estimated the number of
                 words in the English lexicon as 544,000 in 1900,
                 597,000 in 1950, and 1,022,000 in 2000. The lexicon is
                 enjoying a period of enormous growth: The addition of
                 $\approx 8500$ words/year has increased the size of the
                 language by over 70\% during the past 50 years.'' From
                 page 177: ``Consistent with Zipf's famous law, a large
                 fraction of the words in our lexicon (63\%) were in
                 this lowest-frequency bin. As a result, we estimated
                 that 52\% of the English lexicon --- the majority of
                 the words used in English books --- consists of lexical
                 `dark matter' undocumented in standard references
                 (12).''",
}

@Article{Mir:2011:LLD,
  author =       "Tariq Ahmad Mir",
  title =        "Law of the leading digits and the ideological struggle
                 for numbers",
  journal =      "ArXiv e-prints",
  pages =        "11",
  year =         "2011",
  bibdate =      "Mon Nov 21 07:02:48 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  url =          "http://arxiv.org/abs/1104.3948",
  abstract =     "Benford's law states that the occurrence of
                 significant digits in many data sets is not uniform but
                 tends to follow a logarithmic distribution such that
                 the smaller digits appear as first significant digits
                 more frequently than the larger ones. We investigate
                 here numerical data on the country-wise adherent
                 distribution of seven major world religions i.e.,
                 Christianity, Islam, Buddhism, Hinduism, Sikhism,
                 Judaism and Baha'ism to see if the proportion of the
                 leading digits occurring in the distribution conforms
                 to Benford's law. We find that the adherent data of all
                 the religions, except Christianity, excellently does
                 conform to Benford's law. Furthermore, unlike the
                 adherent data on Christianity, the significant digit
                 distribution of the three major Christian denominations
                 i.e. Catholicism, Protestantism and Orthodoxy obeys the
                 law. Thus in spite of their complexity general laws can
                 be established for the evolution of the religious
                 groups.",
  acknowledgement = ack-nhfb,
}

@Article{Muller:2011:HAS,
  author =       "Hans Christian M{\"u}ller",
  title =        "How an arcane statistical law could have prevented the
                 {Greek} disaster",
  journal =      "Economics Intelligence",
  volume =       "??",
  number =       "??",
  pages =        "??",
  day =          "28",
  month =        jul,
  year =         "2011",
  coden =        "????",
  issn =         "????",
  bibdate =      "Sun Nov 20 10:04:08 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  url =          "http://economicsintelligence.com/2011/07/28/how-an-arcane-statistical-law-could-have-prevented-the-greek-disaster/",
  abstract =     "If we had known what we know today, Greece would not
                 have been able to enter the Euro area. The
                 macroeconomic data the country reported to Eurostat in
                 Luxembourg were heavily tweaked. Unfortunately,
                 however, this only became clear years after it was too
                 late.",
  acknowledgement = ack-nhfb,
}

@InCollection{Nigrini:2011:BLA,
  author =       "Mark J. Nigrini",
  title =        "{Benford's Law}: Assessing Conformity",
  crossref =     "Nigrini:2011:FAM",
  pages =        "109--129",
  year =         "2011",
  doi =          "http://dx.doi.org/10.1002/9781118386798.ch6",
  bibdate =      "Sat Feb 23 17:26:17 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Benford's Law; Kolmogorov-Smirnoff tests; mantissa arc
                 test; mean absolute deviation; Z-statistic",
  tableofcontents = "One Digit at a Time: The Z-statistic \\
                 The Chi-square and Kolmogorov--Smirnoff Tests \\
                 The Mean Absolute Deviation (MAD) Test \\
                 Tests Based on the Logarithmic Basis of Benford's Law
                 \\
                 Creating a Perfect Synthetic Benford Set \\
                 The Mantissa Arc Test \\
                 Summary",
}

@InCollection{Nigrini:2011:BLB,
  author =       "Mark J. Nigrini",
  title =        "{Benford's Law}: The Basics",
  crossref =     "Nigrini:2011:FAM",
  pages =        "85--108",
  year =         "2011",
  doi =          "http://dx.doi.org/10.1002/9781118386798.ch5",
  bibdate =      "Sat Feb 23 17:26:17 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  tableofcontents = "An Overview of Benford's Law \\
                 From Theory to Application in 60 Years \\
                 Which Data Sets should Conform to Benford's Law? \\
                 The Effect of Data Set Size \\
                 The Basic Digit Tests \\
                 Running the First-Two Digits Test in Access \\
                 Summary",
}

@InCollection{Nigrini:2011:BLN,
  author =       "Mark J. Nigrini",
  title =        "{Benford's Law}: The Number Duplication and Last-Two
                 Digits Tests",
  crossref =     "Nigrini:2011:FAM",
  pages =        "153--172",
  year =         "2011",
  doi =          "http://dx.doi.org/10.1002/9781118386798.ch8",
  bibdate =      "Sat Feb 23 17:26:17 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Benford's Law; COUNTIF formula; digits tests; last-two
                 digits tests; number duplication",
  tableofcontents = "The Number Duplication Test \\
                 Running the Number Duplication Test in Access \\
                 Running the Number Duplication Test in Excel \\
                 The Last-Two Digits Test \\
                 Summary",
}

@InCollection{Nigrini:2011:BLS,
  author =       "Mark J. Nigrini",
  title =        "{Benford's Law}: The Second-Order and Summation Tests",
  crossref =     "Nigrini:2011:FAM",
  pages =        "130--152",
  year =         "2011",
  doi =          "http://dx.doi.org/10.1002/9781118386798.ch7",
  bibdate =      "Sat Feb 23 17:26:17 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Benford's Law; digits tests; second-order;
                 second-order test; summation test",
  tableofcontents = "A Description of the Second-Order Test \\
                 The Summation Test \\
                 Summary",
}

@Article{Pericchi:2011:QAD,
  author =       "Luis Pericchi and David Torres",
  title =        "Quick anomaly detection by the {Newcomb--Benford} law,
                 with applications to electoral processes data from the
                 {USA}, {Puerto} {Rico} and {Venezuela}",
  journal =      j-STAT-SCI,
  volume =       "26",
  number =       "4",
  pages =        "502--516",
  year =         "2011",
  coden =        "STSCEP",
  doi =          "http://dx.doi.org/10.1214/09-STS296",
  issn =         "0883-4237",
  issn-l =       "0883-4237",
  mrnumber =     "2951385",
  bibdate =      "Thu Feb 14 07:02:03 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  url =          "http://projecteuclid.org/euclid.ss/1330437932",
  acknowledgement = ack-nhfb,
  fjournal =     "Statistical Science. A Review Journal of the Institute
                 of Mathematical Statistics",
}

@Article{Rauch:2011:FFE,
  author =       "Bernhard Rauch and Max G{\"o}ttsche and Gernot
                 Br{\"a}hler and Stefan Engel",
  title =        "Fact and Fiction in {EU}-Governmental Economic Data",
  journal =      j-GER-ECON-REV,
  volume =       "12",
  number =       "3",
  pages =        "243--255",
  month =        aug,
  year =         "2011",
  doi =          "http://dx.doi.org/10.1111/j.1468-0475.2011.00542.x",
  issn =         "1465-6485 (print), 1468-0475 (electronic)",
  issn-l =       "1465-6485",
  bibdate =      "Sun Nov 20 09:58:25 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  url =          "http://onlinelibrary.wiley.com/doi/10.1111/j.1468-0475.2011.00542.x/abstract",
  abstract =     "To detect manipulations or fraud in accounting data,
                 auditors have successfully used Benford's law as part
                 of their fraud detection processes. Benford's law
                 proposes a distribution for first digits of numbers in
                 naturally occurring data. Government accounting and
                 statistics are similar in nature to financial
                 accounting. In the European Union (EU), there is
                 pressure to comply with the Stability and Growth Pact
                 criteria. Therefore, like firms, governments might try
                 to make their economic situation seem better. In this
                 paper, we use a Benford test to investigate the quality
                 of macroeconomic data relevant to the deficit criteria
                 reported to Eurostat by the EU member states. We find
                 that the data reported by Greece shows the greatest
                 deviation from Benford's law among all euro states.",
  acknowledgement = ack-nhfb,
  fjournal =     "German Economic Review",
  keywords =     "auditing; Benford's law; fraud detection; government
                 statistics",
  onlinedate =   "28 April 2011",
}

@Article{Ravisankar:2011:DFS,
  author =       "P. Ravisankar and V. Ravi and G. Raghava Rao and I.
                 Bose",
  title =        "Detection of financial statement fraud and feature
                 selection using data mining techniques",
  journal =      j-DEC-SUPP-SYS,
  volume =       "50",
  number =       "2",
  pages =        "491--500",
  month =        jan,
  year =         "2011",
  coden =        "DSSYDK",
  doi =          "http://dx.doi.org/10.1016/j.dss.2010.11.006",
  issn =         "0167-9236 (print), 1873-5797 (electronic)",
  issn-l =       "0167-9236",
  bibdate =      "Tue Nov 22 11:28:19 MST 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 http://www.sciencedirect.com/",
  url =          "http://www.sciencedirect.com/science/article/pii/S0167923610001879",
  acknowledgement = ack-nhfb,
  fjournal =     "Decision Support Systems",
  keywords =     "Benford's Law",
}

@Article{Romano:2011:NLR,
  author =       "Paul K. Romano and Harry McLaughlin",
  title =        "On Non-Linear Recursive Sequences and {Benford's
                 Law}",
  journal =      j-FIB-QUART,
  volume =       "49",
  number =       "2",
  pages =        "134--138",
  month =        may,
  year =         "2011",
  coden =        "FIBQAU",
  issn =         "0015-0517",
  issn-l =       "0015-0517",
  mrclass =      "11K31 (11B37)",
  mrnumber =     "2801800",
  bibdate =      "Sat Nov 12 09:13:23 2011",
  bibsource =    "http://www.fq.math.ca/49-2.html;
                 http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 http://www.math.utah.edu/pub/tex/bib/fibquart.bib",
  url =          "http://www.fq.math.ca/Abstracts/49-2/romano.pdf",
  acknowledgement = ack-nhfb,
  ajournal =     "Fib. Quart",
  fjournal =     "The Fibonacci Quarterly. Official Organ of the
                 Fibonacci Association",
}

@Article{Ross:2011:BLG,
  author =       "Kenneth A. Ross",
  title =        "{Benford's Law}, a Growth Industry",
  journal =      j-AMER-MATH-MONTHLY,
  volume =       "118",
  number =       "7",
  pages =        "571--583",
  month =        aug # "\slash " # sep,
  year =         "2011",
  coden =        "AMMYAE",
  doi =          "http://dx.doi.org/10.4169/amer.math.monthly.118.07.571",
  issn =         "0002-9890 (print), 1930-0972 (electronic)",
  issn-l =       "0002-9890",
  bibdate =      "Mon Jan 30 08:58:20 MST 2012",
  bibsource =    "http://www.jstor.org/journals/00029890.html;
                 http://www.jstor.org/stable/10.4169/amermathmont.118.issue-7;
                 http://www.math.utah.edu/pub/tex/bib/amermathmonthly2010.bib;
                 http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  url =          "http://www.jstor.org/stable/10.4169;
                 http://www.jstor.org/stable/pdfplus/10.4169/amer.math.monthly.118.07.571.pdf;
                 http://www.maa.org/history/presidents/ross.html",
  acknowledgement = ack-nhfb,
  fjournal =     "American Mathematical Monthly",
  remark =       "The author was President of the Mathematical
                 Association of America (1995--1996).",
}

@Article{Sambridge:2011:BLF,
  author =       "Malcolm Sambridge and Hrvoje Tkal{\v{c}}i{\'c} and
                 Pierre Arroucau",
  title =        "{Benford}'s law of first digits: from mathematical
                 curiosity to change detector",
  journal =      "Asia Pacific Mathematics Newsletter",
  volume =       "1",
  number =       "4",
  pages =        "1--6",
  year =         "2011",
  issn =         "2010-3484",
  mrclass =      "62A99",
  mrnumber =     "2894867",
  bibdate =      "Thu Feb 14 07:02:03 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  ajournal =     "Asia Pac. Math. Newsl.",
  fjournal =     "Asia Pacific Mathematics Newsletter",
}

@Article{SenDe:2011:BLD,
  author =       "Aditi {Sen De} and Ujjwal Sen",
  title =        "{Benford}'s law detects quantum phase transitions
                 similarly as earthquakes",
  journal =      j-EUROPHYS-LETT,
  volume =       "95",
  number =       "5",
  pages =        "50008",
  month =        sep,
  year =         "2011",
  coden =        "EULEEJ",
  doi =          "http://dx.doi.org/10.1209/0295-5075/95/50008",
  issn =         "0295-5075 (print), 1286-4854 (electronic)",
  issn-l =       "0295-5075",
  bibdate =      "Mon Nov 14 17:52:09 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  url =          "http://arxiv.org/abs/1103.5398",
  abstract =     "A century ago, it was predicted that the first
                 significant digit appearing in a data would be
                 nonuniformly distributed, with the number one appearing
                 with the highest frequency. This law goes by the name
                 of Benford's law. It holds for data ranging from
                 infectious disease cases to national greenhouse gas
                 emissions. Quantum phase transitions are cooperative
                 phenomena where qualitative changes occur in many-body
                 systems at zero temperature. We show that the
                 century-old Benford's law can detect quantum phase
                 transitions, much like it detects earthquakes.
                 Therefore, being certainly of very different physical
                 origins, seismic activity and quantum cooperative
                 phenomena may be detected by similar methods. The
                 result has immediate implications in precise
                 measurements in experiments in general, and for
                 realizable quantum computers in particular. It shows
                 that estimation of the first significant digit of
                 measured physical observables is enough to detect the
                 presence of quantum phase transitions in macroscopic
                 systems.",
  acknowledgement = ack-nhfb,
  archiveprefix = "arXiv",
  eprint =       "1103.5398",
  fjournal =     "Europhysics Letters",
  primaryclass = "quant-ph",
}

