{"id":30126187,"url":"https://github.com/phitter-hub/phitter-kernel","last_synced_at":"2025-08-10T16:06:39.920Z","repository":{"id":229880928,"uuid":"652098947","full_name":"phitter-hub/phitter-kernel","owner":"phitter-hub","description":"Phitter is a python library for accurately fitting statistical distributions to datasets, offering intuitive usage, comprehensive visualization, and support for multiple distributions to enhance data analysis projects.","archived":false,"fork":false,"pushed_at":"2025-08-03T21:49:52.000Z","size":430330,"stargazers_count":30,"open_issues_count":0,"forks_count":2,"subscribers_count":1,"default_branch":"main","last_synced_at":"2025-08-03T23:27:00.234Z","etag":null,"topics":["operations-research","probability-distribution","probability-models","simulation"],"latest_commit_sha":null,"homepage":"https://phitter.io/","language":"Jupyter 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Notebook","funding_links":["https://github.com/sponsors/sebastianherreramonterrosa","https://buymeacoffee.com/sebastianjhm"],"categories":["Jupyter Notebook"],"sub_categories":[],"readme":"\u003cp align=\"center\"\u003e\n    \u003cpicture\u003e\n        \u003csource media=\"(prefers-color-scheme: dark)\" srcset=\"https://gist.githubusercontent.com/phitter-hub/66bc7f3674eac01ae646e30ba697a6d7/raw/e96dbba0eb26b20d35e608fefc3984bd87f0010b/DarkPhitterLogo.svg\" width=\"350\"\u003e\n        \u003csource media=\"(prefers-color-scheme: light)\" srcset=\"https://gist.githubusercontent.com/phitter-hub/170ce460d7e766545265772525edecf6/raw/71b4867c6e5683455cf1d68bea5bea7eda55ce7d/LightPhitterLogo.svg\" width=\"350\"\u003e\n        \u003cimg alt=\"phitter-dark-logo\" src=\"https://gist.githubusercontent.com/phitter-hub/170ce460d7e766545265772525edecf6/raw/71b4867c6e5683455cf1d68bea5bea7eda55ce7d/LightPhitterLogo.svg\" width=\"350\"\u003e\n    \u003c/picture\u003e\n\u003c/p\u003e\n\n\u003cp align=\"center\"\u003e\n    \u003ca href=\"https://pypi.org/project/phitter\" target=\"_blank\"\u003e\n        \u003cimg src=\"https://img.shields.io/pypi/dm/phitter.svg?color=blue\" alt=\"Downloads\"\u003e\n    \u003c/a\u003e\n    \u003ca href=\"https://pypi.org/project/phitter\" target=\"_blank\"\u003e\n        \u003cimg src=\"https://img.shields.io/badge/License-MIT-blue.svg\" alt=\"License\"\u003e\n    \u003c/a\u003e\n    \u003ca href=\"https://pypi.org/project/phitter\" target=\"_blank\"\u003e\n        \u003cimg src=\"https://img.shields.io/pypi/pyversions/phitter?color=blue\" alt=\"Supported Python versions\"\u003e\n    \u003c/a\u003e\n    \u003ca href=\"https://doi.org/10.21105/joss.07625\"\u003e\n        \u003cimg src=\"https://img.shields.io/badge/JOSS-10.21105%2Fjoss.07625-blue\" alt=\"DOI badge\"\u003e\n    \u003c/a\u003e\n    \u003ca href=\"https://github.com/phitter-hub/phitter-kernel/actions/workflows/unittest.yml\" target=\"_blank\"\u003e\n        \u003cimg src=\"https://github.com/phitter-hub/phitter-kernel/actions/workflows/unittest.yml/badge.svg\" alt=\"Tests\"\u003e\n    \u003c/a\u003e\n\u003c/p\u003e\n\n\n\u003cp align=\"center\"\u003e\n    ⭐⭐⭐ \u003cem\u003eIf you find this project useful, giving it a star on GitHub. It really helps!\u003c/em\u003e ⭐⭐⭐\n\u003c/p\u003e\n\n\u003cp\u003e\n    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.\n\u003c/p\u003e\n\n\u003cp\u003e\n    Additionally, Phitter enables advanced process simulations, allowing to model and visualize key performance metrics such as minimum observation times. It facilitates the simulation of queuing systems with configurable parameters, including the number of servers, system capacity, maximum population size, and service discipline. Supported queuing models encompass FIFO, LIFO and PBS, ensuring adaptability to various operational and research applications.\n\u003c/p\u003e\n\n\u003cp\u003e\n    This repository contains the implementation of the python library and the kernel of \u003ca href=\"https://phitter.io\"\u003ePhitter Web\u003c/a\u003e\n\u003c/p\u003e\n\n\u003cp align=\"center\"\u003e\n    \u003cimg alt=\"phitter_histogram\" src=\"https://github.com/phitter-hub/phitter-kernel/blob/main/multimedia/plot_histogram_distributions.png?raw=true\" width=\"500\" /\u003e\n\u003c/p\u003e\n\n## 📄 Documentation\n\nFind the complete Phitter documentation [here](https://docs-phitter-kernel.netlify.app/).