Metadata-Version: 2.1
Name: phitter
Version: 0.7
Summary: Find the best probability distribution for your dataset
Author-email: Sebastián José Herrera Monterrosa <phitter.email@gmail.com>
License: The MIT License (MIT)
        
        Copyright (c) 2024 Sebastián José Herrera Monterrosa
        
        Permission is hereby granted, free of charge, to any person obtaining a copy
        of this software and associated documentation files (the "Software"), to deal
        in the Software without restriction, including without limitation the rights
        to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
        copies of the Software, and to permit persons to whom the Software is
        furnished to do so, subject to the following conditions:
        
        The above copyright notice and this permission notice shall be included in
        all copies or substantial portions of the Software.
        
        THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
        IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
        FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
        AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
        LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
        OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN
        THE SOFTWARE.
Project-URL: Homepage, https://phitter.io
Project-URL: Documentation, https://github.com/phitterio/phitter-kernel
Project-URL: Repository, https://github.com/phitterio/phitter-kernel
Keywords: scientific,engineering,mathematics,artificial intelligence,software development,python modules
Classifier: License :: OSI Approved :: MIT License
Classifier: Intended Audience :: Education
Classifier: Intended Audience :: End Users/Desktop
Classifier: Intended Audience :: Developers
Classifier: Intended Audience :: Science/Research
Classifier: Topic :: Scientific/Engineering
Classifier: Topic :: Scientific/Engineering :: Mathematics
Classifier: Topic :: Scientific/Engineering :: Artificial Intelligence
Classifier: Topic :: Software Development
Classifier: Topic :: Software Development :: Libraries
Classifier: Topic :: Software Development :: Libraries :: Python Modules
Classifier: Topic :: Scientific/Engineering :: Bio-Informatics
Classifier: Topic :: Scientific/Engineering :: Information Analysis
Classifier: Programming Language :: Python
Classifier: Programming Language :: Python :: 3 :: Only
Classifier: Programming Language :: Python :: 3.9
Classifier: Programming Language :: Python :: 3.10
Classifier: Programming Language :: Python :: 3.11
Classifier: Programming Language :: Python :: 3.12
Requires-Python: >=3.9
Description-Content-Type: text/markdown
License-File: LICENSE
Requires-Dist: scipy >=1.1.0
Requires-Dist: plotly >=5.14.0
Requires-Dist: kaleido >=0.2.1
Requires-Dist: matplotlib >=3.3

<p align="center">
    <picture>
        <source media="(prefers-color-scheme: dark)" srcset="https://gist.githubusercontent.com/phitterio/66bc7f3674eac01ae646e30ba697a6d7/raw/e96dbba0eb26b20d35e608fefc3984bd87f0010b/DarkPhitterLogo.svg" width="350">
        <source media="(prefers-color-scheme: light)" srcset="https://gist.githubusercontent.com/phitterio/170ce460d7e766545265772525edecf6/raw/71b4867c6e5683455cf1d68bea5bea7eda55ce7d/LightPhitterLogo.svg" width="350">
        <img alt="phitter-dark-logo" src="https://gist.githubusercontent.com/phitterio/170ce460d7e766545265772525edecf6/raw/71b4867c6e5683455cf1d68bea5bea7eda55ce7d/LightPhitterLogo.svg" width="350">
    </picture>
</p>

<p align="center">
    <a href="https://pypi.org/project/phitter" target="_blank">
        <img src="https://img.shields.io/pypi/dm/phitter.svg?color=yellowgreen" alt="Downloads">
    </a>
    <a href="https://pypi.org/project/phitter" target="_blank">
        <img src="https://img.shields.io/badge/License-MIT-yellowgreen.svg" alt="License">
    </a>
    <a href="https://pypi.org/project/phitter" target="_blank">
        <img src="https://img.shields.io/pypi/pyversions/phitter?color=yellowgreen" alt="Supported Python versions">
    </a>
</p>

<p>
    Phitter analyzes datasets and determines the best analytical probability distributions that represent them. Phitter studies over 80 probability distributions, both continuous and discrete, 3 goodness-of-fit tests, and interactive visualizations. For each selected probability distribution, a standard modeling guide is provided along with spreadsheets that detail the methodology for using the chosen distribution in data science, operations research, and artificial intelligence.
</p>
<p>
    This repository contains the implementation of the python library and the kernel of <a href="https://phitter.io">Phitter Web</a>
</p>

## Installation

### Requirements

```console
python: >=3.9
```

### PyPI

```console
pip install phitter
```

## Usage

### Notebook's Tutorials

|             Tutorial             |                                                                                                                  Notebooks                                                                                                                   |
| :------------------------------: | :------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------: |
|        **Fit Continuous**        |    <a target="_blank" href="https://colab.research.google.com/github/phitterio/phitter-kernel/blob/main/examples/fit_continuous_ncdb.ipynb"><img src="https://colab.research.google.com/assets/colab-badge.svg" alt="Open In Colab"/></a>    |
|         **Fit Discrete**         | <a target="_blank" href="https://colab.research.google.com/github/phitterio/phitter-kernel/blob/main/examples/fit_discrete_galton_board.ipynb"><img src="https://colab.research.google.com/assets/colab-badge.svg" alt="Open In Colab"/></a> |
| **Fit Accelerate [Sample>100K]** |      <a target="_blank" href="https://colab.research.google.com/github/phitterio/phitter-kernel/blob/main/examples/fit_accelerate.ipynb"><img src="https://colab.research.google.com/assets/colab-badge.svg" alt="Open In Colab"/></a>       |
|   **Fit Specific Disribution**   | <a target="_blank" href="https://colab.research.google.com/github/phitterio/phitter-kernel/blob/main/examples/fit_specefic_distribution.ipynb"><img src="https://colab.research.google.com/assets/colab-badge.svg" alt="Open In Colab"/></a> |
|     **Working Distribution**     |   <a target="_blank" href="https://colab.research.google.com/github/phitterio/phitter-kernel/blob/main/examples/working_distribution.ipynb"><img src="https://colab.research.google.com/assets/colab-badge.svg" alt="Open In Colab"/></a>    |

### General

```python
import phitter

data: list[int | float] = [...]

phitter_cont = phitter.PHITTER(data)
phitter_cont.fit()
```

### Full continuous implementation

```python
import phitter

data: list[int | float] = [...]

phitter_cont = phitter.PHITTER(
    data=data,
    fit_type="continuous",
    num_bins=15,
    confidence_level=0.95,
    minimum_sse=1e-2,
    distributions_to_fit=["beta", "normal", "fatigue_life", "triangular"],
)
phitter_cont.fit(n_workers=6)
```

### Full discrete implementation

```python
import phitter

data: list[int | float] = [...]

phitter_disc = phitter.PHITTER(
    data=data,
    fit_type="discrete",
    confidence_level=0.95,
    minimum_sse=1e-2,
    distributions_to_fit=["binomial", "geometric"],
)
phitter_disc.fit(n_workers=2)
```

### Phitter: properties and methods

```python
import phitter
data: list[int | float] = [...]
phitter_cont = phitter.PHITTER(data)
phitter_cont.fit()

## Global methods and properties
phitter_cont.summarize(k: int) -> pandas.DataFrame
phitter_cont.summarize_info(k: int) -> pandas.DataFrame
phitter_cont.best_distribution -> dict
phitter_cont.sorted_distributions_sse -> dict
phitter_cont.not_rejected_distributions -> dict
phitter_cont.df_sorted_distributions_sse -> pandas.DataFrame
phitter_cont.df_not_rejected_distributions -> pandas.DataFrame

## Specific distribution methods and properties
phitter_cont.get_parameters(id_distribution: str) -> dict
phitter_cont.get_test_chi_square(id_distribution: str) -> dict
phitter_cont.get_test_kolmmogorov_smirnov(id_distribution: str) -> dict
phitter_cont.get_test_anderson_darling(id_distribution: str) -> dict
phitter_cont.get_sse(id_distribution: str) -> float
phitter_cont.get_n_test_passed(id_distribution: str) -> int
phitter_cont.get_n_test_null(id_distribution: str) -> int
```