@Misc{Shi:2011:ESP,
  author =       "Yun-Quing Shi and DongDong Fu",
  title =        "Apparatus and method for a generalized {Benford's Law}
                 analysis of {DCT} and {JPEG} coefficients",
  howpublished = "US Patent 7940989.",
  day =          "10",
  month =        may,
  year =         "2011",
  bibdate =      "Mon Feb 18 18:49:54 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  note =         "US Patent Application 11/772,636 filed 2 July 2007. US
                 Patent issued 10 May 2011.",
  url =          "http://www.google.com/patents/US7940989",
  acknowledgement = ack-nhfb,
}

@Article{Shikano:2011:WDD,
  author =       "S. Shikano and V. Mack",
  title =        "When does 2nd Digit {Benford's Law}-Test signal an
                 election fraud? {Facts} or misleading test results",
  journal =      "Jahrb{\"u}cher f{\"u}r National{\"o}konomie und
                 Statistik",
  volume =       "231",
  number =       "5--6",
  pages =        "719--732",
  month =        "????",
  year =         "2011",
  doi =          "????",
  bibdate =      "Mon Feb 18 18:51:04 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  url =          "http://benfordonline.net/fullreference/1015",
  acknowledgement = ack-nhfb,
}

@Article{Tang:2011:ESP,
  author =       "Lian Tang and Da Hui Wang",
  title =        "An explanation of the shift parameter {$\rho$} in the
                 {Zipf--Mandelbrot} law",
  journal =      "Beijing Shifan Daxue Xuebao",
  volume =       "47",
  number =       "1",
  pages =        "97--100",
  year =         "2011",
  coden =        "BSDKDH",
  issn =         "0476-0301",
  issn-l =       "0476-0301",
  mrclass =      "94A17",
  mrnumber =     "2807603",
  bibdate =      "Sat Nov 12 09:13:23 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Beijing Shifan Daxue Xuebao. Ziran Kexue Ban. Journal
                 of Beijing Normal University (Natural Science)",
}

@Article{Urzua:2011:TZL,
  author =       "Carlos M. Urz{\'u}a",
  title =        "Testing for {Zipf}'s law: a common pitfall",
  journal =      j-ECONOM-LETT,
  volume =       "112",
  number =       "3",
  pages =        "254--255",
  day =          "1",
  month =        sep,
  year =         "2011",
  coden =        "ECLEDS",
  doi =          "http://dx.doi.org/10.1016/j.econlet.2011.05.049",
  issn =         "0165-1765 (print), 1873-7374 (electronic)",
  issn-l =       "0165-1765",
  mrclass =      "62F03 (91B82)",
  mrnumber =     "2848721",
  bibdate =      "Wed Feb 27 07:32:55 MST 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  url =          "http://www.sciencedirect.com/science/article/pii/S0165176511002266",
  acknowledgement = ack-nhfb,
  fjournal =     "Economics Letters",
  keywords =     "Zipf's Law",
}

@Article{Vallee:2011:BMF,
  author =       "Robert Vall{\'e}e",
  title =        "{Beno{\^\i}t Mandelbrot} --- further notes",
  journal =      "Kybernetes",
  volume =       "40",
  number =       "9--10",
  pages =        "??--??",
  month =        "????",
  year =         "2011",
  coden =        "KBNTA3",
  issn =         "0368-492X (print), 1758-7883 (electronic)",
  issn-l =       "0368-492X",
  bibdate =      "Fri Nov 25 07:38:10 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  url =          "http://www.emeraldinsight.com/journals.htm?issn=0368-492X&volume=40&issue=9/10&articleid=17003220",
  acknowledgement = ack-nhfb,
}

@Misc{Wang:2011:BLD,
  author =       "Jialan Wang",
  title =        "{Benford's Law} and the Decreasing Reliability of
                 Accounting Data for {US} Firms. {Studies} in Everyday
                 Life: Investigations and experiments on food, ethics,
                 economics, and the environment",
  howpublished = "Blog posting",
  day =          "9",
  month =        oct,
  year =         "2011",
  bibdate =      "Mon Feb 18 18:54:40 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  url =          "http://econerdfood.blogspot.com/2011/10/benfords-law-and-decreasing-reliability.html",
  acknowledgement = ack-nhfb,
}

@Misc{Wang:2011:BLR,
  author =       "Jialan Wang",
  title =        "{Benford}'s law: a revised analysis",
  howpublished = "Blog posting",
  day =          "24",
  month =        oct,
  year =         "2011",
  bibdate =      "Tue Feb 19 10:33:15 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  url =          "http://econerdfood.blogspot.com/2011/10/benfords-law-revised-analysis.html",
  acknowledgement = ack-nhfb,
}

@Misc{Weisstein:2011:BL,
  author =       "Eric W. Weisstein",
  title =        "{Benford's Law}",
  howpublished = "MathWorld---A Wolfram Web Resource",
  year =         "2011",
  bibdate =      "Tue Nov 15 08:40:40 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  url =          "http://mathworld.wolfram.com/BenfordsLaw.html",
  acknowledgement = ack-nhfb,
}

@Article{Xu:2011:PCG,
  author =       "B. Xu and J. Wang and G. Liu and Y. Dai",
  title =        "Photorealistic computer graphics forensics based on
                 leading digit law",
  journal =      "Journal of Electronics (China)",
  volume =       "28",
  number =       "1",
  pages =        "95--100",
  month =        "????",
  year =         "2011",
  doi =          "http://dx.doi.org/10.1007/s11767-011-0474-3",
  bibdate =      "Mon Feb 18 18:55:38 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  url =          "????",
  acknowledgement = ack-nhfb,
}

@Article{Zgela:2011:ATC,
  author =       "Mario {\v{Z}}gela and Jasminka Dob{\v{s}}a",
  title =        "Analysis of Top 500 {Central and East European}
                 Companies Net Income Using {Benford's Law}",
  journal =      j-J-INFO-ORG-SCI,
  volume =       "35",
  number =       "2",
  pages =        "215--228",
  month =        dec,
  year =         "2011",
  issn =         "1846-3312 (print), 1846-9418 (electronic)",
  issn-l =       "1846-3312",
  bibdate =      "Mon Feb 18 18:57:10 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  note =         "Prosinac 2011 conference.",
  url =          "http://hrcak.srce.hr/file/111658;
                 http://hrcak.srce.hr/index.php?show=clanak&id_clanak_jezik=111658",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Informational and Organizational Sciences",
}

@Article{Zhang:2011:ETO,
  author =       "Qunzhi Zhang and Didier Sornette",
  title =        "Empirical test of the origin of {Zipf}'s law in
                 growing social networks",
  journal =      j-PHYSICA-A,
  volume =       "390",
  number =       "23--24",
  pages =        "4124--4130",
  day =          "1",
  month =        nov,
  year =         "2011",
  coden =        "PHYADX",
  doi =          "http://dx.doi.org/10.1016/j.physa.2011.06.063",
  issn =         "0378-4371 (print), 1873-2119 (electronic)",
  issn-l =       "0378-4371",
  bibdate =      "Wed Feb 27 07:32:55 MST 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  url =          "http://www.sciencedirect.com/science/article/pii/S0378437111005103",
  acknowledgement = ack-nhfb,
  fjournal =     "Physica A. Statistical Mechanics and its
                 Applications",
  keywords =     "Zipf's Law",
}

@Article{Zorzi:2011:BLP,
  author =       "Alberto Zorzi",
  title =        "{Benford's law} and pi",
  journal =      j-MATH-GAZ,
  volume =       "95",
  number =       "533",
  pages =        "264--266",
  month =        jul,
  year =         "2011",
  coden =        "MAGAAS",
  doi =          "????",
  issn =         "0025-5572",
  issn-l =       "0025-5572",
  bibdate =      "Mon Feb 18 18:59:42 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 http://www.math.utah.edu/pub/tex/bib/pi.bib",
  url =          "????",
  acknowledgement = ack-nhfb,
  fjournal =     "Mathematical Gazette",
  journal-url =  "http://www.m-a.org.uk/jsp/index.jsp?lnk=620",
  remark =       "The journal Web site lacks a search feature, and the
                 archives only cover up to 2007. JSTOR has only issues
                 up to 2007.",
}

@Article{Anonymous:2012:SB,
  author =       "Anonymous",
  title =        "The scam busters",
  journal =      j-ECONOMIST,
  volume =       "??",
  number =       "??",
  pages =        "??--??",
  day =          "15",
  month =        dec,
  year =         "2012",
  coden =        "EONOEH",
  issn =         "0013-0613 (print), 1476-8860 (electronic)",
  issn-l =       "0013-0613",
  bibdate =      "Mon Feb 18 19:01:02 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  url =          "http://www.economist.com/news/finance-and-economics/21568364-how-antitrust-economists-are-getting-better-spotting-cartels-scam-busters",
  acknowledgement = ack-nhfb,
  fjournal =     "The Economist",
  keywords =     "Benford's Law",
}

@TechReport{Balanzario:2012:BLM,
  author =       "E. P. Balanzario",
  title =        "{Benford}'s law for mixtures",
  type =         "Preprint",
  institution =  "????",
  address =      "????",
  month =        "????",
  year =         "2012",
  bibdate =      "Mon Feb 18 19:02:15 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
}

@Article{Chen:2012:MRB,
  author =       "Yanguang Chen",
  title =        "The mathematical relationship between {Zipf}'s law and
                 the hierarchical scaling law",
  journal =      j-PHYSICA-A,
  volume =       "391",
  number =       "11",
  pages =        "3285--3299",
  day =          "1",
  month =        jun,
  year =         "2012",
  coden =        "PHYADX",
  doi =          "http://dx.doi.org/10.1016/j.physa.2011.12.031",
  issn =         "0378-4371 (print), 1873-2119 (electronic)",
  issn-l =       "0378-4371",
  bibdate =      "Wed Feb 27 07:32:55 MST 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  url =          "http://www.sciencedirect.com/science/article/pii/S0378437111009678",
  acknowledgement = ack-nhfb,
  fjournal =     "Physica A. Statistical Mechanics and its
                 Applications",
  keywords =     "Zipf's Law",
}

@Article{Chen:2012:ZLF,
  author =       "Yanguang Chen",
  title =        "{Zipf}'s law, $ 1 / f $ noise, and fractal hierarchy",
  journal =      j-CHAOS-SOLITONS-FRACTALS,
  volume =       "45",
  number =       "1",
  pages =        "63--73",
  day =          "15",
  month =        jan,
  year =         "2012",
  coden =        "CSFOEH",
  doi =          "http://dx.doi.org/10.1016/j.chaos.2011.10.001",
  issn =         "0960-0779 (print), 1873-2887 (electronic)",
  issn-l =       "0960-0779",
  bibdate =      "Wed Feb 27 07:32:55 MST 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  url =          "http://www.sciencedirect.com/science/article/pii/S0960077911001901",
  acknowledgement = ack-nhfb,
  fjournal =     "Chaos, Solitons \& Fractals",
  keywords =     "Zipf's Law",
}

@Article{Chen:2012:ZLH,
  author =       "Yanguang Chen",
  title =        "{Zipf}'s law, hierarchical structure, and
                 cards-shuffling model for urban development",
  journal =      j-DISCRETE-DYN-NAT-SOC,
  pages =        "480196",
  year =         "2012",
  coden =        "DDNSFA",
  doi =          "http://dx.doi.org/10.1155/2012/480196",
  issn =         "1026-0226 (print), 1607-887X (electronic)",
  issn-l =       "1026-0226",
  mrclass =      "91D10",
  mrnumber =     "2914043",
  mrreviewer =   "Sandra L. Arlinghaus",
  bibdate =      "Mon Feb 18 16:48:12 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  ajournal =     "Discrete Dyn. Nat. Soc.",
  fjournal =     "Discrete Dynamics in Nature and Society. An
                 International Multidisciplinary Research and Review
                 Journal",
  pagecount =    "21",
}

@Article{Clippe:2012:BLT,
  author =       "Paulette Clippe and Marcel Ausloos",
  title =        "{Benford}'s law and {Theil} transform of financial
                 data",
  journal =      j-PHYSICA-A,
  volume =       "391",
  number =       "24",
  pages =        "6556--6567",
  day =          "15",
  month =        dec,
  year =         "2012",
  coden =        "PHYADX",
  doi =          "http://dx.doi.org/10.1016/j.physa.2012.07.063",
  issn =         "0378-4371 (print), 1873-2119 (electronic)",
  issn-l =       "0378-4371",
  bibdate =      "Thu Feb 14 05:56:39 MST 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  url =          "http://www.sciencedirect.com/science/article/pii/S0378437112007546",
  acknowledgement = ack-nhfb,
  fjournal =     "Physica A: Statistical Mechanics and its
                 Applications",
}