\n\n## Installation\n\n### Requirements\n\n```console\npython: \u003e=3.9\n```\n\n### PyPI\n\n```console\npip install phitter\n```\n\n## Usage\n\n### **_1. Fit Notebook's Tutorials_**\n\n|             Tutorial             |                                                                                                                      Notebooks                                                                                                                      |\n| :------------------------------: | :-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------: |\n|        **Fit Continuous**        |    \u003ca target=\"_blank\" href=\"https://colab.research.google.com/github/phitter-hub/phitter-kernel/blob/main/examples/fit/fit_continuous_ncdb.ipynb\"\u003e\u003cimg src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/\u003e\u003c/a\u003e    |\n|         **Fit Discrete**         | \u003ca target=\"_blank\" href=\"https://colab.research.google.com/github/phitter-hub/phitter-kernel/blob/main/examples/fit/fit_discrete_galton_board.ipynb\"\u003e\u003cimg src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/\u003e\u003c/a\u003e |\n| **Fit Accelerate [Sample\u003e100K]** |      \u003ca target=\"_blank\" href=\"https://colab.research.google.com/github/phitter-hub/phitter-kernel/blob/main/examples/fit/fit_accelerate.ipynb\"\u003e\u003cimg src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/\u003e\u003c/a\u003e       |\n|  **Fit Specific Distribution**   | \u003ca target=\"_blank\" href=\"https://colab.research.google.com/github/phitter-hub/phitter-kernel/blob/main/examples/fit/fit_specific_distribution.ipynb\"\u003e\u003cimg src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/\u003e\u003c/a\u003e |\n|     **Working Distribution**     |   \u003ca target=\"_blank\" href=\"https://colab.research.google.com/github/phitter-hub/phitter-kernel/blob/main/examples/fit/working_distribution.ipynb\"\u003e\u003cimg src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/\u003e\u003c/a\u003e    |\n\n### **_2. Simulation Notebook's Tutorials_**\n\n|                     Tutorial                      |                                                                                                                           Notebooks                                                                                                                           |\n| :-----------------------------------------------: | :-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------: |\n|              **Process Simulation**               |      \u003ca target=\"_blank\" href=\"https://colab.research.google.com/github/phitter-hub/phitter-kernel/blob/main/examples/simulation/process_simulation.ipynb\"\u003e\u003cimg src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/\u003e\u003c/a\u003e      |\n|               **Own Distribution**                | \u003ca target=\"_blank\" href=\"https://colab.research.google.com/github/phitter-hub/phitter-kernel/blob/main/examples/simulation/own_distribution_explanation.ipynb\"\u003e\u003cimg src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/\u003e\u003c/a\u003e |\n|  **Queue Simulation First-In-First-Out (FIFO)**   |    \u003ca target=\"_blank\" href=\"https://colab.research.google.com/github/phitter-hub/phitter-kernel/blob/main/examples/simulation/queue_simulation_fifo.ipynb\"\u003e\u003cimg src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/\u003e\u003c/a\u003e     |\n|   **Queue Simulation Last-In-First-Out (LIFO)**   |    \u003ca target=\"_blank\" href=\"https://colab.research.google.com/github/phitter-hub/phitter-kernel/blob/main/examples/simulation/queue_simulation_lifo.ipynb\"\u003e\u003cimg src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/\u003e\u003c/a\u003e     |\n| **Queue Simulation Priority-Based Service (PBS)** |     \u003ca target=\"_blank\" href=\"https://colab.research.google.com/github/phitter-hub/phitter-kernel/blob/main/examples/simulation/queue_simulation_pbs.ipynb\"\u003e\u003cimg src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/\u003e\u003c/a\u003e     |\n\n## Documentation\n\n\u003cdetails\u003e\n\n\u003csummary style=\"font-size: 16px; font-weight: bold;\"\u003eDocumentation Fit Module\u003c/summary\u003e\n\n### General Fit\n\n```python\nimport phitter\n\n## Define your dataset\ndata: list[int | float] = [...]\n\n## Make a continuous fit using Phitter\nphi = phitter.Phitter(data=data)\nphi.fit()\n```\n\n### Full continuous implementation\n\n```python\nimport phitter\n\n## Define your dataset\ndata: list[int | float] = [...]