### Histogram Plot

```python
import phitter
data: list[int | float] = [...]
phitter_cont = phitter.PHITTER(data)
phitter_cont.fit()

phitter_cont.plot_histogram()
```

<img alt="phitter_histogram" src="https://github.com/phitterio/phitter-kernel/blob/main/multimedia/histogram.png?raw=true" width="500" />

### Histogram PDF Dsitributions Plot

```python
import phitter
data: list[int | float] = [...]
phitter_cont = phitter.PHITTER(data)
phitter_cont.fit()

phitter_cont.plot_histogram_distributions()
```

<img alt="phitter_histogram" src="https://github.com/phitterio/phitter-kernel/blob/main/multimedia/histogram_pdf_distributions.png?raw=true" width="500" />

### Histogram PDF Dsitribution Plot

```python
import phitter
data: list[int | float] = [...]
phitter_cont = phitter.PHITTER(data)
phitter_cont.fit()

phitter_cont.plot_distribution("beta")
```

<img alt="phitter_histogram" src="https://github.com/phitterio/phitter-kernel/blob/main/multimedia/histogram_pdf_distribution.png?raw=true" width="500" />

### ECDF Plot

```python
import phitter
data: list[int | float] = [...]
phitter_cont = phitter.PHITTER(data)
phitter_cont.fit()

phitter_cont.plot_ecdf()
```

<img alt="phitter_histogram" src="https://github.com/phitterio/phitter-kernel/blob/main/multimedia/ecdf.png?raw=true" width="500" />

### ECDF Distribution Plot

```python
import phitter
data: list[int | float] = [...]
phitter_cont = phitter.PHITTER(data)
phitter_cont.fit()

phitter_cont.plot_ecdf_distribution("beta")
```

<img alt="phitter_histogram" src="https://github.com/phitterio/phitter-kernel/blob/main/multimedia/ecdf_distribution.png?raw=true" width="500" />

### QQ Plot

```python
import phitter
data: list[int | float] = [...]
phitter_cont = phitter.PHITTER(data)
phitter_cont.fit()

phitter_cont.qq_plot("beta")
```

<img alt="phitter_histogram" src="https://github.com/phitterio/phitter-kernel/blob/main/multimedia/qq_plot_distribution.png?raw=true" width="500" />

### QQ - Regression Plot

```python
import phitter
data: list[int | float] = [...]
phitter_cont = phitter.PHITTER(data)
phitter_cont.fit()

phitter_cont.qq_plot_regression("beta")
```

<img alt="phitter_histogram" src="https://github.com/phitterio/phitter-kernel/blob/main/multimedia/qq_plot_distribution_regression.png?raw=true" width="500" />

### Distributions: Methods and properties

```python
import phitter

distribution = phitter.continuous.BETA({"alpha": 5, "beta": 3, "A": 200, "B": 1000})

## CDF, PDF, PPF, PMF receive float or numpy.ndarray. For discrete distributions PMF instead of PDF. Parameters notation are in description of ditribution
distribution.cdf(752) # -> 0.6242831129533498
distribution.pdf(388) # -> 0.0002342575686629883
distribution.ppf(0.623) # -> 751.5512889417921
distribution.sample(2) # -> [550.800114   514.85410326]

## STATS
distribution.mean # -> 700.0
distribution.variance # -> 16666.666666666668
distribution.standard_deviation # -> 129.09944487358058
distribution.skewness # -> -0.3098386676965934
distribution.kurtosis # -> 2.5854545454545454
distribution.median # -> 708.707130841534
distribution.mode # -> 733.3333333333333
```

## Continuous Distributions

#### [1. PDF File Documentation Continuous Distributions](https://github.com/phitterio/phitter-kernel/blob/main/distributions_documentation/continuous/document_continuous_distributions/phitter_continuous_distributions.pdf)