@Article{Cristelli:2012:TMT,
  author =       "Matthieu Cristelli and Michael Batty and Luciano
                 Pietronero",
  title =        "There is More than a Power Law in {Zipf}",
  journal =      j-SCI-REP,
  volume =       "2",
  number =       "??",
  pages =        "1--7",
  month =        nov,
  year =         "2012",
  coden =        "SRCEC3",
  doi =          "http://dx.doi.org/10.1038/srep00812",
  issn =         "2045-2322",
  issn-l =       "2045-2322",
  bibdate =      "Tue Feb 26 07:32:11 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  url =          "http://www.nature.com/srep/2012/121108/srep00812/full/srep00812.html",
  accepted =     "28 August 2012",
  acknowledgement = ack-nhfb,
  articleno =    "812",
  fjournal =     "Scientific Reports",
  onlinedate =   "08 November 2012",
  received =     "15 August 2012",
}

@Article{Diekmann:2012:MUB,
  author =       "Andreas Diekmann",
  title =        "Making Use of ``{Benford's Law}'' for the Randomized
                 Response Technique",
  journal =      j-SOC-METH-RES,
  volume =       "41",
  number =       "2",
  pages =        "325--334",
  month =        may,
  year =         "2012",
  doi =          "http://dx.doi.org/10.1177/0049124112452525",
  issn =         "0049-1241 (print), 1552-8294 (electronic)",
  issn-l =       "0049-1241",
  bibdate =      "Mon Feb 18 19:03:24 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  url =          "http://smr.sagepub.com/content/41/2/325;
                 http://www.socio.ethz.ch/news/Diekmann_Benford_RRT_SMR_2012.pdf",
  acknowledgement = ack-nhfb,
  fjournal =     "Sociological Methods and Research",
}

@Article{Egghe:2012:AGL,
  author =       "Leo Egghe and Raf Guns",
  title =        "Applications of the generalized law of {Benford} to
                 informetric data",
  journal =      j-J-AM-SOC-INF-SCI-TECHNOL,
  volume =       "63",
  number =       "8",
  pages =        "1662--1665",
  month =        aug,
  year =         "2012",
  coden =        "JASIEF",
  doi =          "http://dx.doi.org/10.1002/asi.22690",
  issn =         "1532-2882 (print), 1532-2890 (electronic)",
  issn-l =       "1532-2882",
  bibdate =      "Mon Feb 18 19:05:01 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  url =          "http://onlinelibrary.wiley.com/doi/10.1002/asi.22690/abstract",
  abstract =     "In a previous work (Egghe, 2011), the first author
                 showed that Benford's law (describing the logarithmic
                 distribution of the numbers 1, 2, \ldots{}, 9 as first
                 digits of data in decimal form) is related to the
                 classical law of Zipf with exponent 1. The work of
                 Campanario and Coslado (2011), however, shows that
                 Benford's law does not always fit practical data in a
                 statistical sense. In this article, we use a
                 generalization of Benford's law related to the general
                 law of Zipf with exponent $\beta > 0$. Using data from
                 Campanario and Coslado, we apply nonlinear least
                 squares to determine the optimal $\beta$ and show that
                 this generalized law of Benford fits the data better
                 than the classical law of Benford.",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of the American Society for Information
                 Science and Technology",
}

@Article{Eliahou:2012:MDP,
  author =       "Shalom Eliahou and Bruno Mass{\'e} and Dominique
                 Schneider",
  title =        "On the mantissa distribution of powers of natural and
                 prime numbers",
  journal =      "Acta Mathematica Hungarica",
  volume =       "??",
  number =       "??",
  pages =        "1--5",
  month =        jun,
  year =         "2012",
  doi =          "http://dx.doi.org/10.1007/s10474-012-0244-1",
  issn =         "0001-5954, 0236-5294, 1588-2632",
  issn-l =       "0001-5954",
  bibdate =      "Mon Feb 18 19:06:54 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  url =          "http://link.springer.com/article/10.1007%2Fs10474-012-0244-1",
  acknowledgement = ack-nhfb,
}

@Article{Eliazar:2012:PLC,
  author =       "Iddo I. Eliazar and Morrel H. Cohen",
  title =        "Power-law connections: From {Zipf} to {Heaps} and
                 beyond",
  journal =      j-INFO-PROC-MAN,
  volume =       "23",
  number =       "3",
  pages =        "56--74",
  day =          "1",
  month =        may,
  year =         "2012",
  coden =        "IPMADK",
  doi =          "http://dx.doi.org/10.1016/j.aop.2013.01.013",
  issn =         "0306-4573 (print), 1873-5371 (electronic)",
  issn-l =       "0306-4573",
  bibdate =      "Wed Feb 27 07:32:55 MST 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  url =          "http://www.sciencedirect.com/science/article/pii/S0003491613000171",
  acknowledgement = ack-nhfb,
  fjournal =     "Information Processing and Management",
  keywords =     "Zipf's Law",
}

@Article{Friar:2012:GSB,
  author =       "James L. Friar and Terrance Goldman and Juan
                 P{\'e}rez-Mercader",
  title =        "Genome Sizes and the {Benford} Distribution",
  journal =      j-PLOS-ONE,
  volume =       "7",
  number =       "5",
  pages =        "e36624",
  month =        "????",
  year =         "2012",
  coden =        "POLNCL",
  doi =          "http://dx.doi.org/10.1371/journal.pone.0036624",
  issn =         "1932-6203",
  issn-l =       "1932-6203",
  bibdate =      "Mon Feb 18 19:08:17 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  url =          "????",
  accepted =     "11 April 2012",
  acknowledgement = ack-nhfb,
  fjournal =     "PLoS One",
  onlinedate =   "18 May 2012",
  received =     "7 April 2011",
}

@Article{Gambini:2012:PDD,
  author =       "Alessandro Gambini and Giovanni Mingari Scarpello and
                 Daniele Ritelli",
  title =        "Probability of digits by dividing random numbers: a
                 $\psi$ and $\zeta$ functions approach",
  journal =      j-EXPO-MATH,
  volume =       "30",
  number =       "3",
  pages =        "223--238",
  month =        "????",
  year =         "2012",
  coden =        "????",
  doi =          "http://dx.doi.org/10.1016/j.exmath.2012.03.001",
  issn =         "0723-0869 (print), 1878-0792 (electronic)",
  issn-l =       "0723-0869",
  bibdate =      "Thu Feb 14 05:56:39 MST 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  url =          "http://www.sciencedirect.com/science/article/pii/S0723086912000230",
  acknowledgement = ack-nhfb,
  ajournal =     "Expo. Math.",
  fjournal =     "Expositiones Mathematicae",
  hoc-program-1 = "func p(r) return(1/20 + (1/2)*(psi((r + 11)/10) -
                 psi(r/10 + 1)))",
  hoc-program-2 = "for (r = 0; r < 10; ++r) printf({"}%2d: %.5f {"}, r,
                 p(r)); println {""}",
  keywords =     "Euler $\psi$ function; Hurwitz $\zeta$ function",
  remark =       "This paper proves formulas for the probability of
                 first-digit occurrences in the ratios of random
                 integers, and compares the predictions with the
                 somewhat different ones from Benford's Law. Their work
                 simplifies a result of Ces{\`a}ro (1885), and predicts
                 that the probability of the first quotient digit being
                 $r$ is given by $p(r) = 1 / 20 + (1 / 2)*(\psi((r + 11)
                 / 10) - \psi(r / 10 + 1)))$. That predicts these pairs
                 of $(r, p(r))$: $(0, 0.12673)$, $(1, 0.11736)$, $(2,
                 0.10992)$, $(3, 0.10390)$, $(4, 0.09894)$, $(5,
                 0.09478)$, $(6, 0.09125)$, $(7, 0.08822)$, $(8,
                 0.08560)$, $(9, 0.08330)$. Those values may be compared
                 with the Benford's Law prediction for the second digit
                 (possibly zero) of $(0, 0.120)$, $(1, 0.114)$, $(2,
                 0.109)$, $(3, 0.104)$, $(4, 0.100)$, $(5, 0.097)$, $(6,
                 0.093)$, $(7, 0.090)$, $(8, 0.088)$, and $(9,
                 0.085)$.",
}

@Article{Geyer:2012:ABL,
  author =       "A. Geyer and J. Mart{\'\i}",
  title =        "Applying {Benford}'s law to volcanology",
  journal =      "Geology",
  volume =       "40",
  number =       "4",
  pages =        "327--330",
  month =        apr,
  year =         "2012",
  doi =          "http://dx.doi.org/10.1130/G32787.1",
  bibdate =      "Mon Feb 18 19:11:36 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  url =          "http://geology.gsapubs.org/content/40/4/327",
  acknowledgement = ack-nhfb,
}

@InCollection{Gorroochurn:2012:BPB,
  author =       "Prakash Gorroochurn",
  title =        "{Benford} and the Peculiar Behavior of the First
                 Significant Digit (1938)",
  crossref =     "Gorroochurn:2012:CPP",
  chapter =      "27",
  pages =        "233--239",
  year =         "2012",
  doi =          "http://dx.doi.org/10.1002/9781118314340.ch27",
  bibdate =      "Sat Feb 23 17:26:17 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  keywords =     "(Benford) distribution; a distribution of
                 distributions; and Benford's law; Benford and the
                 peculiar behavior of the first significant digit
                 (1938); First 100 Fibonacci Numbers; first-digit law or
                 Benford's law; scale invariance; the leading digit and
                 its behavior",
}

@InProceedings{Guettler:2012:BGQ,
  author =       "S. Guettler and F. Thiemann and R. A. E. Mueller",
  editor =       "M. Clasen and G. Fr{\"o}hlich and H. Bernhardt and K.
                 Hildebrand and B. Theuvsen",
  booktitle =    "{Informationstechnologie f{\"u}r eine nachhaltige
                 Landbewirtschaftung. Fokus Forstwirtschaft. Referate
                 der 32. GIL-Jahrestagung, 29. Februar--1. M{\"a}rz
                 2012, Freising}. ({German}) [Information technology for
                 sustainable land management. Focus on forestry. Papers
                 of the 32nd GIL Annual Conference 29, February--1 March
                 2012, Freising]",
  title =        "{Benfords Gesetz: Ein Qualit{\"a}tstest f{\"u}r
                 statistische Reihen angewendet auf Handelsdaten f{\"u}r
                 Agrarprodukte}. ({German}) [{Benford's Law}: a quality
                 test applied for statistical series on trade data for
                 agricultural products]",
  volume =       "194",
  publisher =    "Gesellschaft f{\"u}r Informatik.",
  address =      "Bonn, Germany",
  pages =        "111--114",
  year =         "2012",
  isbn =         "3-88579-288-5",
  isbn-13 =      "978-3-88579-288-8",
  issn =         "1617-5468",
  lccn =         "????",
  bibdate =      "Tue Feb 19 05:44:08 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  series =       "Lecture Notes in Informatics",
  url =          "http://www.gil-net.de/Publikationen/24_111.pdf",
  acknowledgement = ack-nhfb,
  bookpages =    "334 (est.)",
  language =     "German",
}

@MastersThesis{Iudica:2012:BLM,
  author =       "Federico Iudica",
  title =        "{Benford's Law}: Mathematical Properties and Forensic
                 Accounting Applications",
  type =         "{Master}'s Thesis",
  school =       "Facolt{\`a} di Impresa e Management, Cattedra di
                 Matematica, Luiss Guido Carli University",
  address =      "Rome, Italy",
  pages =        "iv + 56",
  year =         "2012",
  bibdate =      "Tue Feb 19 05:54:59 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  url =          "http://tesi.eprints.luiss.it/8189/1/iudica-tesi-2012.pdf",
  acknowledgement = ack-nhfb,
  advisor =      "Marco Dall'Aglio",
  language =     "English",
}

@Article{Janvresse:2012:AAU,
  author =       "{\'E}lise Janvresse and Thierry {De La Rue}",
  title =        "Averaging along Uniform Random Integers",
  journal =      "Uniform Distribution Theory",
  volume =       "7",
  number =       "2",
  pages =        "35--60",
  month =        "????",
  year =         "2012",
  doi =          "????",
  issn =         "1336-913X",
  issn-l =       "1336-913X",
  bibdate =      "Tue Feb 19 05:56:13 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  url =          "http://www.boku.ac.at/MATH/udt/vol07/no2/03JanRue16-11.pdf",
  acknowledgement = ack-nhfb,
  journal-url =  "http://www.boku.ac.at/MATH/udt/",
  keywords =     "Benford's Law",
}