\n\n## Make a continuous fit using Phitter\nphi = phitter.Phitter(\n    data=data,\n    fit_type=\"continuous\",\n    num_bins=15,\n    confidence_level=0.95,\n    minimum_sse=1e-2,\n    distributions_to_fit=[\"beta\", \"normal\", \"fatigue_life\", \"triangular\"],\n)\nphi.fit(n_workers=6)\n```\n\n### Full discrete implementation\n\n```python\nimport phitter\n\n## Define your dataset\ndata: list[int | float] = [...]\n\n## Make a discrete fit using Phitter\nphi = phitter.Phitter(\n    data=data,\n    fit_type=\"discrete\",\n    confidence_level=0.95,\n    minimum_sse=1e-2,\n    distributions_to_fit=[\"binomial\", \"geometric\"],\n)\nphi.fit(n_workers=2)\n```\n\n### Phitter: properties and methods\n\n```python\nimport phitter\n\n## Define your dataset\ndata: list[int | float] = [...]\n\n## Make a fit using Phitter\nphi = phitter.Phitter(data=data)\nphi.fit(n_workers=2)\n\n## Global methods and properties\nphi.summarize(k: int) -\u003e pandas.DataFrame\nphi.summarize_info(k: int) -\u003e pandas.DataFrame\nphi.best_distribution -\u003e dict\nphi.sorted_distributions_sse -\u003e dict\nphi.not_rejected_distributions -\u003e dict\nphi.df_sorted_distributions_sse -\u003e pandas.DataFrame\nphi.df_not_rejected_distributions -\u003e pandas.DataFrame\n\n## Specific distribution methods and properties\nphi.get_parameters(id_distribution: str) -\u003e dict\nphi.get_test_chi_square(id_distribution: str) -\u003e dict\nphi.get_test_kolmmogorov_smirnov(id_distribution: str) -\u003e dict\nphi.get_test_anderson_darling(id_distribution: str) -\u003e dict\nphi.get_sse(id_distribution: str) -\u003e float\nphi.get_n_test_passed(id_distribution: str) -\u003e int\nphi.get_n_test_null(id_distribution: str) -\u003e int\n```\n\n### Histogram Plot\n\n```python\nimport phitter\ndata: list[int | float] = [...]\nphi = phitter.Phitter(data=data)\nphi.fit()\n\nphi.plot_histogram()\n```\n\n\u003cimg alt=\"phitter_histogram\" src=\"https://github.com/phitter-hub/phitter-kernel/blob/main/multimedia/plot_histogram.png?raw=true\" width=\"500\" /\u003e\n\n### Histogram PDF Dsitributions Plot\n\n```python\nimport phitter\ndata: list[int | float] = [...]\nphi = phitter.Phitter(data=data)\nphi.fit()\n\nphi.plot_histogram_distributions()\n```\n\n\u003cimg alt=\"phitter_histogram\" src=\"https://github.com/phitter-hub/phitter-kernel/blob/main/multimedia/plot_histogram_distributions.png?raw=true\" width=\"500\" /\u003e\n\n### Histogram PDF Dsitribution Plot\n\n```python\nimport phitter\ndata: list[int | float] = [...]\nphi = phitter.Phitter(data=data)\nphi.fit()\n\nphi.plot_distribution(\"beta\")\n```\n\n\u003cimg alt=\"phitter_histogram\" src=\"https://github.com/phitter-hub/phitter-kernel/blob/main/multimedia/plot_one_distribution.png?raw=true\" width=\"500\" /\u003e\n\n### ECDF Plot\n\n```python\nimport phitter\ndata: list[int | float] = [...]\nphi = phitter.Phitter(data=data)\nphi.fit()\n\nphi.plot_ecdf()\n```\n\n\u003cimg alt=\"phitter_histogram\" src=\"https://github.com/phitter-hub/phitter-kernel/blob/main/multimedia/plot_ecdf.png?raw=true\" width=\"500\" /\u003e\n\n### ECDF Distribution Plot\n\n```python\nimport phitter\ndata: list[int | float] = [...]\nphi = phitter.Phitter(data=data)\nphi.fit()\n\nphi.plot_ecdf_distribution(\"beta\")\n```\n\n\u003cimg alt=\"phitter_histogram\" src=\"https://github.com/phitter-hub/phitter-kernel/blob/main/multimedia/plot_ecdf_distribution.png?raw=true\" width=\"500\" /\u003e\n\n### QQ Plot\n\n```python\nimport phitter\ndata: list[int | float] = [...]\nphi = phitter.Phitter(data=data)\nphi.fit()\n\nphi.qq_plot(\"beta\")\n```\n\n\u003cimg alt=\"phitter_histogram\" src=\"https://github.com/phitter-hub/phitter-kernel/blob/main/multimedia/plot_qq.png?raw=true\" width=\"500\" /\u003e\n\n### QQ - Regression Plot\n\n```python\nimport phitter\ndata: list[int | float] = [...]