#### 2. Resources Continuous Distributions

| Distribution              | Phitter Playground                                                                                           | Excel File                                                                                                                         | Google Sheets Files                                                                                                   |
| :------------------------ | :----------------------------------------------------------------------------------------------------------- | :--------------------------------------------------------------------------------------------------------------------------------- | :-------------------------------------------------------------------------------------------------------------------- |
| alpha                     | ▶️[phitter:alpha](https://phitter.io/distributions/continuous/alpha)                                         | 📊[alpha.xlsx](https://github.com/phitterio/phitter-files/blob/main/continuous/alpha.xlsx)                                         | 🌐[gs:alpha](https://docs.google.com/spreadsheets/d/1yRovxx1YbqgEul65DjjXetysc_4qgX2a_2NQQA1AxCA)                     |
| arcsine                   | ▶️[phitter:arcsine](https://phitter.io/distributions/continuous/arcsine)                                     | 📊[arcsine.xlsx](https://github.com/phitterio/phitter-files/blob/main/continuous/arcsine.xlsx)                                     | 🌐[gs:arcsine](https://docs.google.com/spreadsheets/d/1q8SKX4gmSbpGzimRvjopzaZ4KrEV5NY1EPmf1G1T7NQ)                   |
| argus                     | ▶️[phitter:argus](https://phitter.io/distributions/continuous/argus)                                         | 📊[argus.xlsx](https://github.com/phitterio/phitter-files/blob/main/continuous/argus.xlsx)                                         | 🌐[gs:argus](https://docs.google.com/spreadsheets/d/1u2x7IFUSB7rEyhs7s6-C2btT1Bk5aCr4WiUYEML-8xs)                     |
| beta                      | ▶️[phitter:beta](https://phitter.io/distributions/continuous/beta)                                           | 📊[beta.xlsx](https://github.com/phitterio/phitter-files/blob/main/continuous/beta.xlsx)                                           | 🌐[gs:beta](https://docs.google.com/spreadsheets/d/1P7NDy-9toV3dv64gabnr8l2NjB1xt_Ani5IVMTx3gyU)                      |
| beta_prime                | ▶️[phitter:beta_prime](https://phitter.io/distributions/continuous/beta_prime)                               | 📊[beta_prime.xlsx](https://github.com/phitterio/phitter-files/blob/main/continuous/beta_prime.xlsx)                               | 🌐[gs:beta_prime](https://docs.google.com/spreadsheets/d/1-8cKeS9D6YixQE_uLig7UarXcoQoE-341yHDj8sfXA8)                |
| beta_prime_4p             | ▶️[phitter:beta_prime_4p](https://phitter.io/distributions/continuous/beta_prime_4p)                         | 📊[beta_prime_4p.xlsx](https://github.com/phitterio/phitter-files/blob/main/continuous/beta_prime_4p.xlsx)                         | 🌐[gs:beta_prime_4p](https://docs.google.com/spreadsheets/d/1vlaZrj_jX9oNGwjW0o4Z1AUTuUTGE8Z-Akis_wb7Jq4)             |
| bradford                  | ▶️[phitter:bradford](https://phitter.io/distributions/continuous/bradford)                                   | 📊[bradford.xlsx](https://github.com/phitterio/phitter-files/blob/main/continuous/bradford.xlsx)                                   | 🌐[gs:bradford](https://docs.google.com/spreadsheets/d/1kI8b05IXur3I9SUJdrbYIdv7zMdzVxVGPWx6sK6YmuU)                  |
| burr                      | ▶️[phitter:burr](https://phitter.io/distributions/continuous/burr)                                           | 📊[burr.xlsx](https://github.com/phitterio/phitter-files/blob/main/continuous/burr.xlsx)                                           | 🌐[gs:burr](https://docs.google.com/spreadsheets/d/1vhY3l3VAgBj9BQT1yE3meRTmEZP3HXjjm30nxDKCwCI)                      |
| burr_4p                   | ▶️[phitter:burr_4p](https://phitter.io/distributions/continuous/burr_4p)                                     | 📊[burr_4p.xlsx](https://github.com/phitterio/phitter-files/blob/main/continuous/burr_4p.xlsx)                                     | 🌐[gs:burr_4p](https://docs.google.com/spreadsheets/d/1tEk3O2yvANj_PlLqACuwvRSqYYGQVRFH1SPMdLGYnz4)                   |
| cauchy                    | ▶️[phitter:cauchy](https://phitter.io/distributions/continuous/cauchy)                                       | 📊[cauchy.xlsx](https://github.com/phitterio/phitter-files/blob/main/continuous/cauchy.xlsx)                                       | 🌐[gs:cauchy](https://docs.google.com/spreadsheets/d/1xoJJvuSvfg-umC7Ogio9fde1l4TiWuAlR2IxucYK0y8)                    |
| chi_square                | ▶️[phitter:chi_square](https://phitter.io/distributions/continuous/chi_square)                               | 📊[chi_square.xlsx](https://github.com/phitterio/phitter-files/blob/main/continuous/chi_square.xlsx)                               | 🌐[gs:chi_square](https://docs.google.com/spreadsheets/d/1VatJuUON_2qghjPEYMdcjGE7TYbYqduzgdYe5YNyVf4)                |
| chi_square_3p             | ▶️[phitter:chi_square_3p](https://phitter.io/distributions/continuous/chi_square_3p)                         | 📊[chi_square_3p.xlsx](https://github.com/phitterio/phitter-files/blob/main/continuous/chi_square_3p.xlsx)                         | 🌐[gs:chi_square_3p](https://docs.google.com/spreadsheets/d/15tf3ZKbEgR3JWQRbMT2OaNij3INTGGUuNsR01NCDFJw)             |
| dagum                     | ▶️[phitter:dagum](https://phitter.io/distributions/continuous/dagum)                                         | 📊[dagum.xlsx](https://github.com/phitterio/phitter-files/blob/main/continuous/dagum.xlsx)                                         | 🌐[gs:dagum](https://docs.google.com/spreadsheets/d/1qct7LByxY_z2-Rl-pWFG1LQsUxW8VQaCgLizn93YPxk)                     |
| dagum_4p                  | ▶️[phitter:dagum_4p](https://phitter.io/distributions/continuous/dagum_4p)                                   | 📊[dagum_4p.xlsx](https://github.com/phitterio/phitter-files/blob/main/continuous/dagum_4p.xlsx)                                   | 🌐[gs:dagum_4p](https://docs.google.com/spreadsheets/d/1ZkKqvVdy7CvhvXwK830F6GWJrdNxoXBxJYeFD6XC2DM)                  |
| erlang                    | ▶️[phitter:erlang](https://phitter.io/distributions/continuous/erlang)                                       | 📊[erlang.xlsx](https://github.com/phitterio/phitter-files/blob/main/continuous/erlang.xlsx)                                       | 🌐[gs:erlang](https://docs.google.com/spreadsheets/d/1uG3Otntnm3cvMSkhkEiBVKuFn1pCLSWmiCxfN01D824)                    |
| erlang_3p                 | ▶️[phitter:erlang_3p](https://phitter.io/distributions/continuous/erlang_3p)                                 | 📊[erlang_3p.xlsx](https://github.com/phitterio/phitter-files/blob/main/continuous/erlang_3p.xlsx)                                 | 🌐[gs:erlang_3p](https://docs.google.com/spreadsheets/d/1EvFPyOAL-TPQyNf7sAXfqgHqap8sGynH0XxrLRVP12M)                 |
| error_function            | ▶️[phitter:error_function](https://phitter.io/distributions/continuous/error_function)                       | 📊[error_function.xlsx](https://github.com/phitterio/phitter-files/blob/main/continuous/error_function.xlsx)                       | 🌐[gs:error_function](https://docs.google.com/spreadsheets/d/1QT1vSgTWVgDmNz4FrH3fhwRGpgvPohgqZSCADHfBXkM)            |