@PhdThesis{Janvresse:2012:QCP,
  author =       "{\'E}lise Janvresse",
  title =        "Quelques contributions aux probabilit{\'e}s et {\`a}
                 la th{\'e}orie ergodique. ({French}) [Some
                 contributions to probability theory and ergodic
                 theory]",
  type =         "Document de synth{\`e}se pr{\'e}sent{\'e} pour
                 l'{Habilitation {\`a} Diriger des Recherches}",
  school =       "l'Universit{\'e} de Rouen",
  address =      "Rouen, France",
  pages =        "67",
  day =          "17",
  month =        feb,
  year =         "2012",
  bibdate =      "Tue Feb 19 05:57:33 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  url =          "http://www.univ-rouen.fr/LMRS/Persopage/Janvresse/hdr_Janvresse.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "Benford's Law",
  language =     "French",
}

@InProceedings{Khosravani:2012:TIB,
  author =       "A. Khosravani and C. Rasinariu",
  title =        "Transformation invariance of {Benford} variables and
                 their numerical modeling",
  crossref =     "Niola:2012:RRA",
  pages =        "57--61",
  year =         "2012",
  bibdate =      "Tue Feb 19 06:01:26 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  url =          "http://www.wseas.us/e-library/conferences/2012/SaintMalo/ACMIN/ACMIN-06.pdf",
  acknowledgement = ack-nhfb,
}

@Article{Kim:2012:BLN,
  author =       "Sangrak Kim",
  title =        "{Benford}'s law in non-equilibrium processes: Droplet
                 collisions case",
  journal =      j-PHYSICA-A,
  volume =       "391",
  number =       "20",
  pages =        "4970--4975",
  day =          "15",
  month =        oct,
  year =         "2012",
  coden =        "PHYADX",
  doi =          "http://dx.doi.org/10.1016/j.physa.2012.05.043",
  issn =         "0378-4371 (print), 1873-2119 (electronic)",
  issn-l =       "0378-4371",
  bibdate =      "Thu Feb 14 05:56:39 MST 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  url =          "http://www.sciencedirect.com/science/article/pii/S0378437112004141",
  acknowledgement = ack-nhfb,
  fjournal =     "Physica A: Statistical Mechanics and its
                 Applications",
}

@Article{LimKaiJie:2012:CES,
  author =       "Shawn {Lim Kai Jie} and Mohandas Kalaichelvan",
  title =        "A Critical Evaluation of the Significance of Round
                 Numbers in {European} Equity Markets in Light of the
                 Predictions from {Benford's Law}",
  journal =      "International Research Journal of Finance and
                 Economics",
  volume =       "95",
  number =       "??",
  pages =        "196--210",
  day =          "28",
  month =        aug,
  year =         "2012",
  doi =          "????",
  issn =         "1450-2887",
  bibdate =      "Tue Feb 19 06:04:47 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  url =          "http://mpra.ub.uni-muenchen.de/40960/;
                 http://mpra.ub.uni-muenchen.de/40960/1/IRJFE_95_15.pdf",
  acknowledgement = ack-nhfb,
}

@Article{Masse:2012:RNS,
  author =       "B. Mass{\'e} and D. Schneider.",
  title =        "Random number sequences and the first digit
                 phenomenon",
  journal =      "Electronic Journal of Probabability",
  volume =       "17",
  number =       "86",
  pages =        "1--17",
  month =        "????",
  year =         "2012",
  doi =          "http://dx.doi.org/10.1214/EJP.v17-1900",
  bibdate =      "Tue Feb 19 06:06:14 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  url =          "????",
  acknowledgement = ack-nhfb,
}

@Article{Mir:2012:LDD,
  author =       "T. A. Mir",
  title =        "The leading digit distribution of the worldwide
                 illicit financial flows",
  journal =      "ArXiv e-prints",
  year =         "2012",
  bibdate =      "Tue Feb 19 06:07:33 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  url =          "http://arxiv.org/abs/1201.3432",
  acknowledgement = ack-nhfb,
  keywords =     "Benford's Law",
}

@Article{Mir:2012:LLD,
  author =       "Tariq Ahmad Mir",
  title =        "The law of the leading digits and the world
                 religions",
  journal =      j-PHYSICA-A,
  volume =       "391",
  number =       "3",
  pages =        "792--798",
  day =          "1",
  month =        feb,
  year =         "2012",
  coden =        "PHYADX",
  doi =          "http://dx.doi.org/10.1016/j.physa.2011.09.001",
  issn =         "0378-4371 (print), 1873-2119 (electronic)",
  issn-l =       "0378-4371",
  bibdate =      "Mon Nov 21 07:04:12 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 http://www.sciencedirect.com/",
  url =          "http://www.sciencedirect.com/science/article/pii/S0378437111007175",
  acknowledgement = ack-nhfb,
  fjournal =     "Physica A: Statistical Mechanics and its
                 Applications",
}

@Article{Nebel:2012:DHG,
  author =       "J.-C. Nebel and S. Pezzulli",
  title =        "Distribution of Human Genes Observes {Zipf's Law}",
  journal =      "Kingston University Research \& Innovation Reports
                 (KURIR)",
  volume =       "8",
  number =       "??",
  pages =        "1--9",
  month =        "????",
  year =         "2012",
  doi =          "????",
  issn =         "1749-5652",
  issn-l =       "1749-5652",
  bibdate =      "Tue Feb 19 06:09:05 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  url =          "http://staffnet.kingston.ac.uk/~ku33185/Papers/PDFformat/Kurir12.pdf",
  acknowledgement = ack-nhfb,
  journal-url =  "http://kurir.kingston.ac.uk/",
  remark =       "Kingston University, London, UK. Year 2012 volume is
                 not yet online on 19 February 2013.",
}

@Book{Nigrini:2012:BLA,
  author =       "Mark J. (Mark John) Nigrini",
  title =        "{Benford's Law}: Applications for Forensic Accounting,
                 Auditing, and Fraud Detection",
  publisher =    pub-WILEY,
  address =      pub-WILEY:adr,
  pages =        "xviii + 330",
  year =         "2012",
  isbn =         "1-118-15285-9 (hardcover), 1-118-28226-4,
                 1-118-28284-1, 1-118-28686-3",
  isbn-13 =      "978-1-118-15285-0 (hardcover), 978-1-118-28226-7,
                 978-1-118-28284-7, 978-1-118-28686-9",
  lccn =         "HV6691 .N54 2012",
  bibdate =      "Sun Feb 17 10:03:10 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  url =          "http://www.scribd.com/doc/86733139/Benford-s-Law-Applications-for-Forensic-Accounting-Auditing-and-Fraud-Detection",
  acknowledgement = ack-nhfb,
  tableofcontents = "Foreword / xi \\
                 Preface / xiii \\
                 About the Author / xix \\
                 Chapter 1: Introduction and Mathematical Foundations /
                 1 \\
                 Benford's Expected Digit Frequencies / 5 \\
                 Defining the First and First-Two Digits / 6 \\
                 Digit Patterns of U.S. Census Data / 8 \\
                 Logging on to Benford's Law / 10 \\
                 General Significant Digit Law / 13 \\
                 Log and Behold, the Census Data / 13 \\
                 Love at First Sight / 15 \\
                 Mantissa Test and Census Data / 19 \\
                 Number of Records and Benford's Law Tests / 20 \\
                 When Should Data Conform to Benford's Law? / 21 \\
                 Conclusions / 23 \\
                 Chapter 2: Theorems, Truisms, and a Little Trivia / 25
                 \\
                 Digits of Corporate Payments Data / 26 \\
                 Digits of Lake Data / 28 \\
                 Scale Invariance Theorem / 31 \\
                 Mean Absolute Deviation / 34 \\
                 Scale Invariance and Census Data / 34 \\
                 Scale Invariance and Corporate Payments / 35 \\
                 Scale Invariance and Lake Data / 36 \\
                 A Level Playing Field Becomes Benford / 38 \\
                 Multiplication by $1 / x$ / 42 \\
                 All Distributions Lead to Benford / 43 \\
                 Getting a Gripf on Benford and Zipf / 46 \\
                 Conclusions / 50 \\
                 Chapter 3: More Formulas and Facts, and a Little
                 Fibonacci / 51 \\
                 Fibonacci Numbers / 51 \\
                 Lucas Numbers / 53 \\
                 Back to Square One / 55 \\
                 $3 n + 1$ Problem / 58 \\
                 Ultimate Uniform Distribution / 60 \\
                 Benford Embraces Other Bases / 62 \\
                 Nigrini's Second Last Theorem / 65 \\
                 Conclusions / 69 \\
                 Chapter 4: Primary Benford's Law Tests / 71 \\
                 Corporate Payments Data / 72 \\
                 Data Profile / 72 \\
                 First Come, First Served / 74 \\
                 Playing Second Fiddle / 75 \\
                 First-Two Digits Test / 78 \\
                 Running the Digit Tests in Excel / 80 \\
                 Running the Digit Tests in Access / 83 \\
                 Conclusions / 87 \\
                 Chapter 5: Advanced Benford's Law Tests / 89 \\
                 Summation Test / 90 \\
                 Running the Summation Test in Excel / 94 \\
                 Running the Summation Test in Access / 95 \\
                 Second-Order Test / 97 \\
                 An Analysis of Payments Data / 102 \\
                 An Analysis of Journal Entry Data / 104 \\
                 An Analysis of Census Data / 107 \\
                 Running the Second-Order Test in Excel / 108 \\
                 Excel, Thanks a Million(s) / 110 \\
                 Scale Invariance and the Second-Order Test / 113 \\
                 Conclusions / 114 \\
                 Chapter 6: Associated Benford's Law Tests / 117 \\
                 Number Duplication Test / 117 \\
                 An Analysis of Payments Data / 119 \\
                 An Analysis of Census Data / 121 \\
                 Running the Number Duplication Test in Excel / 122 \\
                 Running the Number Duplication Test in Access / 126 \\
                 Last-Two Digits Test / 129 \\
                 An Analysis of Payments Data / 130 \\
                 An Analysis of Census Data / 131 \\
                 An Analysis of Election Results / 132 \\
                 Running the Last-Two Digits Test in Excel / 135 \\
                 Running the Last-Two Digits Test in Access / 136 \\
                 Distortion Factor Model / 138 \\
                 Distortion and the Census Data / 145 \\
                 Conclusions / 146 \\
                 Chapter 7: Assessing Conformity to Benford's Law / 149
                 \\
                 $Z$-Statistic / 150 \\
                 Chi-Square Test / 153 \\
                 Kolmogorov--Smirnoff Test / 157 \\
                 Mean Absolute Deviation Test / 158 \\
                 The Logarithmic Basis of Benford's Law / 160 \\
                 Creating a Perfect Synthetic Benford Set / 163 \\
                 Mantissa Arc Test / 165 \\
                 Conclusions / 169 \\
                 Chapter 8: Examples of Fraudulent Data / 171 \\
                 The Inside Story / 172 \\
                 The Vendor Who Never Was / 174 \\
                 Not Paying Attention / 175 \\
                 Funny Money / 177 \\
                 The Heart of the Matter / 181 \\
                 Going the Extra Mile / 182 \\
                 Laugh All the Way to the Bank / 184 \\
                 Culture Shock / 187 \\
                 Having a Bad Hair Day / 189 \\
                 An Unclean Bill of Health / 191 \\
                 Turning the Table on Tax Evasion / 193 \\
                 Conclusions / 196 \\
                 Chapter 9: Fraudulent Financial Statements, Part I /
                 199 \\
                 Number Crunching / 200 \\
                 Wrong Numbers / 205 \\
                 A Look at Enron's and AIG's Numbers / 207 \\
                 Figuring Out the Controllers / 210 \\
                 Conclusions / 213 \\
                 Chapter 10: Fraudulent Financial Statements, Part II /
                 215 \\
                 Digital Yoga by Absaroka / 216 \\
                 Can't See the Forest for the Trees / 218 \\
                 Digit a Little Deeper into Papua New Guinea / 221 \\
                 The Good, the Bad, and the Ugly / 227 \\
                 Dig a Little Deeper / 233 \\
                 There Are More Questions than Answers / 237 \\
                 Conclusions / 244 \\
                 Chapter 11: Madoff and Other Ponzi Schemes / 247 \\
                 The Madoff Claims / 248 \\
                 Don't Bank on Kaupthing / 249 \\
                 The Whole Ball of Waxenberg / 252 \\
                 General Motors Demoted to Private / 253 \\
                 Chrysler Unable to Dodge Bankruptcy / 255 \\
                 Discussion of the Claims Results / 258 \\
                 A Review of the Madoff Returns / 259 \\
                 Apple, Dell, Berkshire, and Benford / 262 \\
                 Discussion of the Returns Results / 265 \\
                 Chapter 12: Earth Science and Income Tax Applications /
                 267 \\
                 Still Waters Run Deep / 268 \\
                 The Lay of the Lake / 274 \\
                 For a Few Dollars Less / 281 \\
                 A Clean Bill of Clinton / 286 \\
                 Conclusions / 290 \\
                 Chapter 13: Future Directions and Conclusions / 293 \\
                 My Law / 295 \\
                 Insights into Number Invention / 300 \\
                 Lehman's Charitable Gifts / 306 \\
                 The Bottom Line / 310 \\
                 Glossary of Selected Terms / 315 \\
                 References / 323 \\
                 Index / 327",
}