\nphi = phitter.Phitter(data=data)\nphi.fit()\n\nphi.qq_plot_regression(\"beta\")\n```\n\n\u003cimg alt=\"phitter_histogram\" src=\"https://github.com/phitter-hub/phitter-kernel/blob/main/multimedia/plot_qq_regression.png?raw=true\" width=\"500\" /\u003e\n\n### Working with distributions: Methods and properties\n\n```python\nimport phitter\n\ndistribution = phitter.continuous.Beta({\"alpha\": 5, \"beta\": 3, \"A\": 200, \"B\": 1000})\n\n## CDF, PDF, PPF, PMF receive float or numpy.ndarray. For discrete distributions PMF instead of PDF. Parameters notation are in description of ditribution\ndistribution.cdf(752) # -\u003e 0.6242831129533498\ndistribution.pdf(388) # -\u003e 0.0002342575686629883\ndistribution.ppf(0.623) # -\u003e 751.5512889417921\ndistribution.sample(2) # -\u003e [550.800114   514.85410326]\n\n## STATS\ndistribution.mean # -\u003e 700.0\ndistribution.variance # -\u003e 16666.666666666668\ndistribution.standard_deviation # -\u003e 129.09944487358058\ndistribution.skewness # -\u003e -0.3098386676965934\ndistribution.kurtosis # -\u003e 2.5854545454545454\ndistribution.median # -\u003e 708.707130841534\ndistribution.mode # -\u003e 733.3333333333333\n```\n\n## Continuous Distributions\n\n#### [1. PDF File Documentation Continuous Distributions](https://github.com/phitter-hub/phitter-kernel/blob/main/distributions_documentation/continuous/document_continuous_distributions/phitter_continuous_distributions.pdf)\n\n#### 2. Resources Continuous Distributions\n\n| Distribution              | Phitter Playground                                                                                     | Excel File                                                                                                                      | Google Sheets Files                                                                                                |\n| :------------------------ | :----------------------------------------------------------------------------------------------------- | :------------------------------------------------------------------------------------------------------------------------------ | :----------------------------------------------------------------------------------------------------------------- |\n| alpha                     | ▶️[phitter:alpha](https://phitter.io/distributions/continuous/alpha)                                   | 📊[alpha.xlsx](https://github.com/phitter-hub/phitter-files/blob/main/continuous/alpha.xlsx)                                   | 🌐[gs:alpha](https://docs.google.com/spreadsheets/d/1yRovxx1YbqgEul65DjjXetysc_4qgX2a_2NQQA1AxCA)                  |\n| arcsine                   | ▶️[phitter:arcsine](https://phitter.io/distributions/continuous/arcsine)                               | 📊[arcsine.xlsx](https://github.com/phitter-hub/phitter-files/blob/main/continuous/arcsine.xlsx)                               | 🌐[gs:arcsine](https://docs.google.com/spreadsheets/d/1q8SKX4gmSbpGzimRvjopzaZ4KrEV5NY1EPmf1G1T7NQ)                |\n| argus                     | ▶️[phitter:argus](https://phitter.io/distributions/continuous/argus)                                   | 📊[argus.xlsx](https://github.com/phitter-hub/phitter-files/blob/main/continuous/argus.xlsx)                                   | 🌐[gs:argus](https://docs.google.com/spreadsheets/d/1u2x7IFUSB7rEyhs7s6-C2btT1Bk5aCr4WiUYEML-8xs)                  |\n| beta                      | ▶️[phitter:beta](https://phitter.io/distributions/continuous/beta)                                     | 📊[beta.xlsx](https://github.com/phitter-hub/phitter-files/blob/main/continuous/beta.xlsx)                                     | 🌐[gs:beta](https://docs.google.com/spreadsheets/d/1P7NDy-9toV3dv64gabnr8l2NjB1xt_Ani5IVMTx3gyU)                   |\n| beta_prime                | ▶️[phitter:beta_prime](https://phitter.io/distributions/continuous/beta_prime)                         | 📊[beta_prime.xlsx](https://github.com/phitter-hub/phitter-files/blob/main/continuous/beta_prime.xlsx)                         | 🌐[gs:beta_prime](https://docs.google.com/spreadsheets/d/1-8cKeS9D6YixQE_uLig7UarXcoQoE-341yHDj8sfXA8)             |\n| beta_prime_4p             | ▶️[phitter:beta_prime_4p](https://phitter.io/distributions/continuous/beta_prime_4p)                   | 📊[beta_prime_4p.xlsx](https://github.com/phitter-hub/phitter-files/blob/main/continuous/beta_prime_4p.xlsx)                   | 🌐[gs:beta_prime_4p](https://docs.google.com/spreadsheets/d/1vlaZrj_jX9oNGwjW0o4Z1AUTuUTGE8Z-Akis_wb7Jq4)          |\n| bradford                  | ▶️[phitter:bradford](https://phitter.io/distributions/continuous/bradford)                             | 📊[bradford.xlsx](https://github.com/phitter-hub/phitter-files/blob/main/continuous/bradford.xlsx)                             | 🌐[gs:bradford](https://docs.google.com/spreadsheets/d/1kI8b05IXur3I9SUJdrbYIdv7zMdzVxVGPWx6sK6YmuU)               |\n| burr                      | ▶️[phitter:burr](https://phitter.io/distributions/continuous/burr)                                     | 📊[burr.xlsx](https://github.com/phitter-hub/phitter-files/blob/main/continuous/burr.xlsx)                                     | 🌐[gs:burr](https://docs.google.com/spreadsheets/d/1vhY3l3VAgBj9BQT1yE3meRTmEZP3HXjjm30nxDKCwCI)                   |\n| burr_4p                   | ▶️[phitter:burr_4p](https://phitter.io/distributions/continuous/burr_4p)                               | 📊[burr_4p.xlsx](https://github.com/phitter-hub/phitter-files/blob/main/continuous/burr_4p.xlsx)                               | 🌐[gs:burr_4p](https://docs.google.com/spreadsheets/d/1tEk3O2yvANj_PlLqACuwvRSqYYGQVRFH1SPMdLGYnz4)                |\n| cauchy                    | ▶️[phitter:cauchy](https://phitter.io/distributions/continuous/cauchy)                                 | 📊[cauchy.xlsx](https://github.com/phitter-hub/phitter-files/blob/main/continuous/cauchy.xlsx)                                 | 🌐[gs:cauchy](https://docs.google.com/spreadsheets/d/1xoJJvuSvfg-umC7Ogio9fde1l4TiWuAlR2IxucYK0y8)                 |\n| chi_square                | ▶️[phitter:chi_square](https://phitter.io/distributions/continuous/chi_square)                         | 📊[chi_square.xlsx](https://github.com/phitter-hub/phitter-files/blob/main/continuous/chi_square.xlsx)                         | 🌐[gs:chi_square](https://docs.google.com/spreadsheets/d/1VatJuUON_2qghjPEYMdcjGE7TYbYqduzgdYe5YNyVf4)             |\n| chi_square_3p             | ▶️[phitter:chi_square_3p](https://phitter.io/distributions/continuous/chi_square_3p)                   | 📊[chi_square_3p.xlsx](https://github.com/phitter-hub/phitter-files/blob/main/continuous/chi_square_3p.xlsx)                   | 🌐[gs:chi_square_3p](https://docs.google.com/spreadsheets/d/15tf3ZKbEgR3JWQRbMT2OaNij3INTGGUuNsR01NCDFJw)          |\n| dagum                     | ▶️[phitter:dagum](https://phitter.io/distributions/continuous/dagum)                                   | 📊[dagum.xlsx](https://github.com/phitter-hub/phitter-files/blob/main/continuous/dagum.xlsx)                                   | 🌐[gs:dagum](https://docs.google.com/spreadsheets/d/1qct7LByxY_z2-Rl-pWFG1LQsUxW8VQaCgLizn93YPxk)                  |\n| dagum_4p                  | ▶️[phitter:dagum_4p](https://phitter.io/distributions/continuous/dagum_4p)                             | 📊[dagum_4p.xlsx](https://github.com/phitter-hub/phitter-files/blob/main/continuous/dagum_4p.xlsx)                             | 🌐[gs:dagum_4p](https://docs.google.com/spreadsheets/d/1ZkKqvVdy7CvhvXwK830F6GWJrdNxoXBxJYeFD6XC2DM)               |\n| erlang                    | ▶️[phitter:erlang](https://phitter.io/distributions/continuous/erlang)                                 | 📊[erlang.xlsx](https://github.com/phitter-hub/phitter-files/blob/main/continuous/erlang.xlsx)                                 | 🌐[gs:erlang](https://docs.google.com/spreadsheets/d/1uG3Otntnm3cvMSkhkEiBVKuFn1pCLSWmiCxfN01D824)                 |\n| erlang_3p                 | ▶️[phitter:erlang_3p](https://phitter.io/distributions/continuous/erlang_3p)                           | 📊[erlang_3p.xlsx](https://github.com/phitter-hub/phitter-files/blob/main/continuous/erlang_3p.xlsx)                           | 🌐[gs:erlang_3p](https://docs.google.com/spreadsheets/d/1EvFPyOAL-TPQyNf7sAXfqgHqap8sGynH0XxrLRVP12M)              |\n| error_function            | ▶️[phitter:error_function](https://phitter.io/distributions/continuous/error_function)                 | 📊[error_function.xlsx](https://github.com/phitter-hub/phitter-files/blob/main/continuous/error_function.xlsx)                 | 🌐[gs:error_function](https://docs.google.com/spreadsheets/d/1QT1vSgTWVgDmNz4FrH3fhwRGpgvPohgqZSCADHfBXkM)         |\n| exponential               | ▶️[phitter:exponential](https://phitter.io/distributions/continuous/exponential)                       | 📊[exponential.xlsx](https://github.com/phitter-hub/phitter-files/blob/main/continuous/exponential.xlsx)                       | 🌐[gs:exponential](https://docs.google.com/spreadsheets/d/1c8aCgHTq3fEyIkVM1Ph3fzebxQMuourz1UkWbH4h3HA)            |\n| exponential_2p            | ▶️[phitter:exponential_2p](https://phitter.io/distributions/continuous/exponential_2p)                 | 📊[exponential_2p.xlsx](https://github.com/phitter-hub/phitter-files/blob/main/continuous/exponential_2p.xlsx)                 | 🌐[gs:exponential_2p](https://docs.google.com/spreadsheets/d/1XtrdS8iSCM1l33rbaXSz1uWZ3vnQsYPK-07NYE-ZYBs)         |\n| f                         | ▶️[phitter:f](https://phitter.io/distributions/continuous/f)                                           | 📊[f.xlsx](https://github.com/phitter-hub/phitter-files/blob/main/continuous/f.xlsx)                                           | 🌐[gs:f](https://docs.google.com/spreadsheets/d/137gYI8B6MDnqFoQ4bY1crdpFSKtPzRgaJS564SY_CUY)                      |\n| f_4p                      | ▶️[phitter:f_4p](https://phitter.io/distributions/continuous/f_4p)                                     | 📊[f_4p.xlsx](https://github.com/phitter-hub/phitter-files/blob/main/continuous/f_4p.xlsx)                                     | 🌐[gs:f_4p](https://docs.google.com/spreadsheets/d/11MgyMqzOyGNtFLdGviRTeNhAQMYBCJ8QRMHGxoPCzwM)                   |\n| fatigue_life              | ▶️[phitter:fatigue_life](https://phitter.io/distributions/continuous/fatigue_life)                     | 📊[fatigue_life.xlsx](https://github.com/phitter-hub/phitter-files/blob/main/continuous/fatigue_life.xlsx)                     | 🌐[gs:fatigue_life](https://docs.google.com/spreadsheets/d/1j-U_YMX89VHe2jVq3pazpzqYeA1j1zopW22C9yJcPS0)           |\n| folded_normal             | ▶️[phitter:folded_normal](https://phitter.io/distributions/continuous/folded_normal)                   | 📊[folded_normal.xlsx](https://github.com/phitter-hub/phitter-files/blob/main/continuous/folded_normal.xlsx)                   | 🌐[gs:folded_normal](https://docs.google.com/spreadsheets/d/17NlSnru_46J8pSjxMPLDlzxoG2fPKWjeFvTh0ydfX4k)          |\n| frechet                   | ▶️[phitter:frechet](https://phitter.io/distributions/continuous/frechet)                               | 📊[frechet.xlsx](https://github.com/phitter-hub/phitter-files/blob/main/continuous/frechet.xlsx)                               | 🌐[gs:frechet](https://docs.google.com/spreadsheets/d/1PNGvHImwOFIragM_hHrQJcTN7OcqCKFoHKXlPq76fnI)                |\n| gamma                     | ▶️[phitter:gamma](https://phitter.io/distributions/continuous/gamma)                                   | 📊[gamma.xlsx](https://github.com/phitter-hub/phitter-files/blob/main/continuous/gamma.xlsx)                                   | 🌐[gs:gamma](https://docs.google.com/spreadsheets/d/1HgD3a1zOml7Hy9PMVvFwQwrbmbs8iPbH-zQMowH0LVE)                  |\n| gamma_3p                  | ▶️[phitter:gamma_3p](https://phitter.io/distributions/continuous/gamma_3p)                             | 📊[gamma_3p.xlsx](https://github.com/phitter-hub/phitter-files/blob/main/continuous/gamma_3p.xlsx)                             | 🌐[gs:gamma_3p](https://docs.google.com/spreadsheets/d/1NkyFZFOMzk2V9qkFEI_zhGUGWiGV-K9vU-RLaFB7ip8)               |\n| generalized_extreme_value | ▶️[phitter:gen_extreme_value](https://phitter.io/distributions/continuous/generalized_extreme_value)   | 📊[gen_extreme_value.xlsx](https://github.com/phitter-hub/phitter-files/blob/main/continuous/generalized_extreme_value.xlsx)   | 🌐[gs:gen_extreme_value](https://docs.google.com/spreadsheets/d/19qHvnTJGVVZ7zhi-yhauCOGhu0iAdkYJ5FFgwv1q5OI)      |\n| generalized_gamma         | ▶️[phitter:gen_gamma](https://phitter.io/distributions/continuous/generalized_gamma)                   | 📊[gen_gamma.xlsx](https://github.com/phitter-hub/phitter-files/blob/main/continuous/generalized_gamma.xlsx)                   | 🌐[gs:gen_gamma](https://docs.google.com/spreadsheets/d/1xx8b_VSG4jznZzaKq2yKumw5VcNX5Wj86YqLO7n4S5A)              |\n| generalized_gamma_4p      | ▶️[phitter:gen_gamma_4p](https://phitter.io/distributions/continuous/generalized_gamma_4p)             | 📊[gen_gamma_4p.xlsx](https://github.com/phitter-hub/phitter-files/blob/main/continuous/generalized_gamma_4p.xlsx)             | 🌐[gs:gen_gamma_4p](https://docs.google.com/spreadsheets/d/1TN72MSkZ2bRyoNy29h4VIxFudXAroSi1PnmFijPvO0M)           |\n| generalized_logistic      | ▶️[phitter:gen_logistic](https://phitter.io/distributions/continuous/generalized_logistic)             | 📊[gen_logistic.xlsx](https://github.com/phitter-hub/phitter-files/blob/main/continuous/generalized_logistic.xlsx)             | 🌐[gs:gen_logistic](https://docs.google.com/spreadsheets/d/1vwppGjHbwEA3xd3OtV51sPZhpOWyzmPIOV_Tued-I1Y)           |\n| generalized_normal        | ▶️[phitter:gen_normal](https://phitter.io/distributions/continuous/generalized_normal)                 | 📊[gen_normal.xlsx](https://github.com/phitter-hub/phitter-files/blob/main/continuous/generalized_normal.xlsx)                 | 🌐[gs:gen_normal](https://docs.google.com/spreadsheets/d/1_77JSp0mhHxqvQugVRRWIoQOTa91WdyNqNmOfDNuSfA)             |\n| generalized_pareto        | ▶️[phitter:gen_pareto](https://phitter.io/distributions/continuous/generalized_pareto)                 | 📊[gen_pareto.xlsx](https://github.com/phitter-hub/phitter-files/blob/main/continuous/generalized_pareto.xlsx)                 | 🌐[gs:gen_pareto](https://docs.google.com/spreadsheets/d/1E28WYhX4Ba9Nj-JNxqAm-Gh7o1EOOIOwXIdCFl1PXI0)             |\n| gibrat                    | ▶️[phitter:gibrat](https://phitter.io/distributions/continuous/gibrat)                                 | 📊[gibrat.xlsx](https://github.com/phitter-hub/phitter-files/blob/main/continuous/gibrat.xlsx)                                 | 🌐[gs:gibrat](https://docs.google.com/spreadsheets/d/1pM7skBPnH8V3GCJo0iSst46Oc2OzqWdX2qATYBqc_GQ)                 |\n| gumbel_left               | ▶️[phitter:gumbel_left](https://phitter.io/distributions/continuous/gumbel_left)                       | 📊[gumbel_left.xlsx](https://github.com/phitter-hub/phitter-files/blob/main/continuous/gumbel_left.xlsx)                       | 🌐[gs:gumbel_left](https://docs.google.com/spreadsheets/d/1WoW97haebsHk1sB8smC4Zq8KqW8leJY0bPK757B2IdI)            |\n| gumbel_right              | ▶️[phitter:gumbel_right](https://phitter.io/distributions/continuous/gumbel_right)                     | 📊[gumbel_right.xlsx](https://github.com/phitter-hub/phitter-files/blob/main/continuous/gumbel_right.xlsx)                     | 🌐[gs:gumbel_right](https://docs.google.com/spreadsheets/d/1CpzfSwAdptFrI8DhV3tWRsEFd9cr6h3Jaj7t3gigims)           |\n| half_normal               | ▶️[phitter:half_normal](https://phitter.io/distributions/continuous/half_normal)                       | 📊[half_normal.xlsx](https://github.com/phitter-hub/phitter-files/blob/main/continuous/half_normal.xlsx)                       | 🌐[gs:half_normal](https://docs.google.com/spreadsheets/d/1HQpNSNIhZPzMQvWWKyShnYNH74d1Bhs_d6k9La52V9M)            |\n| hyperbolic_secant         | ▶️[phitter:hyperbolic_secant](https://phitter.io/distributions/continuous/hyperbolic_secant)           | 📊[hyperbolic_secant.xlsx](https://github.com/phitter-hub/phitter-files/blob/main/continuous/hyperbolic_secant.xlsx)           | 🌐[gs:hyperbolic_secant](https://docs.google.com/spreadsheets/d/1lTcLlwX0fmgUjhT4ljvKL_dqSReK_lEthsZNBtDxAF8)      |\n| inverse_gamma             | ▶️[phitter:inverse_gamma](https://phitter.io/distributions/continuous/inverse_gamma)                   | 📊[inverse_gamma.xlsx](https://github.com/phitter-hub/phitter-files/blob/main/continuous/inverse_gamma.xlsx)                   | 🌐[gs:inverse_gamma](https://docs.google.com/spreadsheets/d/1uOgfUvhBHKAXhbYATUwdHRQnBMIMnu6rWecqKx6MoIA)          |\n| inverse_gamma_3p          | ▶️[phitter:inverse_gamma_3p](https://phitter.io/distributions/continuous/inverse_gamma_3p)             | 📊[inverse_gamma_3p.xlsx](https://github.com/phitter-hub/phitter-files/blob/main/continuous/inverse_gamma_3p.xlsx)             | 🌐[gs:inverse_gamma_3p](https://docs.google.com/spreadsheets/d/16LCC6j_j1Cm7stc7LEd-C0ObUcZ-agL51ALGYxoZtrI)       |\n| inverse_gaussian          | ▶️[phitter:inverse_gaussian](https://phitter.io/distributions/continuous/inverse_gaussian)             | 📊[inverse_gaussian.xlsx](https://github.com/phitter-hub/phitter-files/blob/main/continuous/inverse_gaussian.xlsx)             | 🌐[gs:inverse_gaussian](https://docs.google.com/spreadsheets/d/10LaEnmnRxNESViLTlw6FDyt1YSWNbMlBXaWc9t4q5qA)       |\n| inverse_gaussian_3p       | ▶️[phitter:inverse_gaussian_3p](https://phitter.io/distributions/continuous/inverse_gaussian_3p)       | 📊[inverse_gaussian_3p.xlsx](https://github.com/phitter-hub/phitter-files/blob/main/continuous/inverse_gaussian_3p.xlsx)       | 🌐[gs:inverse_gaussian_3p](https://docs.google.com/spreadsheets/d/1wkcSlXnUdMe4by2N9nPA_Cdsz3D0kHL7MVchsjl_CTQ)    |\n| johnson_sb                | ▶️[phitter:johnson_sb](https://phitter.io/distributions/continuous/johnson_sb)                         | 📊[johnson_sb.xlsx](https://github.com/phitter-hub/phitter-files/blob/main/continuous/johnson_sb.xlsx)                         | 