| exponential               | ▶️[phitter:exponential](https://phitter.io/distributions/continuous/exponential)                             | 📊[exponential.xlsx](https://github.com/phitterio/phitter-files/blob/main/continuous/exponential.xlsx)                             | 🌐[gs:exponential](https://docs.google.com/spreadsheets/d/1c8aCgHTq3fEyIkVM1Ph3fzebxQMuourz1UkWbH4h3HA)               |
| exponential_2p            | ▶️[phitter:exponential_2p](https://phitter.io/distributions/continuous/exponential_2p)                       | 📊[exponential_2p.xlsx](https://github.com/phitterio/phitter-files/blob/main/continuous/exponential_2p.xlsx)                       | 🌐[gs:exponential_2p](https://docs.google.com/spreadsheets/d/1XtrdS8iSCM1l33rbaXSz1uWZ3vnQsYPK-07NYE-ZYBs)            |
| f                         | ▶️[phitter:f](https://phitter.io/distributions/continuous/f)                                                 | 📊[f.xlsx](https://github.com/phitterio/phitter-files/blob/main/continuous/f.xlsx)                                                 | 🌐[gs:f](https://docs.google.com/spreadsheets/d/137gYI8B6MDnqFoQ4bY1crdpFSKtPzRgaJS564SY_CUY)                         |
| f_4p                      | ▶️[phitter:f_4p](https://phitter.io/distributions/continuous/f_4p)                                           | 📊[f_4p.xlsx](https://github.com/phitterio/phitter-files/blob/main/continuous/f_4p.xlsx)                                           | 🌐[gs:f_4p](https://docs.google.com/spreadsheets/d/11MgyMqzOyGNtFLdGviRTeNhAQMYBCJ8QRMHGxoPCzwM)                      |
| fatigue_life              | ▶️[phitter:fatigue_life](https://phitter.io/distributions/continuous/fatigue_life)                           | 📊[fatigue_life.xlsx](https://github.com/phitterio/phitter-files/blob/main/continuous/fatigue_life.xlsx)                           | 🌐[gs:fatigue_life](https://docs.google.com/spreadsheets/d/1j-U_YMX89VHe2jVq3pazpzqYeA1j1zopW22C9yJcPS0)              |
| folded_normal             | ▶️[phitter:folded_normal](https://phitter.io/distributions/continuous/folded_normal)                         | 📊[folded_normal.xlsx](https://github.com/phitterio/phitter-files/blob/main/continuous/folded_normal.xlsx)                         | 🌐[gs:folded_normal](https://docs.google.com/spreadsheets/d/17NlSnru_46J8pSjxMPLDlzxoG2fPKWjeFvTh0ydfX4k)             |
| frechet                   | ▶️[phitter:frechet](https://phitter.io/distributions/continuous/frechet)                                     | 📊[frechet.xlsx](https://github.com/phitterio/phitter-files/blob/main/continuous/frechet.xlsx)                                     | 🌐[gs:frechet](https://docs.google.com/spreadsheets/d/1PNGvHImwOFIragM_hHrQJcTN7OcqCKFoHKXlPq76fnI)                   |
| gamma                     | ▶️[phitter:gamma](https://phitter.io/distributions/continuous/gamma)                                         | 📊[gamma.xlsx](https://github.com/phitterio/phitter-files/blob/main/continuous/gamma.xlsx)                                         | 🌐[gs:gamma](https://docs.google.com/spreadsheets/d/1HgD3a1zOml7Hy9PMVvFwQwrbmbs8iPbH-zQMowH0LVE)                     |
| gamma_3p                  | ▶️[phitter:gamma_3p](https://phitter.io/distributions/continuous/gamma_3p)                                   | 📊[gamma_3p.xlsx](https://github.com/phitterio/phitter-files/blob/main/continuous/gamma_3p.xlsx)                                   | 🌐[gs:gamma_3p](https://docs.google.com/spreadsheets/d/1NkyFZFOMzk2V9qkFEI_zhGUGWiGV-K9vU-RLaFB7ip8)                  |
| generalized_extreme_value | ▶️[phitter:generalized_extreme_value](https://phitter.io/distributions/continuous/generalized_extreme_value) | 📊[generalized_extreme_value.xlsx](https://github.com/phitterio/phitter-files/blob/main/continuous/generalized_extreme_value.xlsx) | 🌐[gs:generalized_extreme_value](https://docs.google.com/spreadsheets/d/19qHvnTJGVVZ7zhi-yhauCOGhu0iAdkYJ5FFgwv1q5OI) |
| generalized_gamma         | ▶️[phitter:generalized_gamma](https://phitter.io/distributions/continuous/generalized_gamma)                 | 📊[generalized_gamma.xlsx](https://github.com/phitterio/phitter-files/blob/main/continuous/generalized_gamma.xlsx)                 | 🌐[gs:generalized_gamma](https://docs.google.com/spreadsheets/d/1xx8b_VSG4jznZzaKq2yKumw5VcNX5Wj86YqLO7n4S5A)         |
| generalized_gamma_4p      | ▶️[phitter:generalized_gamma_4p](https://phitter.io/distributions/continuous/generalized_gamma_4p)           | 📊[generalized_gamma_4p.xlsx](https://github.com/phitterio/phitter-files/blob/main/continuous/generalized_gamma_4p.xlsx)           | 🌐[gs:generalized_gamma_4p](https://docs.google.com/spreadsheets/d/1TN72MSkZ2bRyoNy29h4VIxFudXAroSi1PnmFijPvO0M)      |
| generalized_logistic      | ▶️[phitter:generalized_logistic](https://phitter.io/distributions/continuous/generalized_logistic)           | 📊[generalized_logistic.xlsx](https://github.com/phitterio/phitter-files/blob/main/continuous/generalized_logistic.xlsx)           | 🌐[gs:generalized_logistic](https://docs.google.com/spreadsheets/d/1vwppGjHbwEA3xd3OtV51sPZhpOWyzmPIOV_Tued-I1Y)      |
| generalized_normal        | ▶️[phitter:generalized_normal](https://phitter.io/distributions/continuous/generalized_normal)               | 📊[generalized_normal.xlsx](https://github.com/phitterio/phitter-files/blob/main/continuous/generalized_normal.xlsx)               | 🌐[gs:generalized_normal](https://docs.google.com/spreadsheets/d/1_77JSp0mhHxqvQugVRRWIoQOTa91WdyNqNmOfDNuSfA)        |
| generalized_pareto        | ▶️[phitter:generalized_pareto](https://phitter.io/distributions/continuous/generalized_pareto)               | 📊[generalized_pareto.xlsx](https://github.com/phitterio/phitter-files/blob/main/continuous/generalized_pareto.xlsx)               | 🌐[gs:generalized_pareto](https://docs.google.com/spreadsheets/d/1E28WYhX4Ba9Nj-JNxqAm-Gh7o1EOOIOwXIdCFl1PXI0)        |
| gibrat                    | ▶️[phitter:gibrat](https://phitter.io/distributions/continuous/gibrat)                                       | 📊[gibrat.xlsx](https://github.com/phitterio/phitter-files/blob/main/continuous/gibrat.xlsx)                                       | 🌐[gs:gibrat](https://docs.google.com/spreadsheets/d/1pM7skBPnH8V3GCJo0iSst46Oc2OzqWdX2qATYBqc_GQ)                    |
| gumbel_left               | ▶️[phitter:gumbel_left](https://phitter.io/distributions/continuous/gumbel_left)                             | 📊[gumbel_left.xlsx](https://github.com/phitterio/phitter-files/blob/main/continuous/gumbel_left.xlsx)                             | 🌐[gs:gumbel_left](https://docs.google.com/spreadsheets/d/1WoW97haebsHk1sB8smC4Zq8KqW8leJY0bPK757B2IdI)               |
| gumbel_right              | ▶️[phitter:gumbel_right](https://phitter.io/distributions/continuous/gumbel_right)                           | 📊[gumbel_right.xlsx](https://github.com/phitterio/phitter-files/blob/main/continuous/gumbel_right.xlsx)                           | 🌐[gs:gumbel_right](https://docs.google.com/spreadsheets/d/1CpzfSwAdptFrI8DhV3tWRsEFd9cr6h3Jaj7t3gigims)              |