@InCollection{Odueke:2012:TFA,
  author =       "Adeola Odueke and George R. S. Weir",
  editor =       "George R. S. Weir and A. Al-Nemrat",
  booktitle =    "Issues in Cybercrime, Security and Digtal Forensics",
  title =        "Triage in Forensic Accounting using {Zipf's Law}",
  publisher =    "University of Strathclyde Publishing",
  address =      "Glasgow, UK",
  pages =        "33--43",
  year =         "2012",
  isbn =         "????",
  isbn-13 =      "????",
  lccn =         "????",
  bibdate =      "Tue Feb 19 06:11:19 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  url =          "http://www.cis.strath.ac.uk/cis/research/publications/papers/strath_cis_publication_2590.pdf",
  acknowledgement = ack-nhfb,
  bookpages =    "????",
}

@Misc{Regan:2012:BLB,
  author =       "K. W. Regan",
  title =        "{Benford's Law} and Baseball",
  howpublished = "Web document",
  day =          "29",
  month =        jul,
  year =         "2012",
  bibdate =      "Sat Feb 16 12:48:17 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  url =          "http://rjlipton.wordpress.com/2012/07/29/benfords-law-and-baseball/",
  acknowledgement = ack-nhfb,
}

@Article{Ross:2012:FDS,
  author =       "Kenneth A. Ross",
  title =        "First Digits of Squares and Cubes",
  journal =      j-MATH-MAG,
  volume =       "85",
  number =       "1",
  pages =        "37--43",
  month =        feb,
  year =         "2012",
  coden =        "MAMGA8",
  issn =         "0025-570X",
  issn-l =       "0025-570X",
  bibdate =      "Tue Feb 19 06:14:55 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  url =          "http://www.maa.org/history/presidents/ross.html",
  acknowledgement = ack-nhfb,
  fjournal =     "Mathematics Magazine",
  journal-url =  "http://www.maa.org/pubs/mathmag.html",
  keywords =     "Benford's Law",
  remark =       "The author was President of the Mathematical
                 Association of America (1995--1996).",
}

@Article{Shelburne:2012:ED,
  author =       "Brian Shelburne",
  title =        "The {ENIAC}'s 1949 Determination of $\pi$",
  journal =      j-IEEE-ANN-HIST-COMPUT,
  volume =       "99",
  number =       "PrePrints",
  year =         "2012",
  coden =        "IAHCEX",
  doi =          "http://dx.doi.org/10.1109/MAHC.2011.61",
  issn =         "1058-6180 (print), 1934-1547 (electronic)",
  issn-l =       "1058-6180",
  bibdate =      "Fri Feb 3 15:38:23 2012",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/v/von-neumann-john.bib;
                 http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 http://www.math.utah.edu/pub/tex/bib/pi.bib",
  abstract =     "In January 1950, George W. Reitwiesner published ``An
                 ENIAC Determination of $\pi$ and $e$ to more than 2000
                 Decimal Places'' in Mathematical Tables and Other Aides
                 to Computation \cite{Reitwiesner:1950:EDM} which
                 described the first use of a computer, the ENIAC, to
                 calculate the decimal expansion of $\pi$. Since the
                 history of $\pi$ stretches back over thousands of
                 years, the use of the ENIAC to determine $\pi$ is an
                 important historical and technological milestone. It is
                 especially interesting since the ENIAC was not designed
                 to perform this type of calculation as it could only
                 store 200 decimal digits while the determination of e
                 and $\pi$ required manipulating numbers 2000+ digits
                 long. Starting with Reitwiesner's description of the
                 calculation, the known architecture of the ENIAC, how
                 it was programmed, and the mathematics used, we examine
                 why the calculation was undertaken, how the calculation
                 had to be done, and what was subsequently learned.",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE annals of the history of computing",
  pdfdate =      "8 August 2011",
  remark =       "This paper contains an interesting survey of work on
                 the calculation of $\pi$ up to the early 1950s, with a
                 detailed reconstruction of its determination on the
                 ENIAC. From page 1 of the paper: ``Early in June, 1949,
                 Professor John von Neumann expressed an interest in the
                 possibility that the ENIAC might sometime be employed
                 to determine the value of $\pi$ and $e$ to many decimal
                 places with a view toward obtaining a statistical
                 measure of the randomness of the distribution of the
                 digits.'' From page 2: ``\ldots{} Augustus De Morgan
                 (1806--1871) who noticed the smaller number of
                 appearances of the digit 7 in Shank's 607 digit
                 determination of $\pi$. It was later determined that
                 Shank's determination had an error beginning at the
                 528th digit.'' From page 11: ``A preliminary
                 investigation has indicated that the digits of $e$
                 deviate significantly from randomness (in the sense of
                 staying closer to their expected values than a random
                 sequence of this length normally would) while for $\pi$
                 no significant deviations have so far been detected.''
                 See \cite{Metropolis:1950:STV} for that analysis.",
}

@InCollection{Sorell:2012:ZLV,
  author =       "C. Joseph Sorell",
  editor =       "Carol A. Chapelle",
  booktitle =    "The Encyclopedia of Applied Linguistics",
  title =        "{Zipf's Law} and Vocabulary",
  publisher =    pub-WILEY,
  address =      pub-WILEY:adr,
  year =         "2012",
  doi =          "http://dx.doi.org/10.1002/9781405198431.wbeal1302",
  isbn =         "1-4051-9843-5",
  isbn-13 =      "978-1-4051-9843-1",
  bibdate =      "Mon Feb 25 06:13:56 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  book-doi =     "http://dx.doi.org/10.1002/9781405198431",
  keywords =     "child language; computational linguistics; corpus;
                 pragmatics; second language acquisition; vocabulary",
}

@Article{Sottili:2012:BLT,
  author =       "Gianluca Sottili and Danilo M. Palladino and Biagio
                 Giaccio and Paolo Messina",
  title =        "{Benford's Law} in Time Series Analysis of Seismic
                 Clusters",
  journal =      j-MATH-GEOSCI,
  volume =       "44",
  number =       "5",
  pages =        "619--634",
  month =        jul,
  year =         "2012",
  coden =        "????",
  doi =          "http://dx.doi.org/10.1007/s11004-012-9398-1",
  issn =         "1874-8953 (print), 1874-8961 (electronic)",
  issn-l =       "1874-8953",
  bibdate =      "Tue Feb 19 06:15:52 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  url =          "http://link.springer.com/article/10.1007%2Fs11004-012-9398-1",
  acknowledgement = ack-nhfb,
  fjournal =     "Mathematical Geosciences",
  journal-url =  "http://link.springer.com/journal/11004",
}

@Article{Strauch:2012:UP,
  author =       "O. Strauch",
  title =        "Unsolved Problems",
  journal =      "Uniform Distribution Theory",
  volume =       "??",
  number =       "??",
  publisher =    "Mathematical Institute of the Slovak Academy of
                 Sciences and BOKU --- University of Natural Resources
                 and Life Sciences",
  address =      "Bratislava, Slovakia and Vienna, Austria",
  pages =        "1--98",
  month =        "????",
  year =         "2012",
  doi =          "????",
  issn =         "1336-913X",
  issn-l =       "1336-913X",
  bibdate =      "Tue Feb 19 06:17:17 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  note =         "Unsolved Problems Section on the home page of
                 \booktitle{Uniform Distribution Theory}.",
  url =          "http://www.boku.ac.at/MATH/udt/unsolvedproblems.pdf",
  acknowledgement = ack-nhfb,
  journal-url =  "http://www.boku.ac.at/MATH/udt/",
}

@Article{Valadier:2012:BPR,
  author =       "Michel Valadier",
  title =        "The {Benford} phenomenon for random variables.
                 {Discussion} of {Feller}'s way",
  journal =      "ArXiv e-prints",
  pages =        "23",
  day =          "9",
  month =        mar,
  year =         "2012",
  bibdate =      "Tue Feb 19 06:20:32 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  url =          "http://arxiv.org/abs/1203.2518",
  acknowledgement = ack-nhfb,
}

@Article{Zeng:2012:TMB,
  author =       "Jianping Zeng and Jiangjiao Duan and Wenjun Cao and
                 Chengrong Wu",
  title =        "Topics modeling based on selective {Zipf}
                 distribution",
  journal =      j-EXPERT-SYST-APPL,
  volume =       "39",
  number =       "7",
  pages =        "6541--6546",
  day =          "1",
  month =        jun,
  year =         "2012",
  coden =        "ESAPEH",
  doi =          "http://dx.doi.org/10.1016/j.eswa.2011.12.051",
  issn =         "0957-4174 (print), 1873-6793 (electronic)",
  issn-l =       "0957-4174",
  bibdate =      "Wed Feb 27 07:32:55 MST 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  url =          "http://www.sciencedirect.com/science/article/pii/S0957417411017222",
  acknowledgement = ack-nhfb,
  fjournal =     "Expert Systems with Applications",
  journal-url =  "http://www.sciencedirect.com/science/journal/09574174",
  keywords =     "Zipf's Law",
}

@Article{Banks:2013:BLM,
  author =       "David G. Banks",
  title =        "{Benford's Law} Made Easy: Common Software Eases use
                 of Fraud Search Theorem",
  journal =      "Fraud Magazine",
  volume =       "??",
  number =       "??",
  pages =        "??--??",
  month =        jan # "\slash " # feb,
  year =         "2013",
  issn =         "1553-6645",
  issn-l =       "1553-6645",
  bibdate =      "Sun Feb 17 08:11:01 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  url =          "http://www.fraud-magazine.com/article.aspx?id=4294968485",
  acknowledgement = ack-nhfb,
  fjournal =     "Fraud Magazine. {A} Publication of the Association of
                 Certified Fraud Examiners",
}

@Article{Deligny:2013:RRL,
  author =       "Hugues Deligny and Paul Jolissaint",
  title =        "Relations de r{\'e}currence lin{\'e}aires,
                 primitivit{\'e} et loi de {Benford}. ({French})
                 [{Linear} recurrence relations, primitivity, and
                 {Benford}'s law]",
  journal =      j-ELEM-MATH,
  volume =       "68",
  number =       "1",
  pages =        "9--21",
  year =         "2013",
  doi =          "http://dx.doi.org/10.4171/EM/213",
  issn =         "0013-6018 (print), 1420-8962 (electronic)",
  issn-l =       "0013-6018",
  mrnumber =     "3016461",
  bibdate =      "Thu Feb 14 07:02:03 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Elemente der Mathematik",
  language =     "French",
}

@Article{diGiovanni:2013:FET,
  author =       "Julian di Giovanni and Andrei A. Levchenko",
  title =        "Firm entry, trade, and welfare in {Zipf}'s world",
  journal =      j-J-INT-ECON,
  volume =       "89",
  number =       "2",
  pages =        "283--296",
  day =          "15",
  month =        mar,
  year =         "2013",
  coden =        "JIECBE",
  doi =          "http://dx.doi.org/10.1016/j.jinteco.2012.08.002",
  issn =         "0022-1996 (print), 1873-0353 (electronic)",
  issn-l =       "0022-1996",
  bibdate =      "Wed Feb 27 07:32:55 MST 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  url =          "http://www.sciencedirect.com/science/article/pii/S0022199612001365",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of International Economics",
  journal-url =  "http://www.sciencedirect.com/science/journal/09247963",
  keywords =     "Zipf's Law",
}

@InCollection{Gangopadhyay:2013:EZL,
  author =       "Kausik Gangopadhyay and Banasri Basu",
  title =        "Evolution of {Zipf}'s law for {Indian} urban
                 agglomerations via-{\`a}-vis {Chinese} urban
                 agglomerations",
  crossref =     "Abergel:2013:ESR",
  pages =        "119--129",
  year =         "2013",
  doi =          "http://dx.doi.org/10.1007/978-88-470-2553-0_8",
  mrclass =      "91B80",
  mrnumber =     "2963609",
  bibdate =      "Mon Feb 18 16:48:12 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  series =       "New Econ. Windows",
  acknowledgement = ack-nhfb,
}

@InProceedings{Haferkorn:2013:HVA,
  author =       "Martin Haferkorn",
  editor =       "Fethi Rabhi and Peter Gomber",
  booktitle =    "{Enterprise applications and services in the finance
                 industry: 6th International Workshop, FinanceCom 2012,
                 Barcelona, Spain, June 10, 2012. Revised papers}",
  title =        "Humans vs. Algorithms --- Who Follows
                 {Newcomb--Benford's Law} Better with Their Order
                 Volume?",
  chapter =      "4",
  publisher =    pub-SV,
  address =      pub-SV:adr,
  pages =        "61--70",
  year =         "2013",
  doi =          "http://dx.doi.org/10.1007/978-3-642-36219-4_4",
  isbn =         "3-642-36219-2",
  isbn-13 =      "978-3-642-36219-4",
  lccn =         "HG173 .I58 2012",
  bibdate =      "Wed Feb 13 19:15:28 2013",
  bibsource =    "fsz3950.oclc.org:210/WorldCat;
                 http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  url =          "http://link.springer.com/content/pdf/10.1007/978-3-642-36219-4_4",
  acknowledgement = ack-nhfb,
  book-url =     "http://link.springer.com/content/pdf/10.1007/978-3-642-36219-4",
  remark =       "This may be the first publication to reference this
                 bibliography. It examines trading patterns of several
                 days on the German Stock Exchange (Deutsche B{\"o}rse),
                 with a total volume of almost 10 million trades, split
                 almost equally between human and algorithmic traders.
                 It finds that the algorithmic trades follow Benford's
                 Law closely, but the human trades do not. It points out
                 that algorithmic trading could be manipulated to make
                 it look more like human trades, so as not to alert
                 competitors to its actions.",
  subject =      "Financial services industry; Information technology;
                 Congresses; Data processing",
}