| half_normal               | ▶️[phitter:half_normal](https://phitter.io/distributions/continuous/half_normal)                             | 📊[half_normal.xlsx](https://github.com/phitterio/phitter-files/blob/main/continuous/half_normal.xlsx)                             | 🌐[gs:half_normal](https://docs.google.com/spreadsheets/d/1HQpNSNIhZPzMQvWWKyShnYNH74d1Bhs_d6k9La52V9M)               |
| hyperbolic_secant         | ▶️[phitter:hyperbolic_secant](https://phitter.io/distributions/continuous/hyperbolic_secant)                 | 📊[hyperbolic_secant.xlsx](https://github.com/phitterio/phitter-files/blob/main/continuous/hyperbolic_secant.xlsx)                 | 🌐[gs:hyperbolic_secant](https://docs.google.com/spreadsheets/d/1lTcLlwX0fmgUjhT4ljvKL_dqSReK_lEthsZNBtDxAF8)         |
| inverse_gamma             | ▶️[phitter:inverse_gamma](https://phitter.io/distributions/continuous/inverse_gamma)                         | 📊[inverse_gamma.xlsx](https://github.com/phitterio/phitter-files/blob/main/continuous/inverse_gamma.xlsx)                         | 🌐[gs:inverse_gamma](https://docs.google.com/spreadsheets/d/1uOgfUvhBHKAXhbYATUwdHRQnBMIMnu6rWecqKx6MoIA)             |
| inverse_gamma_3p          | ▶️[phitter:inverse_gamma_3p](https://phitter.io/distributions/continuous/inverse_gamma_3p)                   | 📊[inverse_gamma_3p.xlsx](https://github.com/phitterio/phitter-files/blob/main/continuous/inverse_gamma_3p.xlsx)                   | 🌐[gs:inverse_gamma_3p](https://docs.google.com/spreadsheets/d/16LCC6j_j1Cm7stc7LEd-C0ObUcZ-agL51ALGYxoZtrI)          |
| inverse_gaussian          | ▶️[phitter:inverse_gaussian](https://phitter.io/distributions/continuous/inverse_gaussian)                   | 📊[inverse_gaussian.xlsx](https://github.com/phitterio/phitter-files/blob/main/continuous/inverse_gaussian.xlsx)                   | 🌐[gs:inverse_gaussian](https://docs.google.com/spreadsheets/d/10LaEnmnRxNESViLTlw6FDyt1YSWNbMlBXaWc9t4q5qA)          |
| inverse_gaussian_3p       | ▶️[phitter:inverse_gaussian_3p](https://phitter.io/distributions/continuous/inverse_gaussian_3p)             | 📊[inverse_gaussian_3p.xlsx](https://github.com/phitterio/phitter-files/blob/main/continuous/inverse_gaussian_3p.xlsx)             | 🌐[gs:inverse_gaussian_3p](https://docs.google.com/spreadsheets/d/1wkcSlXnUdMe4by2N9nPA_Cdsz3D0kHL7MVchsjl_CTQ)       |
| johnson_sb                | ▶️[phitter:johnson_sb](https://phitter.io/distributions/continuous/johnson_sb)                               | 📊[johnson_sb.xlsx](https://github.com/phitterio/phitter-files/blob/main/continuous/johnson_sb.xlsx)                               | 🌐[gs:johnson_sb](https://docs.google.com/spreadsheets/d/1H3bpJd729k0VK3LtvgxvKJiduIdP04UkHhgJoq4ayHQ)                |
| johnson_su                | ▶️[phitter:johnson_su](https://phitter.io/distributions/continuous/johnson_su)                               | 📊[johnson_su.xlsx](https://github.com/phitterio/phitter-files/blob/main/continuous/johnson_su.xlsx)                               | 🌐[gs:johnson_su](https://docs.google.com/spreadsheets/d/15kw_NZr3RFjN9orvF844ITWXroWRsCFkY7Uvq0NZ4K8)                |
| kumaraswamy               | ▶️[phitter:kumaraswamy](https://phitter.io/distributions/continuous/kumaraswamy)                             | 📊[kumaraswamy.xlsx](https://github.com/phitterio/phitter-files/blob/main/continuous/kumaraswamy.xlsx)                             | 🌐[gs:kumaraswamy](https://docs.google.com/spreadsheets/d/10YJUDlAEygfOn07YxHBJxDqiXxygv8jKpJ8WvCZhe84)               |
| laplace                   | ▶️[phitter:laplace](https://phitter.io/distributions/continuous/laplace)                                     | 📊[laplace.xlsx](https://github.com/phitterio/phitter-files/blob/main/continuous/laplace.xlsx)                                     | 🌐[gs:laplace](https://docs.google.com/spreadsheets/d/110gPFTHOnQqecbXrjq3Wqv52I5Cw93UjL7eoSVC1DIs)                   |
| levy                      | ▶️[phitter:levy](https://phitter.io/distributions/continuous/levy)                                           | 📊[levy.xlsx](https://github.com/phitterio/phitter-files/blob/main/continuous/levy.xlsx)                                           | 🌐[gs:levy](https://docs.google.com/spreadsheets/d/1OIA4C6iqhwK0Y17wb_O5ce9YXy4JIBf1yq3TqcmDp3U)                      |
| loggamma                  | ▶️[phitter:loggamma](https://phitter.io/distributions/continuous/loggamma)                                   | 📊[loggamma.xlsx](https://github.com/phitterio/phitter-files/blob/main/continuous/loggamma.xlsx)                                   | 🌐[gs:loggamma](https://docs.google.com/spreadsheets/d/1SXCmxXs7hkajo_W_qL-e0MJQEaUJqTpUno1nYGXxmxI)                  |
| logistic                  | ▶️[phitter:logistic](https://phitter.io/distributions/continuous/logistic)                                   | 📊[logistic.xlsx](https://github.com/phitterio/phitter-files/blob/main/continuous/logistic.xlsx)                                   | 🌐[gs:logistic](https://docs.google.com/spreadsheets/d/1WokfLcAM2f2TE9xcZwwuy3qjl4itw-y0cwAb7fyKxb0)                  |
| loglogistic               | ▶️[phitter:loglogistic](https://phitter.io/distributions/continuous/loglogistic)                             | 📊[loglogistic.xlsx](https://github.com/phitterio/phitter-files/blob/main/continuous/loglogistic.xlsx)                             | 🌐[gs:loglogistic](https://docs.google.com/spreadsheets/d/1WWXRuI6AP9n_n47ikOHWUjkfCYUOQgzhDjRsKBKEHXA)               |
| loglogistic_3p            | ▶️[phitter:loglogistic_3p](https://phitter.io/distributions/continuous/loglogistic_3p)                       | 📊[loglogistic_3p.xlsx](https://github.com/phitterio/phitter-files/blob/main/continuous/loglogistic_3p.xlsx)                       | 🌐[gs:loglogistic_3p](https://docs.google.com/spreadsheets/d/1RaLZ5L0rTrv9_fAi6izElf02ucuFy9LwagL_gQn3R0Y)            |
| lognormal                 | ▶️[phitter:lognormal](https://phitter.io/distributions/continuous/lognormal)                                 | 📊[lognormal.xlsx](https://github.com/phitterio/phitter-files/blob/main/continuous/lognormal.xlsx)                                 | 🌐[gs:lognormal](https://docs.google.com/spreadsheets/d/1lS1cR4C2R45ug0ZyLxBlRBtcXH6hNPE1L-5wP68gUpA)                 |
| maxwell                   | ▶️[phitter:maxwell](https://phitter.io/distributions/continuous/maxwell)                                     | 📊[maxwell.xlsx](https://github.com/phitterio/phitter-files/blob/main/continuous/maxwell.xlsx)                                     | 🌐[gs:maxwell](https://docs.google.com/spreadsheets/d/15tPw2RM2_a0vJMjVwNgsJnJUKFk9xbcEALqOf1m5qH0)                   |
| moyal                     | ▶️[phitter:moyal](https://phitter.io/distributions/continuous/moyal)                                         | 📊[moyal.xlsx](https://github.com/phitterio/phitter-files/blob/main/continuous/moyal.xlsx)                                         | 🌐[gs:moyal](https://docs.google.com/spreadsheets/d/1_58zWuk_-wSEesJbCc2FTHxv4HO5WouGwlStIZitt1I)                     |
| nakagami                  | ▶️[phitter:nakagami](https://phitter.io/distributions/continuous/nakagami)                                   | 📊[nakagami.xlsx](https://github.com/phitterio/phitter-files/blob/main/continuous/nakagami.xlsx)                                   | 🌐[gs:nakagami](https://docs.google.com/spreadsheets/d/1fY8ID5gz1R6oWFm4w91GFdQMCd0wJ5ZRgfWi-yQtGqs)                  |
| non_central_chi_square    | ▶️[phitter:non_central_chi_square](https://phitter.io/distributions/continuous/non_central_chi_square)       | 📊[non_central_chi_square.xlsx](https://github.com/phitterio/phitter-files/blob/main/continuous/non_central_chi_square.xlsx)       | 🌐[gs:non_central_chi_square](https://docs.google.com/spreadsheets/d/17KWXPKOuMfTG0w4Gqe3lU3vWY2e9k31AX22PXTzOrFk)    |
| non_central_f             | ▶️[phitter:non_central_f](https://phitter.io/distributions/continuous/non_central_f)                         | 📊[non_central_f.xlsx](https://github.com/phitterio/phitter-files/blob/main/continuous/non_central_f.xlsx)                         | 🌐[gs:non_central_f](https://docs.google.com/spreadsheets/d/14mZ563hIw2vXNM89DUncpsOdGgBXEUIIxJNa3-MVNIM)             |
| non_central_t_student     | ▶️[phitter:non_central_t_student](https://phitter.io/distributions/continuous/non_central_t_student)         | 📊[non_central_t_student.xlsx](https://github.com/phitterio/phitter-files/blob/main/continuous/non_central_t_student.xlsx)         | 🌐[gs:non_central_t_student](https://docs.google.com/spreadsheets/d/1u8pseBDM3brw0AXlru1cprOsfQuHMWfvfDbz2XxKoOY)     |
| normal                    | ▶️[phitter:normal](https://phitter.io/distributions/continuous/normal)                                       | 📊[normal.xlsx](https://github.com/phitterio/phitter-files/blob/main/continuous/normal.xlsx)                                       | 🌐[gs:normal](https://docs.google.com/spreadsheets/d/18QTB3YYprvdFhr6PJI-DFcZOnYAuffdH8JHOtH1f83I)                    |
| pareto_first_kind         | ▶️[phitter:pareto_first_kind](https://phitter.io/distributions/continuous/pareto_first_kind)                 | 📊[pareto_first_kind.xlsx](https://github.com/phitterio/phitter-files/blob/main/continuous/pareto_first_kind.xlsx)                 | 🌐[gs:pareto_first_kind](https://docs.google.com/spreadsheets/d/1T-Sjp0yCxbJpP9njbovOiFpbP8PrwI5jlj66odxAw5E)         |
| pareto_second_kind        | ▶️[phitter:pareto_second_kind](https://phitter.io/distributions/continuous/pareto_second_kind)               | 📊[pareto_second_kind.xlsx](https://github.com/phitterio/phitter-files/blob/main/continuous/pareto_second_kind.xlsx)               | 🌐[gs:pareto_second_kind](https://docs.google.com/spreadsheets/d/1hnBOqkbcRNuyRxaLP8eHei5MRwUFDb1bgdcZYkpYKio)        |
| pert                      | ▶️[phitter:pert](https://phitter.io/distributions/continuous/pert)                                           | 📊[pert.xlsx](https://github.com/phitterio/phitter-files/blob/main/continuous/pert.xlsx)                                           | 🌐[gs:pert](https://docs.google.com/spreadsheets/d/1NeKJKq4D_BB-ouefgJ35FzcORA7fH1OQwC5dCZKI_38)                      |
| power_function            | ▶️[phitter:power_function](https://phitter.io/distributions/continuous/power_function)                       | 📊[power_function.xlsx](https://github.com/phitterio/phitter-files/blob/main/continuous/power_function.xlsx)                       | 🌐[gs:power_function](https://docs.google.com/spreadsheets/d/1Hbi-XZiCK--JGFnoY-8iDLmNgYclDo5L4LKYKCCxfzw)            |
| rayleigh                  | ▶️[phitter:rayleigh](https://phitter.io/distributions/continuous/rayleigh)                                   | 📊[rayleigh.xlsx](https://github.com/phitterio/phitter-files/blob/main/continuous/rayleigh.xlsx)                                   | 🌐[gs:rayleigh](https://docs.google.com/spreadsheets/d/1UWtjOwokob4x43OcMLLFbNTYUqOo5dJWqSTfWbS-yyw)                  |
| reciprocal                | ▶️[phitter:reciprocal](https://phitter.io/distributions/continuous/reciprocal)                               | 📊[reciprocal.xlsx](https://github.com/phitterio/phitter-files/blob/main/continuous/reciprocal.xlsx)                               | 🌐[gs:reciprocal](https://docs.google.com/spreadsheets/d/1ghFeCj8Q_hbpWqv9xXaNl1UKUe-5kOomZPWyI1JsoGA)                |
| rice                      | ▶️[phitter:rice](https://phitter.io/distributions/continuous/rice)                                           | 📊[rice.xlsx](https://github.com/phitterio/phitter-files/blob/main/continuous/rice.xlsx)                                           | 🌐[gs:rice](https://docs.google.com/spreadsheets/d/1hGVFWbF0w7D0l54t_p0vUId0rO2s61BRdrgslDYTnWc)                      |
| semicircular              | ▶️[phitter:semicircular](https://phitter.io/distributions/continuous/semicircular)                           | 📊[semicircular.xlsx](https://github.com/phitterio/phitter-files/blob/main/continuous/semicircular.xlsx)                           | 🌐[gs:semicircular](https://docs.google.com/spreadsheets/d/195c9VbAKtvEndJKnFp52TrENYK2iytMzIXLMKFAGgx4)              |
| t_student                 | ▶️[phitter:t_student](https://phitter.io/distributions/continuous/t_student)                                 | 📊[t_student.xlsx](https://github.com/phitterio/phitter-files/blob/main/continuous/t_student.xlsx)                                 | 🌐[gs:t_student](https://docs.google.com/spreadsheets/d/1fGxJfFL5eXAWk8xNI6HgCX9SQuXi-m5mR83N1dMLJrg)                 |
| t_student_3p              | ▶️[phitter:t_student_3p](https://phitter.io/distributions/continuous/t_student_3p)                           | 📊[t_student_3p.xlsx](https://github.com/phitterio/phitter-files/blob/main/continuous/t_student_3p.xlsx)                           | 🌐[gs:t_student_3p](https://docs.google.com/spreadsheets/d/1K8bpbc-0mwe0mvRYXUQmoE8vaTigciJWDS4CPXmJodU)              |
| trapezoidal               | ▶️[phitter:trapezoidal](https://phitter.io/distributions/continuous/trapezoidal)                             | 📊[trapezoidal.xlsx](https://github.com/phitterio/phitter-files/blob/main/continuous/trapezoidal.xlsx)                             | 🌐[gs:trapezoidal](https://docs.google.com/spreadsheets/d/1Gsk5M_R2q9Or8RTggKtTkqEk-cN6IuDgYqbmhFm5Xlw)               |
| triangular                | ▶️[phitter:triangular](https://phitter.io/distributions/continuous/triangular)                               | 📊[triangular.xlsx](https://github.com/phitterio/phitter-files/blob/main/continuous/triangular.xlsx)                               | 🌐[gs:triangular](https://docs.google.com/spreadsheets/d/1nirKOt7O7rUf2nlYu61cnNYT91GKSzb6pVlc1-pzzGw)                |
| uniform                   | ▶️[phitter:uniform](https://phitter.io/distributions/continuous/uniform)                                     | 📊[uniform.xlsx](https://github.com/phitterio/phitter-files/blob/main/continuous/uniform.xlsx)                                     | 🌐[gs:uniform](https://docs.google.com/spreadsheets/d/1TSaKNHOsVLYUobyKTpHR6qCuCAgfkKmRSETvdeZLcw4)                   |
| weibull                   | ▶️[phitter:weibull](https://phitter.io/distributions/continuous/weibull)                                     | 📊[weibull.xlsx](https://github.com/phitterio/phitter-files/blob/main/continuous/weibull.xlsx)                                     | 🌐[gs:weibull](https://docs.google.com/spreadsheets/d/1DdNwWHmu0PZAhMYf475EMU3scTMXok3wOhzsg7gn8Ek)                   |
| weibull_3p                | ▶️[phitter:weibull_3p](https://phitter.io/distributions/continuous/weibull_3p)                               | 📊[weibull_3p.xlsx](https://github.com/phitterio/phitter-files/blob/main/continuous/weibull_3p.xlsx)                               | 🌐[gs:weibull_3p](https://docs.google.com/spreadsheets/d/1agwpFGpXm62srDxgPOoDQGN8nGd8zaoztXg84Bgedlo)                |