@Article{Lu:2013:DZH,
  author =       "Linyuan L{\"u} and Zi-Ke Zhang and Tao Zhou",
  title =        "Deviation of {Zipf}'s and {Heaps' Laws} in Human
                 Languages with Limited Dictionary Sizes",
  journal =      j-SCI-REP,
  volume =       "3",
  number =       "??",
  pages =        "1--7",
  month =        "????",
  year =         "2013",
  coden =        "SRCEC3",
  doi =          "http://dx.doi.org/10.1038/srep01082",
  issn =         "2045-2322",
  bibdate =      "Tue Feb 26 07:39:15 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  url =          "http://www.nature.com/srep/2013/130130/srep01082/full/srep01082.html",
  accepted =     "21 December 2012",
  acknowledgement = ack-nhfb,
  articleno =    "1082",
  fjournal =     "Scientific Reports",
  onlinedate =   "30 January 2013",
  received =     "11 June 2012",
}

@Article{Piva:2013:OIF,
  author =       "Alessandro Piva",
  title =        "An Overview on Image Forensics",
  journal =      "ISRN Signal Processing",
  volume =       "2013",
  number =       "??",
  pages =        "496701",
  month =        "????",
  year =         "2013",
  doi =          "http://dx.doi.org/10.1155/2013/496701",
  issn =         "2090-5041 (print), 2090-505X (electronic)",
  issn-l =       "2090-5041",
  bibdate =      "Tue Feb 19 06:21:47 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  url =          "http://www.isrn.com/journals/sp/2013/496701/",
  accepted =     "26 November 2012",
  acknowledgement = ack-nhfb,
  fjournal =     "International Scholarly Research Network Signal
                 Processing",
  journal-url =  "http://www.isrn.com/journals/sp/",
  keywords =     "Benford's Law",
  pagecount =    "22",
  received =     "6 November 2012",
}

@Article{Soo:2013:ZGG,
  author =       "Kwok Tong Soo",
  title =        "{Zipf}, {Gibrat} and geography: Evidence from {China},
                 {India} and {Brazil}",
  journal =      j-PAP-REG-SCI,
  pages =        "??--??",
  year =         "2013",
  doi =          "http://dx.doi.org/10.1111/j.1435-5957.2012.00477.x",
  issn =         "1056-8190 (print), 1435-5957 (electronic)",
  issn-l =       "1056-8190",
  bibdate =      "Mon Feb 25 06:13:56 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Papers in Regional Science",
  keywords =     "dynamic panel data models; Gibrat's Law; state
                 populations; Zipf's Law",
  xxnote =       "Online, but not yet in print with assigned page
                 numbers, on 25 February 2013.",
}

@Article{Young:2013:ATL,
  author =       "D. S. Young",
  title =        "Approximate tolerance limits for {Zipf--Mandelbrot}
                 distributions",
  journal =      j-PHYSICA-A,
  volume =       "392",
  number =       "7",
  pages =        "1702--1711",
  day =          "1",
  month =        apr,
  year =         "2013",
  coden =        "PHYADX",
  doi =          "http://dx.doi.org/10.1016/j.physa.2012.11.056",
  issn =         "0378-4371 (print), 1873-2119 (electronic)",
  issn-l =       "0378-4371",
  bibdate =      "Wed Feb 27 07:32:55 MST 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  url =          "http://www.sciencedirect.com/science/article/pii/S0378437112010497",
  acknowledgement = ack-nhfb,
  fjournal =     "Physica A. Statistical Mechanics and its
                 Applications",
  keywords =     "Zipf's Law",
}

%%% ====================================================================
%%% Cross-referenced entries must come last:

@Book{Sterbenz:1974:FPC,
  author =       "Pat H. Sterbenz",
  title =        "Floating Point Computation",
  publisher =    pub-PH,
  address =      pub-PH:adr,
  pages =        "xiv + 316",
  year =         "1974",
  isbn =         "0-13-322495-3",
  isbn-13 =      "978-0-13-322495-5",
  lccn =         "QA76.8.I12 S771 1974",
  mrclass =      "68A05 (65G05)",
  mrnumber =     "50 1556",
  bibdate =      "Sat May 29 08:01:36 1999",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 http://www.math.utah.edu/pub/bibnet/authors/v/von-neumann-john.bib;
                 http://www.math.utah.edu/pub/tex/bib/benfords-law.bib
                 http://www.math.utah.edu/pub/tex/bib/fparith.bib",
  series =       "Prentice-Hall Series in Automatic Computation.",
  acknowledgement = ack-nj # " and " # ack-nhfb,
  keywords =     "Compiling (Electronic computers); Computation by
                 computer systems --- Floating point representation;
                 Floating-point arithmetic; IBM 360 (Computer) ---
                 Programming",
  remark =       "From p. 116: ``There is general agreement that the
                 mantissas of floating-point numbers are not uniformly
                 distributed. [See Hamming (1962)
                 [\cite{Hamming:1962:NMS}], Pinkham (1961)
                 [Pinkham:1961:DFS], or Knuth (1969) [Knuth:1969:SNM].]
                 Instead, it is customary to assume that they are
                 distributed logarithmically, that is, that the
                 probability density function is

                 $$(3.12.9) f(m)= \frac{1}{m \ln r}, \qquad r^{-1} \leq
                 m \leq 1.$$

                 This assumption is based on the following observations:
                 First, this distribution reproduces itself under
                 multiplication, but a uniform distribution does not.
                 [See Hamming (1962) [\cite{Hamming:1962:NMS}] and
                 Exercise 20.] A second justification is based on the
                 fact that many of the numbers that arise in computation
                 represent measurable quantities such as lengths,
                 forces, etc., and it is reasonable to believe that the
                 distribution of the mantissas of such quantities is
                 independent of the units in which they are measured.
                 Pinkham (1961) shows that this leads to the conclusion
                 that the distribution of mantissas must be
                 logarithmic.''",
  reviewer =     "F. J. Murray",
}

@Proceedings{Apers:1989:VLD,
  editor =       "P. M. G. (Petrus Maria Gerardus) Apers and Gio
                 Wiederhold",
  booktitle =    "Very large data bases: proceedings: proceedings of the
                 Fifteenth International Conference on Very Large Data
                 Bases, August 22--25, 1989, Amsterdam, The
                 Netherlands",
  title =        "Very large data bases: proceedings: proceedings of the
                 Fifteenth International Conference on Very Large Data
                 Bases, August 22--25, 1989, Amsterdam, The
                 Netherlands",
  publisher =    pub-MORGAN-KAUFMANN,
  address =      pub-MORGAN-KAUFMANN:adr,
  pages =        "xii + 467",
  year =         "1989",
  isbn =         "1-55860-101-5",
  isbn-13 =      "978-1-55860-101-7",
  lccn =         "QA 76.9 D3 I61 1989",
  bibdate =      "Sat Dec 7 13:05:35 MST 1996",
  bibsource =    "DBLP; http://dblp.uni-trier.de;
                 http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  keywords =     "database management -- congresses",
}

@Proceedings{ACM:2000:PIC,
  editor =       "{ACM}",
  booktitle =    "{Proceedings of the 2000 International Conference on
                 Software Engineering: ICSE 2000, the new millennium:
                 June 4--11, 2000, Limerick, Ireland}",
  title =        "{Proceedings of the 2000 International Conference on
                 Software Engineering: ICSE 2000, the new millennium:
                 June 4--11, 2000, Limerick, Ireland}",
  publisher =    pub-ACM,
  address =      pub-ACM:adr,
  pages =        "xviii + 843",
  year =         "2000",
  isbn =         "1-58113-206-9, 0-7803-6325-6 (casebound),
                 0-7803-6326-4 (microfiche)",
  isbn-13 =      "978-1-58113-206-9, 978-0-7803-6325-0 (casebound),
                 978-0-7803-6326-7 (microfiche)",
  lccn =         "QA76 N271 2000",
  bibdate =      "Sun Feb 17 08:56:25 MST 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 z3950.bibsys.no:2100/BIBSYS",
  acknowledgement = ack-nhfb,
}

@Proceedings{Raidl:2003:AEC,
  editor =       "Gunther Raidl",
  booktitle =    "{Applications of evolutionary computing: {EvoWorkshops
                 2003}: {EvoBIO}, {EvoCOP}, {EvoIASP}, {EvoMUSART},
                 {EvoROB}, and {EvoSTIM}, Essex, {UK}, April 14--16,
                 2003: Proceedings}",
  title =        "{Applications of evolutionary computing: {EvoWorkshops
                 2003}: {EvoBIO}, {EvoCOP}, {EvoIASP}, {EvoMUSART},
                 {EvoROB}, and {EvoSTIM}, Essex, {UK}, April 14--16,
                 2003: Proceedings}",
  volume =       "2611",
  publisher =    pub-SV,
  address =      pub-SV:adr,
  pages =        "xxi + 708",
  year =         "2003",
  coden =        "LNCSD9",
  doi =          "????",
  isbn =         "3-540-00976-0 (softcover)",
  isbn-13 =      "978-3-540-00976-4 (softcover)",
  issn =         "0302-9743 (print), 1611-3349 (electronic)",
  issn-l =       "0302-9743",
  lccn =         "QA76.618 .E899 2003",
  bibdate =      "Thu Aug 21 09:09:03 MDT 2003",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/m/mandelbrot-benoit.bib;
                 http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 http://www.math.utah.edu/pub/tex/bib/lncs.bib",
  series =       ser-LNCS,
  url =          "http://link.springer-ny.com/link/service/series/0558/tocs/t2611.htm;
                 http://www.springerlink.com/content/978-3-540-00976-4;
                 http://www.springerlink.com/openurl.asp?genre=issue&issn=0302-9743&volume=2611",
  acknowledgement = ack-nhfb,
  keywords =     "evolutionary computation --- congresses; evolutionary
                 programming (computer science) --- congresses",
}

@Book{Warren:2003:HD,
  author =       "Henry S. Warren",
  booktitle =    "Hacker's delight",
  title =        "Hacker's delight",
  publisher =    pub-AW,
  address =      pub-AW:adr,
  pages =        "xiv + 306",
  year =         "2003",
  isbn =         "0-201-91465-4",
  isbn-13 =      "978-0-201-91465-8",
  lccn =         "QA76.6 .W375 2003",
  bibdate =      "Tue Jan 03 18:20:34 2006",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 http://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 http://www.math.utah.edu/pub/tex/bib/master.bib;
                 z3950.loc.gov:7090/Voyager",
  note =         "While this book does not specifically address
                 computational aspects of floating-point arithmetic
                 (apart from the nine-page Chapter 15), it has extensive
                 coverage of, and clever algorithms for, integer
                 arithmetic operations that are fundamental for
                 implementing hardware floating-arithmetic and software
                 multiple-precision arithmetic.",
  url =          "http://www.awprofessional.com/bookstore/product.asp?isbn=0201914654;
                 http://www.hackersdelight.org/;
                 http://www.hackersdelight.org/hackerTOC.pdf;
                 http://www.informit.com/content/images/chap3_0201914654/elementLinks/0201914654.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "DEC PDP-10; division by constants; Gray code; Hilbert
                 curves; IEEE 754 floating-point arithmetic; integer
                 cube root; integer division; integer exponentiation;
                 integer logarithm; integer square root; prime numbers;
                 unusual number bases",
  remark =       "Foreword by Guy L. Steele, Jr., who begins ``When I
                 first got a summer job at MIT's Project MAC almost 30
                 years ago, I was delighted to be able to work with the
                 DEC PDP-10 computer, which was more fun to program in
                 assembly language than any other computer, bar none,
                 because of its rich yet tractable set of instructions
                 for performing bit tests, bit masking, field
                 manipulation, and operations on integers. Though the
                 PDP-10 has not been manufactured for quite some years,
                 there remains a thriving cult of enthusiasts who keep
                 old PDP-10 hardware running and who run old PDP-10
                 software---entire operating systems and their
                 applications---by using personal computers to simulate
                 the PDP-10 instruction set.''",
  subject =      "Computer programming; Computer hackers",
  tableofcontents = "Preface\par

                 1. Introduction\par

                 Notation\par

                 Instruction Set and Execution Time Model\par

                 2. Basis\par

                 Manipulating Rightmost Bits \\
                 Addition Combined with Logical Operations \\
                 Inequalities among Logical and Arithmetic Expressions
                 \\
                 Absolute Value Function \\
                 Sign Extension \\
                 Shift Right Signed from Unsigned \\
                 Sign Function \\
                 Three-Valued Compare \\
                 Transfer of Sign \\
                 Decoding a `Zero Means 2**n' Field \\
                 Comparison Predicates \\
                 Overflow Detection \\
                 Condition Code Result of Add, Subtract, and Multiply
                 \\
                 Rotate Shifts \\
                 Double-Length Add/Subtract \\
                 Double-Length Shifts \\
                 Multibyte Add, Subtract, Absolute Value \\
                 Doz, Max, Min \\
                 Exchanging Registers \\
                 Alternating among Two or More Values\par