## Discrete Distributions

#### [1. PDF File Documentation Discrete Distributions](https://github.com/phitterio/phitter-kernel/blob/main/distributions_documentation/discrete/document_discrete_distributions/phitter_discrete_distributions.pdf)

#### 2. Resources Discrete Distributions

| Distribution      | Phitter Playground                                                                           | Excel File                                                                                                       | Google Sheets Files                                                                                           |
| :---------------- | :------------------------------------------------------------------------------------------- | :--------------------------------------------------------------------------------------------------------------- | :------------------------------------------------------------------------------------------------------------ |
| bernoulli         | ▶️[phitter:bernoulli](https://phitter.io/distributions/continuous/bernoulli)                 | 📊[bernoulli.xlsx](https://github.com/phitterio/phitter-files/blob/main/discrete/bernoulli.xlsx)                 | 🌐[gs:bernoulli](https://docs.google.com/spreadsheets/d/1sWJZYZWW8cVLFXYV-fb3Lq4y2YgWzgTGWHfhIJ0zM5c)         |
| binomial          | ▶️[phitter:binomial](https://phitter.io/distributions/continuous/binomial)                   | 📊[binomial.xlsx](https://github.com/phitterio/phitter-files/blob/main/discrete/binomial.xlsx)                   | 🌐[gs:binomial](https://docs.google.com/spreadsheets/d/1bPOiZVUhjLMmbFqVjWMqg1NzTvsZxVIw95fi5hIhkn0)          |
| geometric         | ▶️[phitter:geometric](https://phitter.io/distributions/continuous/geometric)                 | 📊[geometric.xlsx](https://github.com/phitterio/phitter-files/blob/main/discrete/geometric.xlsx)                 | 🌐[gs:geometric](https://docs.google.com/spreadsheets/d/1cEU6n8UxpJ_Had6WfFnAXZ2FcaLGYu8g5srQ_iEfjgg)         |
| hypergeometric    | ▶️[phitter:hypergeometric](https://phitter.io/distributions/continuous/hypergeometric)       | 📊[hypergeometric.xlsx](https://github.com/phitterio/phitter-files/blob/main/discrete/hypergeometric.xlsx)       | 🌐[gs:hypergeometric](https://docs.google.com/spreadsheets/d/10xUqKVoFzUiukuYt6VFwlaetMDTdGulHQPEWl1rJiMA)    |
| logarithmic       | ▶️[phitter:logarithmic](https://phitter.io/distributions/continuous/logarithmic)             | 📊[logarithmic.xlsx](https://github.com/phitterio/phitter-files/blob/main/discrete/logarithmic.xlsx)             | 🌐[gs:logarithmic](https://docs.google.com/spreadsheets/d/1N-YXrSfOYkPKwerL5I1QmfxuwbZzVUzgBWTcKzcmLhE)       |
| negative_binomial | ▶️[phitter:negative_binomial](https://phitter.io/distributions/continuous/negative_binomial) | 📊[negative_binomial.xlsx](https://github.com/phitterio/phitter-files/blob/main/discrete/negative_binomial.xlsx) | 🌐[gs:negative_binomial](https://docs.google.com/spreadsheets/d/1xmCWBiswdW5s7SIhwT2nrdQxLFAb6hw73iy52_nvjQE) |
| poisson           | ▶️[phitter:poisson](https://phitter.io/distributions/continuous/poisson)                     | 📊[poisson.xlsx](https://github.com/phitterio/phitter-files/blob/main/discrete/poisson.xlsx)                     | 🌐[gs:poisson](https://docs.google.com/spreadsheets/d/1fwoe70JH5Ve6sETb7AwBdb4eep_h2DeGlpHIWcHeZA8)           |
| uniform           | ▶️[phitter:uniform](https://phitter.io/distributions/continuous/uniform)                     | 📊[uniform.xlsx](https://github.com/phitterio/phitter-files/blob/main/discrete/uniform.xlsx)                     | 🌐[gs:uniform](https://docs.google.com/spreadsheets/d/1Ahl2ugOKkUCVWzzc_aNHwlA5Af4sHpTwqSiFIyYPsfM)           |

## Benchmarks

### _Fit time continuous distributions_

| Sample Size / Workers |     1     |    2     |    6     |    10    |    20    |
| :-------------------: | :-------: | :------: | :------: | :------: | :------: |
|        **1K**         |  8.2981   |  7.1242  |  8.9667  |  9.9287  | 16.2246  |
|        **10K**        |  20.8711  | 14.2647  | 10.5612  | 11.6004  | 17.8562  |
|       **100K**        | 152.6296  | 97.2359  | 57.7310  | 51.6182  | 53.2313  |
|       **500K**        | 914.9291  | 640.8153 | 370.0323 | 267.4597 | 257.7534 |
|        **1M**         | 1580.8501 | 972.3985 | 573.5429 | 496.5569 | 425.7809 |

### _Estimation time parameters discrete distributions_

| Sample Size / Workers |    1    |    2    |    4    |
| :-------------------: | :-----: | :-----: | :-----: |
|        **1K**         | 0.1688  | 2.6402  | 2.8719  |
|        **10K**        | 0.4462  | 2.4452  | 3.0471  |
|       **100K**        | 4.5598  | 6.3246  | 7.5869  |
|       **500K**        | 19.0172 | 21.8047 | 19.8420 |
|        **1M**         | 39.8065 | 29.8360 | 30.2334 |