                 3. Power-of-2 Boundaries\par

                 Rounding Up/Down to a Multiple of a Known Power of 2
                 \\
                 Rounding Up/Down to the Next Power of 2 \\
                 Detecting a Power-of-2 Boundary Crossing\par

                 4. Arithmetic Bounds\par

                 Checking Bounds of Integers \\
                 Propagating Bounds through Adds and Subtracts \\
                 Propagating Bounds through Logical Operations \\
                 Signed Bounds\par

                 5. Counting Bits\par

                 Counting 1-bits \\
                 Parity \\
                 Counting Leading 0's \\
                 Counting Trailing 0's\par

                 6. Searching Words\par

                 Find First 0-Byte \\
                 Find First String of 1-Bits of a Given Length\par

                 7. Rearranging Bits and Bytes\par

                 Reversing Bits and Bytes \\
                 Shuffling Bits \\
                 Transposing a Bit Matrix \\
                 Compress, or Generalized Extract \\
                 General Permutations, Sheep and Goats Operation \\
                 Rearrangements and Index Transformations\par

                 8. Multiplication\par

                 Multiword Multiplication \\
                 High-Order Half of 64-Bit Product \\
                 High-Order Product Signed from/to Unsigned \\
                 Multiplication by Constants\par

                 9. Integer Division\par

                 Preliminaries \\
                 Multiword Division \\
                 Unsigned Short Division from Signed Division \\
                 Unsigned Long Division\par

                 10. Integer Division by Constants\par

                 Signed Division by a Known Power of 2 \\
                 Signed Remainder from Division by a Known Power of 2
                 \\
                 Signed Division and Remainder by Non-powers of 2 \\
                 Signed Division by Divisors >= 2 \\
                 Signed Division by Divisors <= -2 \\
                 Incorporation into a Compiler \\
                 Miscellaneous Topics \\
                 Unsigned Division \\
                 Unsigned Division by Divisors >= 1 \\
                 Incorporation into a Compiler (Unsigned) \\
                 Miscellaneous Topics (Unsigned) \\
                 Applicability to Modulus and Floor Division \\
                 Similar Methods \\
                 Sample Magic Numbers \\
                 Exact Division by Constants \\
                 Test for Zero Remainder after Division by a
                 Constant\par

                 11. Some Elementary Functions\par

                 Integer Square Root \\
                 Integer Cube Root \\
                 Integer Exponentiation \\
                 Integer Logarithm\par

                 12. Unusual Bases for Number Systems\par

                 Base -2 \\
                 Base -1 + i \\
                 Other Bases \\
                 What is the Most Efficient Base?\par

                 13. Gray Code \\
                 Gray Code \\
                 Incrementing a Gray Coded Integer \\
                 Negabinary Gray Code \\
                 Brief History and Applications\par

                 14. Hilbert's Curve\par

                 A Recursive Algorithm for Generating the Hilbert Curve
                 \\
                 Coordinates from Distance along the Hilbert Curve \\
                 Distance from Coordinates on the Hilbert Curve \\
                 Incrementing the Coordinates on the Hilbert Curve \\
                 Non-recursive Generating Algorithms \\
                 Other Space-Filling Curves \\
                 Applications\par

                 15. Floating-Point\par

                 IEEE Format \\
                 Comparing Floating-Point Numbers Using Integer
                 Operations \\
                 The Distribution of Leading Digits \\
                 Table of Miscellaneous Values\par

                 16. Formulas for Primes\par

                 Introduction \\
                 Willans's Formulas \\
                 Wormell's Formula \\
                 Formulas for Other Difficult Functions\par

                 Appendix A. Arithmetic Tables for a 4-Bit
                 Machine\par

                 Appendix B. Newton's Method\par

                 Bibliography.",
}

@Proceedings{Gama:2005:MLE,
  editor =       "Jo{\~a}ao Gama and Rui Camacho and Pavel Brazdil and
                 Al{\'\i}pio M{\'a}rio Jorge and Lu{\'\i}s Torgo",
  booktitle =    "{Machine learning --- ECML 2005: 16th European
                 Conference on Machine Learning, Porto, Portugal,
                 October 3--7, 2005: proceedings}",
  title =        "{Machine learning --- ECML 2005: 16th European
                 Conference on Machine Learning, Porto, Portugal,
                 October 3--7, 2005: proceedings}",
  volume =       "3720",
  publisher =    pub-SV,
  address =      pub-SV:adr,
  pages =        "xxiii + 769",
  year =         "2005",
  isbn =         "3-540-29243-8",
  isbn-13 =      "978-3-540-29243-2",
  issn =         "0302-9743 (print), 1611-3349 (electronic)",
  lccn =         "Q325.5 .E26 2005",
  bibdate =      "Tue Nov 15 08:57:03 MST 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 z3950.loc.gov:7090/Voyager",
  series =       ser-LNCS # " and " # ser-LNAI,
  url =          "http://www.loc.gov/catdir/enhancements/fy0663/2005933045-d.html;
                 http://www.springerlink.com/openurl.asp?genre=issue\%26issn=0302-9743\%26volume=3720",
  acknowledgement = ack-nhfb,
  meetingname =  "ECML 2005 (2005: Porto, Portugal)",
  subject =      "Machine learning; Congresses",
}

@Proceedings{Neumann:2005:CAE,
  editor =       "L{\'a}szl{\'o} Neumann and Mateu Sbert and Bruce Gooch
                 and Werner Purgathofer",
  booktitle =    "{Computational aesthetics 2005: Eurographics Workshop
                 on Computational Aesthetics in Graphics, Visualization
                 and Imaging, Girona, Spain, 18--20 May 2005}",
  title =        "{Computational aesthetics 2005: Eurographics Workshop
                 on Computational Aesthetics in Graphics, Visualization
                 and Imaging, Girona, Spain, 18--20 May 2005}",
  publisher =    "Eurographics Association",
  address =      "Aire-la-Ville, Switzerland",
  pages =        "245",
  year =         "2005",
  isbn =         "3-905673-27-4",
  isbn-13 =      "978-3-905673-27-2",
  issn =         "1816-0859",
  bibdate =      "Tue Nov 15 06:34:24 2011",
  bibsource =    "fsz3950.oclc.org:210/WorldCat;
                 http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  series =       "Computational aesthetics",
  acknowledgement = ack-nhfb,
}

@Book{Horgan:2009:PRI,
  author =       "Jane M. Horgan",
  booktitle =    "Probability with {R}: an introduction with computer
                 science applications",
  title =        "Probability with {R}: an introduction with computer
                 science applications",
  publisher =    pub-WILEY,
  address =      pub-WILEY:adr,
  pages =        "xviii + 393",
  year =         "2009",
  isbn =         "0-470-28073-5 (cloth)",
  isbn-13 =      "978-0-470-28073-7 (cloth)",
  lccn =         "QA76.9.M35 H863 2009",
  bibdate =      "Wed Sep 15 09:37:35 MDT 2010",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 http://www.math.utah.edu/pub/tex/bib/s-plus.bib;
                 z3950.loc.gov:7090/Voyager",
  url =          "http://www.loc.gov/catdir/toc/ecip0819/2008022817.html;
                 http://www.wiley.com/WileyCDA/WileyTitle/productCd-0470280735.html",
  acknowledgement = ack-nhfb,
  subject =      "computer science; mathematics; probabilities; R
                 (computer programming language)",
}

@Proceedings{Paredaens:2009:PTE,
  editor =       "Jan Paredaens and Jianwen Su",
  booktitle =    "{Proceedings of the twenty-eighth ACM
                 SIGMOD-SIGACT-SIGART symposium on Principles of
                 database systems: PODS'09, Providence, Rhode Island,
                 June 29--July 1, 2009}",
  title =        "{Proceedings of the twenty-eighth ACM
                 SIGMOD-SIGACT-SIGART symposium on Principles of
                 database systems, PODS'09, Providence, Rhode Island,
                 June 29--July 1, 2009}",
  publisher =    pub-ACM,
  address =      pub-ACM:adr,
  pages =        "x + 288",
  year =         "2009",
  isbn =         "1-60558-553-X",
  isbn-13 =      "978-1-60558-553-6",
  lccn =         "????",
  bibdate =      "Thu Jul 02 12:41:14 2009",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
}

@Book{Nigrini:2011:FAM,
  author =       "Mark J. (Mark John) Nigrini",
  booktitle =    "Forensic analytics: methods and techniques for
                 forensic accounting investigations",
  title =        "Forensic analytics: methods and techniques for
                 forensic accounting investigations",
  publisher =    pub-WILEY,
  address =      pub-WILEY:adr,
  pages =        "xvi + 463",
  year =         "2011",
  doi =          "http://dx.doi.org/10.1002/9781118386798",
  isbn =         "0-470-89046-0, 1-118-08763-1 (e-book), 1-118-08766-6
                 (e-book), 1-118-08768-2 (e-book), 1-118-38679-5
                 (e-book)",
  isbn-13 =      "978-0-470-89046-2, 978-1-118-08763-3 (e-book),
                 978-1-118-08766-4 (e-book), 978-1-118-08768-8 (e-book),
                 978-1-118-38679-8 (e-book)",
  lccn =         "HV6768 .N54 2011",
  bibdate =      "Sat Feb 23 17:38:11 MST 2013",
  bibsource =    "fsz3950.oclc.org:210/WorldCat;
                 http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  series =       "Wiley corporate F and A",
  url =          "http://catdir.loc.gov/catdir/enhancements/fy1107/2011007210-d.html;
                 http://catdir.loc.gov/catdir/enhancements/fy1107/2011007210-t.html;
                 http://catdir.loc.gov/catdir/enhancements/fy1109/2011007210-b.html",
  abstract =     "The book will review and discuss (with Access and
                 Excel examples) the methods and techniques that
                 investigators can use to uncover anomalies in corporate
                 and public sector data. These anomalies would include
                 errors, biases, duplicates, number rounding, and
                 omissions. The focus will be the detection of fraud,
                 intentional errors, and unintentional errors using data
                 analytics. Despite the quantitative and computing bias,
                 the book will still be interesting to read with
                 interesting vignettes and illustrations. Most chapters
                 will be understandable by accountants and auditors that
                 usually are lacking in the rigors of mathematics and
                 statistics. The data interrogation methods are based on
                 (a) known statistical techniques, and (b) the author's
                 own published research in the field.",
  acknowledgement = ack-nhfb,
  subject =      "Forensic accounting; Fraud; Misleading financial
                 statements; LAW / Forensic Science",
  tableofcontents = "Front Matter \\
                 Using Access in Forensic Investigations \\
                 Using Excel in Forensic Investigations \\
                 Using PowerPoint in Forensic Presentations \\
                 High-Level Data Overview Tests \\
                 Benford's Law: The Basics \\
                 Benford's Law: Assessing Conformity \\
                 Benford's Law: The Second-Order and Summation Tests \\
                 Benford's Law: The Number Duplication and Last-Two
                 Digits Tests \\
                 Testing the Internal Diagnostics of Current Period and
                 Prior Period Data \\
                 Identifying Fraud Using the Largest Subsets and Largest
                 Growth Tests \\
                 Identifying Anomalies Using the Relative Size Factor
                 Test \\
                 Identifying Fraud Using Abnormal Duplications within
                 Subsets \\
                 Identifying Fraud Using Correlation \\
                 Identifying Fraud Using Time-Series Analysis \\
                 Fraud Risk Assessments of Forensic Units \\
                 Examples of Risk Scoring with Access Queries \\
                 The Detection of Financial Statement Fraud \\
                 Using Analytics on Purchasing Card Transactions \\
                 References \\
                 Index",
}

@Book{Zenil:2011:RTC,
  editor =       "Hector Zenil",
  booktitle =    "Randomness through computation: some answers, more
                 questions",
  title =        "Randomness through computation: some answers, more
                 questions",
  publisher =    pub-WORLD-SCI,
  address =      pub-WORLD-SCI:adr,
  pages =        "xviii + 419",
  year =         "2011",
  isbn =         "981-4327-74-3",
  isbn-13 =      "978-981-4327-74-9",
  lccn =         "QA274 .R363 2011",
  bibdate =      "Mon Feb 18 18:30:30 MST 2013",
  bibsource =    "fsz3950.oclc.org:210/WorldCat;
                 http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  subject =      "Stochastic processes; Computational complexity; Random
                 polynomials",
  tableofcontents = "Is randomness necessary? / R. Graham \\
                 Probability is a lot of logic at once: if you don't
                 know which one to pick, take 'em all / T. Toffoli \\
                 Statistical testing of randomness: new and old
                 procedures / A. L. Rukhin \\
                 Scatter and regularity imply Benford's law\ldots{} and
                 more / N. Gauvrit, J.-P. Delahaye \\
                 Some bridging results and challenges in classical,
                 quantum and computational randomness / G. Longo, C.
                 Palamidessi, T. Paul \\
                 Metaphysics, metamathematics and metabiology / G.
                 Chaitin \\
                 Uncertainty in physics and computation / M. A. Stay \\
                 Indeterminism and randomness through physics / K.
                 Svozil \\
                 The Martin-L{\"o}f--Chaitin thesis: the identification
                 by recursion theory of the mathematical notion of
                 random sequence / J.-P. Delahaye \\
                 The road to intrinsic randomness / S. Wolfram \\
                 Algorithmic probability its discovery, it's properties
                 and application to strong AI / R. J. Solomonoff \\
                 Algorithmic randomness as foundation of inductive
                 reasoning and artificial intelligence / M. Hutter \\
                 Randomness, Occam's razor, AI, creativity and digital
                 physics / J. Schmidhuber \\
                 Randomness everywhere: my path to algorithmic
                 information theory / C. S. Calude \\
                 The impact of algorithmic information theory on our
                 current views on complexity, randomness, information
                 and prediction / P. G\'acs \\
                 Randomness, computability and information / J. S.
                 Miller \\
                 Studying randomness through computation / A. Nies \\
                 Computability, algorithmic randomness and complexity /
                 R. G. Downey \\
                 Is randomness native to computer science? Ten years
                 after / M. Ferbus-Zanda, S. Grigorieff \\
                 Randomness as circuit complexity (and the connection to
                 pseudorandomness) / E. Allender \\
                 Randomness: a tool for constructing and analyzing
                 computer programs / A. Ku{\v{c}}era \\
                 Connecting randomness to computation / M. Li \\
                 From error-correcting codes to algorithmic
                 informational theory / L. Staiger \\
                 Randomness in algorithms / O. Watanabe \\
                 Is the universe random? / C. S. Calude, J. L. Casti, G.
                 J. Chaitin, P. C. W. Davies, K. Svozil, S. Wolfram \\
                 What is computation? (How) Does nature computer? / C.
                 S. Calude, G. J. Chaitin, E. Fredkin, A. J. Leggett, R.
                 de Ruyter, T. Toffoli, S. Wolfram",
}

@Book{Gorroochurn:2012:CPP,
  author =       "Prakash Gorroochurn",
  booktitle =    "Classic Problems of Probability",
  title =        "Classic Problems of Probability",
  publisher =    pub-WILEY,
  address =      pub-WILEY:adr,
  pages =        "xi + 314",
  year =         "2012",
  doi =          "http://dx.doi.org/10.1002/9781118314340",
  isbn =         "1-118-06325-2 (paperback), 1-118-31432-8,
                 1-118-31433-6 (e-book), 1-118-31434-4 (e-book),
                 1-118-31431-X (e-book)",
  isbn-13 =      "978-1-118-06325-5 (paperback), 978-1-118-31432-6,
                 978-1-118-31433-3 (e-book), 978-1-118-31434-0 (e-book),
                 978-1-118-31431-9 (e-book)",
  lccn =         "QA273.A4",
  bibdate =      "Mon Feb 25 05:50:42 2013",
  bibsource =    "fsz3950.oclc.org:210/WorldCat;
                 http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  tableofcontents = "Front Matter / i?-xi \\
                 Chapter 1: Cardano and Games of Chance (1564) / 1--8
                 \\
                 Chapter 2: Galileo and a Discovery Concerning Dice
                 (1620) / 9--12 \\
                 Chapter 3: The Chevalier de M{\'e}r{\'e} Problem I: The
                 Problem of Dice (1654) / 13--19 \\
                 Chapter 4: The Chevalier de M{\'e}r{\'e} Problem II:
                 The Problem of Points (1654) / 20--38 \\
                 Chapter 5: Huygens and the Gambler's Ruin (1657) /
                 39--48 \\
                 Chapter 6: The Pepys--Newton Connection (1693) / 49--53
                 \\
                 Chapter 7: Rencontres with Montmort (1708) / 54--61 \\
                 Chapter 8: Jacob Bernoulli and his Golden Theorem
                 (1713) / 62--80 \\
                 Chapter 9: De Moivre's Problem (1730) / 81--88 \\
                 Chapter 10: De Moivre, Gauss, and the Normal Curve
                 (1730, 1809) / 89--107 \\
                 Chapter 11: Daniel Bernoulli and the St. Petersburg
                 Problem (1738) / 108--118 \\
                 Chapter 12: d'Alembert and the ?Croix ou Pile? Article
                 (1754) / 119--123 \\
                 Chapter 13: d'Alembert and the Gambler's Fallacy (1761)
                 / 124--128 \\
                 Chapter 14: Bayes, Laplace, and Philosophies of
                 Probability (1764, 1774) / 129--155 \\
                 Chapter 15: Leibniz's Error (1768) / 156--158 \\
                 Chapter 16: The Buffon Needle Problem (1777) / 159--168
                 \\
                 Chapter 17: Bertrand's Ballot Problem (1887) / 169--174
                 \\
                 Chapter 18: Bertrand's Strange Three Boxes (1889) /
                 175--178 \\
                 Chapter 19: Bertrand's Chords (1889) / 179--185 \\
                 Chapter 20: Three Coins and a Puzzle from Galton (1894)
                 / 186--188 \\
                 Chapter 21: Lewis Carroll's Pillow Problem No. 72
                 (1894) / 189--193 \\
                 Chapter 22: Borel and a Different Kind of Normality
                 (1909) / 194--198 \\
                 Chapter 23: Borel's Paradox and Kolmogorov's Axioms
                 (1909, 1933) / 199--207 \\
                 Chapter 24: Of Borel, Monkeys, and the New Creationism
                 (1913) / 208--214 \\
                 Chapter 25: Kraitchik's Neckties and Newcomb's Problem
                 (1930, 1960) / 215--223 \\
                 Chapter 26: Fisher and the Lady Tasting Tea (1935) /
                 224--232 \\
                 Chapter 27: Benford and the Peculiar Behavior of the
                 First Significant Digit (1938) / 233--239 \\
                 Chapter 28: Coinciding Birthdays (1939) / 240--246 \\
                 Chapter 29: L{\'e}vy and the Arc Sine Law (1939) /
                 247--252 \\
                 Chapter 30: Simpson's Paradox (1951) / 253--259 \\
                 Chapter 31: Gamow, Stern, and Elevators (1958) /
                 260--263 \\
                 Chapter 32: Monty Hall, Cars, and Goats (1975) /
                 264--270 \\
                 Chapter 33: Parrondo's Perplexing Paradox (1996) /
                 271--276 \\
                 Bibliography / 277--295 \\
                 Photo Credits / 296--298 \\
                 Index / 299--314",
}

@Proceedings{Niola:2012:RRA,
  editor =       "Vincenzo Niola and Michel Kadoch and Alexander
                 Zemliak",
  booktitle =    "{Recent researches in automatic control and
                 electronics: proceedings of the 14th International
                 conference on automatic control, modelling and
                 simulation (ACMOS '12): proceedings of the 11th
                 International conference on microelectronics,
                 nanoelectronics, optoelectronics (MINO '12): Saint Malo
                 and Mont Saint-Michel, France, April 2--4, 2012}",
  title =        "{Recent researches in automatic control and
                 electronics: proceedings of the 14th International
                 conference on automatic control, modelling and
                 simulation (ACMOS '12): proceedings of the 11th
                 International conference on microelectronics,
                 nanoelectronics, optoelectronics (MINO '12): Saint Malo
                 and Mont Saint-Michel, France, April 2--4, 2012}",
  publisher =    "WSEAS",
  address =      "???, Greece",
  pages =        "209",
  year =         "2012",
  isbn =         "1-61804-080-4 (paperback)",
  isbn-13 =      "978-1-61804-080-0 (paperback)",
  lccn =         "????",
  bibdate =      "Tue Feb 19 06:02:11 MST 2013",
  bibsource =    "fsz3950.oclc.org:210/WorldCat;
                 http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
}

@Book{Tijms:2012:UPC,
  author =       "Henk C. Tijms",
  booktitle =    "Understanding probability: chance rules in everyday
                 life",
  title =        "Understanding probability: chance rules in everyday
                 life",
  publisher =    pub-CAMBRIDGE,
  address =      pub-CAMBRIDGE:adr,
  edition =      "Third",
  pages =        "x + 562",
  year =         "2012",
  isbn =         "1-107-65856-X",
  isbn-13 =      "978-1-107-65856-1",
  lccn =         "QA273",
  bibdate =      "Mon Feb 18 06:48:08 MST 2013",
  bibsource =    "fsz3950.oclc.org:210/WorldCat;
                 http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  tableofcontents = "Preface \\
                 Introduction \\
                 Part I. Probability in Action \\
                 1. Probability questions \\
                 2. The law of large numbers and simulation \\
                 3. Probabilities in everyday life \\
                 4. Rare events and lotteries \\
                 5. Probability and statistics \\
                 6. Chance trees and Bayes' rule \\
                 Part II. Essentials of Probability \\
                 7. Foundations of probability theory \\
                 8. Conditional probability and Bayes \\
                 9. Basic rules for discrete random variables \\
                 10. Continuous random variables \\
                 11. Jointly distributed random variables \\
                 12. Multivariate normal distribution \\
                 13. Conditioning by random variables \\
                 14. Generating functions \\
                 15. Discrete-time Markov chains \\
                 16. Continuous-time Markov chains \\
                 Appendix \\
                 Counting methods and ex \\
                 Recommended reading \\
                 Answers to odd-numbered problems \\
                 Bibliography \\
                 Index",
}

@Book{Abergel:2013:ESR,
  editor =       "Fr{\'e}d{\'e}ric Abergel and Bikas K. Chakrabarti and
                 Anirban Chakraborti and Asim Ghosh",
  booktitle =    "Econophysics of systemic risk and network dynamics",
  title =        "Econophysics of systemic risk and network dynamics",
  publisher =    "Springer Italia",
  address =      "Milan, Italy",
  pages =        "119--129",
  year =         "2013",
  doi =          "http://dx.doi.org/10.1007/978-88-470-2553-0",
  isbn =         "88-470-2553-2, 88-470-2552-4",
  isbn-13 =      "978-88-470-2553-0, 978-88-470-2552-3",
  bibdate =      "Mon Feb 18 16:48:12 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  series =       "New Econ. Windows",
  acknowledgement = ack-nhfb,
  bookpages =    "????",
  tableofcontents = "Part 1. Systemic risk, network dynamics and other
                 empirical studies \\
                 Diffusion of Defaults Among Financial Institutions /
                 Gabrielle Demange \\
                 Systemic Risk and Complex Systems: A Graph-Theory
                 Analysis / Delphine Lautier and Franck Raynaud \\
                 Omori Law After Exogenous Shocks on Supplier-Customer
                 Network / Yoshi Fujiwara \\
                 Aftershock Prediction for High-Frequency Financial
                 Markets' Dynamics / Fulvio Baldovin, Francesco Camana,
                 Michele Caraglio, Attilio L. Stella and Marco Zamparo
                 \\
                 How Unstable Are Complex Financial Systems? Analyzing
                 an Inter-bank Network of Credit Relations / Sitabhra
                 Sinha, Maximilian Thess and Sheri Markose \\
                 Study of Statistical Correlations in Intraday and Daily
                 Financial Return Time Series / Gayatri Tilak, Tam{\'a}s
                 Sz{\'e}ll, R{\'e}my Chicheportiche and Anirban
                 Chakraborti \\
                 A Robust Measure of Investor Contrarian Behaviour /
                 Damien Challet and David Morton de Lachapelle \\
                 Evolution of Zipf's Law for Indian Urban Agglomerations
                 Vis-{\`a}-Vis Chinese Urban Agglomerations / Kausik
                 Gangopadhyay and Banasri Basu \\
                 Part 2. Model-based studies \\
                 Reaction to Extreme Events in a Minimal Agent Based
                 Model / Andrea Zaccaria, Matthieu Cristelli and Luciano
                 Pietronero \\
                 Predatory Trading and Risk Minimisation: How to (B)Eat
                 the Competition / Anita Mehta \\
                 Statistical Mechanics of Labor Markets / He Chen and
                 Jun-ichi Inoue \\
                 Kolkata Paise Restaurant Problem: An Introduction /
                 Asim Ghosh, Soumyajyoti Biswas, Arnab Chatterjee,
                 Anindya Sundar Chakrabarti and Tapan Naskar, et al. \\
                 Kolkata Paise Restaurant Problem and the Cyclically
                 Fair Norm / Priyodorshi Banerjee, Manipushpak Mitra and
                 Conan Mukherjee \\
                 An Introduction to Multi-player, Multi-choice Quantum
                 Games: Quantum Minority Games and Kolkata Restaurant
                 Problems / Puya Sharif and Hoshang Heydari \\
                 Part 3. Miscellaneous reports \\
                 Cluster Analysis and Gaussian Mixture Estimation of
                 Correlated Time-Series by Means of Multi-dimensional
                 Scaling / Takero Ibuki, Sei Suzuki and Jun-ichi Inoue
                 \\
                 Analyzing Crisis in Global Financial Indices / Sunil
                 Kumar and Nivedita Deo \\
                 Study of Systemic Risk Involved in Mutual Funds /
                 Kishore C. Dash and Monika Dash \\
                 Characterizing Price Index Behavior Through Fluctuation
                 Dynamics / Prasanta K. Panigrahi, Sayantan Ghosh, Arjun
                 Banerjee, Jainendra Bahadur and P. Manimaran",
}