### _Estimation time parameters continuous distributions_

| Distribution / Sample Size |   1K   |  10K   |  100K   |  500K   |    1M    |    10M    |
| :------------------------: | :----: | :----: | :-----: | :-----: | :------: | :-------: |
|           alpha            | 0.3345 | 0.4625 | 2.5933  | 18.3856 | 39.6533  | 362.2951  |
|          arcsine           | 0.0000 | 0.0000 | 0.0000  | 0.0000  |  0.0000  |  0.0000   |
|           argus            | 0.0559 | 0.2050 | 2.2472  | 13.3928 | 41.5198  | 362.2472  |
|            beta            | 0.1880 | 0.1790 | 0.1940  | 0.2110  |  0.1800  |  0.3134   |
|         beta_prime         | 0.1766 | 0.7506 | 7.6039  | 40.4264 | 85.0677  | 812.1323  |
|       beta_prime_4p        | 0.0720 | 0.3630 | 3.9478  | 20.2703 | 40.2709  | 413.5239  |
|          bradford          | 0.0110 | 0.0000 | 0.0000  | 0.0000  |  0.0000  |  0.0010   |
|            burr            | 0.0733 | 0.6931 | 5.5425  | 36.7684 | 79.8269  | 668.2016  |
|          burr_4p           | 0.1552 | 0.7981 | 8.4716  | 44.4549 | 87.7292  | 858.0035  |
|           cauchy           | 0.0090 | 0.0160 | 0.1581  | 1.1052  |  2.1090  |  21.5244  |
|         chi_square         | 0.0000 | 0.0000 | 0.0000  | 0.0000  |  0.0000  |  0.0000   |
|       chi_square_3p        | 0.0000 | 0.0000 | 0.0000  | 0.0000  |  0.0000  |  0.0000   |
|           dagum            | 0.3381 | 0.8278 | 9.6907  | 45.5855 | 98.6691  | 917.6713  |
|          dagum_4p          | 0.3646 | 1.3307 | 13.3437 | 70.9462 | 140.9371 | 1396.3368 |
|           erlang           | 0.0010 | 0.0000 | 0.0000  | 0.0000  |  0.0000  |  0.0000   |
|         erlang_3p          | 0.0000 | 0.0000 | 0.0000  | 0.0000  |  0.0000  |  0.0000   |
|       error_function       | 0.0000 | 0.0000 | 0.0000  | 0.0000  |  0.0000  |  0.0000   |
|        exponential         | 0.0000 | 0.0000 | 0.0000  | 0.0000  |  0.0000  |  0.0000   |
|       exponential_2p       | 0.0000 | 0.0000 | 0.0000  | 0.0000  |  0.0000  |  0.0000   |
|             f              | 0.0592 | 0.2948 | 2.6920  | 18.9458 | 29.9547  | 402.2248  |
|        fatigue_life        | 0.0352 | 0.1101 | 1.7085  | 9.0090  | 20.4702  | 186.9631  |
|       folded_normal        | 0.0020 | 0.0020 | 0.0020  | 0.0022  |  0.0033  |  0.0040   |
|          frechet           | 0.1313 | 0.4359 | 5.7031  | 39.4202 | 43.2469  | 671.3343  |
|            f_4p            | 0.3269 | 0.7517 | 0.6183  | 0.6037  |  0.5809  |  0.2073   |
|           gamma            | 0.0000 | 0.0000 | 0.0000  | 0.0000  |  0.0000  |  0.0000   |
|          gamma_3p          | 0.0000 | 0.0000 | 0.0000  | 0.0000  |  0.0000  |  0.0000   |
| generalized_extreme_value  | 0.0833 | 0.2054 | 2.0337  | 10.3301 | 22.1340  | 243.3120  |
|     generalized_gamma      | 0.0298 | 0.0178 | 0.0227  | 0.0236  |  0.0170  |  0.0241   |
|    generalized_gamma_4p    | 0.0371 | 0.0116 | 0.0732  | 0.0725  |  0.0707  |  0.0730   |
|    generalized_logistic    | 0.1040 | 0.1073 | 0.1037  | 0.0819  |  0.0989  |  0.0836   |
|     generalized_normal     | 0.0154 | 0.0736 | 0.7367  | 2.4831  |  5.9752  |  55.2417  |
|     generalized_pareto     | 0.3189 | 0.8978 | 8.9370  | 51.3813 | 101.6832 | 1015.2933 |
|           gibrat           | 0.0328 | 0.0432 | 0.4287  | 2.7159  |  5.5721  |  54.1702  |
|        gumbel_left         | 0.0000 | 0.0000 | 0.0000  | 0.0000  |  0.0010  |  0.0010   |
|        gumbel_right        | 0.0000 | 0.0000 | 0.0000  | 0.0000  |  0.0000  |  0.0000   |
|        half_normal         | 0.0010 | 0.0000 | 0.0000  | 0.0010  |  0.0000  |  0.0000   |
|     hyperbolic_secant      | 0.0000 | 0.0000 | 0.0000  | 0.0000  |  0.0000  |  0.0000   |
|       inverse_gamma        | 0.0308 | 0.0632 | 0.7233  | 5.0127  | 10.7885  |  99.1316  |
|      inverse_gamma_3p      | 0.0787 | 0.1472 | 1.6513  | 11.1161 | 23.4587  | 227.6125  |
|      inverse_gaussian      | 0.0000 | 0.0000 | 0.0000  | 0.0000  |  0.0000  |  0.0000   |
|    inverse_gaussian_3p     | 0.0000 | 0.0000 | 0.0000  | 0.0000  |  0.0000  |  0.0000   |
|         johnson_sb         | 0.2966 | 0.7466 | 4.0707  | 40.2028 | 56.2130  | 728.2447  |
|         johnson_su         | 0.0070 | 0.0010 | 0.0010  | 0.0143  |  0.0010  |  0.0010   |
|        kumaraswamy         | 0.0164 | 0.0120 | 0.0130  | 0.0123  |  0.0125  |  0.0150   |
|          laplace           | 0.0000 | 0.0000 | 0.0000  | 0.0000  |  0.0000  |  0.0000   |
|            levy            | 0.0100 | 0.0314 | 0.2296  | 1.1365  |  2.7211  |  26.4966  |
|          loggamma          | 0.0085 | 0.0050 | 0.0050  | 0.0070  |  0.0062  |  0.0080   |
|          logistic          | 0.0000 | 0.0000 | 0.0000  | 0.0000  |  0.0000  |  0.0000   |
|        loglogistic         | 0.0000 | 0.0000 | 0.0000  | 0.0000  |  0.0000  |  0.0000   |
|       loglogistic_3p       | 0.0000 | 0.0000 | 0.0000  | 0.0000  |  0.0000  |  0.0000   |
|         lognormal          | 0.0000 | 0.0000 | 0.0000  | 0.0000  |  0.0010  |  0.0000   |
|          maxwell           | 0.0000 | 0.0000 | 0.0000  | 0.0000  |  0.0000  |  0.0010   |
|           moyal            | 0.0000 | 0.0000 | 0.0000  | 0.0000  |  0.0000  |  0.0000   |
|          nakagami          | 0.0000 | 0.0030 | 0.0213  | 0.1215  |  0.2649  |  2.2457   |
|   non_central_chi_square   | 0.0000 | 0.0000 | 0.0000  | 0.0000  |  0.0000  |  0.0000   |
|       non_central_f        | 0.0190 | 0.0182 | 0.0210  | 0.0192  |  0.0190  |  0.0200   |
|   non_central_t_student    | 0.0874 | 0.0822 | 0.0862  | 0.1314  |  0.2516  |  0.1781   |
|           normal           | 0.0000 | 0.0000 | 0.0000  | 0.0000  |  0.0000  |  0.0000   |
|     pareto_first_kind      | 0.0010 | 0.0030 | 0.0390  | 0.2494  |  0.5226  |  5.5246   |
|     pareto_second_kind     | 0.0643 | 0.1522 | 1.1722  | 10.9871 | 23.6534  | 201.1626  |
|            pert            | 0.0052 | 0.0030 | 0.0030  | 0.0040  |  0.0040  |  0.0092   |
|       power_function       | 0.0075 | 0.0040 | 0.0040  | 0.0030  |  0.0040  |  0.0040   |
|          rayleigh          | 0.0000 | 0.0000 | 0.0000  | 0.0000  |  0.0000  |  0.0000   |
|         reciprocal         | 0.0000 | 0.0000 | 0.0000  | 0.0000  |  0.0000  |  0.0000   |
|            rice            | 0.0182 | 0.0030 | 0.0040  | 0.0060  |  0.0030  |  0.0050   |
|        semicircular        | 0.0000 | 0.0000 | 0.0000  | 0.0000  |  0.0000  |  0.0000   |
|        trapezoidal         | 0.0083 | 0.0072 | 0.0073  | 0.0060  |  0.0070  |  0.0060   |
|         triangular         | 0.0000 | 0.0000 | 0.0000  | 0.0000  |  0.0000  |  0.0000   |
|         t_student          | 0.0000 | 0.0000 | 0.0000  | 0.0000  |  0.0000  |  0.0000   |
|        t_student_3p        | 0.3892 | 1.1860 | 11.2759 | 71.1156 | 143.1939 | 1409.8578 |
|          uniform           | 0.0000 | 0.0000 | 0.0000  | 0.0000  |  0.0000  |  0.0000   |
|          weibull           | 0.0010 | 0.0000 | 0.0000  | 0.0000  |  0.0010  |  0.0010   |
|         weibull_3p         | 0.0061 | 0.0040 | 0.0030  | 0.0040  |  0.0050  |  0.0050   |

### _Estimation time parameters discrete distributions_

| Distribution / Sample Size |   1K   |  10K   |  100K  |  500K  |   1M   |  10M   |
| :------------------------: | :----: | :----: | :----: | :----: | :----: | :----: |
|         bernoulli          | 0.0000 | 0.0000 | 0.0000 | 0.0000 | 0.0000 | 0.0000 |
|          binomial          | 0.0000 | 0.0000 | 0.0000 | 0.0000 | 0.0000 | 0.0000 |
|         geometric          | 0.0000 | 0.0000 | 0.0000 | 0.0000 | 0.0000 | 0.0000 |
|       hypergeometric       | 0.0773 | 0.0061 | 0.0030 | 0.0020 | 0.0030 | 0.0051 |
|        logarithmic         | 0.0210 | 0.0035 | 0.0171 | 0.0050 | 0.0030 | 0.0756 |
|     negative_binomial      | 0.0293 | 0.0000 | 0.0000 | 0.0000 | 0.0000 | 0.0000 |
|          poisson           | 0.0000 | 0.0000 | 0.0000 | 0.0000 | 0.0000 | 0.0000 |
|          uniform           | 0.0000 | 0.0000 | 0.0000 | 0.0000 | 0.0000 | 0.0000 |

## Contribution

If you would like to contribute to the Phitter project, please create a pull request with your proposed changes or enhancements. All contributions are welcome!