🌐[gs:johnson_sb](https://docs.google.com/spreadsheets/d/1H3bpJd729k0VK3LtvgxvKJiduIdP04UkHhgJoq4ayHQ)             |\n| johnson_su                | ▶️[phitter:johnson_su](https://phitter.io/distributions/continuous/johnson_su)                         | 📊[johnson_su.xlsx](https://github.com/phitter-hub/phitter-files/blob/main/continuous/johnson_su.xlsx)                         | 🌐[gs:johnson_su](https://docs.google.com/spreadsheets/d/15kw_NZr3RFjN9orvF844ITWXroWRsCFkY7Uvq0NZ4K8)             |\n| kumaraswamy               | ▶️[phitter:kumaraswamy](https://phitter.io/distributions/continuous/kumaraswamy)                       | 📊[kumaraswamy.xlsx](https://github.com/phitter-hub/phitter-files/blob/main/continuous/kumaraswamy.xlsx)                       | 🌐[gs:kumaraswamy](https://docs.google.com/spreadsheets/d/10YJUDlAEygfOn07YxHBJxDqiXxygv8jKpJ8WvCZhe84)            |\n| laplace                   | ▶️[phitter:laplace](https://phitter.io/distributions/continuous/laplace)                               | 📊[laplace.xlsx](https://github.com/phitter-hub/phitter-files/blob/main/continuous/laplace.xlsx)                               | 🌐[gs:laplace](https://docs.google.com/spreadsheets/d/110gPFTHOnQqecbXrjq3Wqv52I5Cw93UjL7eoSVC1DIs)                |\n| levy                      | ▶️[phitter:levy](https://phitter.io/distributions/continuous/levy)                                     | 📊[levy.xlsx](https://github.com/phitter-hub/phitter-files/blob/main/continuous/levy.xlsx)                                     | 🌐[gs:levy](https://docs.google.com/spreadsheets/d/1OIA4C6iqhwK0Y17wb_O5ce9YXy4JIBf1yq3TqcmDp3U)                   |\n| loggamma                  | ▶️[phitter:loggamma](https://phitter.io/distributions/continuous/loggamma)                             | 📊[loggamma.xlsx](https://github.com/phitter-hub/phitter-files/blob/main/continuous/loggamma.xlsx)                             | 🌐[gs:loggamma](https://docs.google.com/spreadsheets/d/1SXCmxXs7hkajo_W_qL-e0MJQEaUJqTpUno1nYGXxmxI)               |\n| logistic                  | ▶️[phitter:logistic](https://phitter.io/distributions/continuous/logistic)                             | 📊[logistic.xlsx](https://github.com/phitter-hub/phitter-files/blob/main/continuous/logistic.xlsx)                             | 🌐[gs:logistic](https://docs.google.com/spreadsheets/d/1WokfLcAM2f2TE9xcZwwuy3qjl4itw-y0cwAb7fyKxb0)               |\n| loglogistic               | ▶️[phitter:loglogistic](https://phitter.io/distributions/continuous/loglogistic)                       | 📊[loglogistic.xlsx](https://github.com/phitter-hub/phitter-files/blob/main/continuous/loglogistic.xlsx)                       | 🌐[gs:loglogistic](https://docs.google.com/spreadsheets/d/1WWXRuI6AP9n_n47ikOHWUjkfCYUOQgzhDjRsKBKEHXA)            |\n| loglogistic_3p            | ▶️[phitter:loglogistic_3p](https://phitter.io/distributions/continuous/loglogistic_3p)                 | 📊[loglogistic_3p.xlsx](https://github.com/phitter-hub/phitter-files/blob/main/continuous/loglogistic_3p.xlsx)                 | 🌐[gs:loglogistic_3p](https://docs.google.com/spreadsheets/d/1RaLZ5L0rTrv9_fAi6izElf02ucuFy9LwagL_gQn3R0Y)         |\n| lognormal                 | ▶️[phitter:lognormal](https://phitter.io/distributions/continuous/lognormal)                           | 📊[lognormal.xlsx](https://github.com/phitter-hub/phitter-files/blob/main/continuous/lognormal.xlsx)                           | 🌐[gs:lognormal](https://docs.google.com/spreadsheets/d/1lS1cR4C2R45ug0ZyLxBlRBtcXH6hNPE1L-5wP68gUpA)              |\n| maxwell                   | ▶️[phitter:maxwell](https://phitter.io/distributions/continuous/maxwell)                               | 📊[maxwell.xlsx](https://github.com/phitter-hub/phitter-files/blob/main/continuous/maxwell.xlsx)                               | 🌐[gs:maxwell](https://docs.google.com/spreadsheets/d/15tPw2RM2_a0vJMjVwNgsJnJUKFk9xbcEALqOf1m5qH0)                |\n| moyal                     | ▶️[phitter:moyal](https://phitter.io/distributions/continuous/moyal)                                   | 📊[moyal.xlsx](https://github.com/phitter-hub/phitter-files/blob/main/continuous/moyal.xlsx)                                   | 🌐[gs:moyal](https://docs.google.com/spreadsheets/d/1_58zWuk_-wSEesJbCc2FTHxv4HO5WouGwlStIZitt1I)                  |\n| nakagami                  | ▶️[phitter:nakagami](https://phitter.io/distributions/continuous/nakagami)                             | 📊[nakagami.xlsx](https://github.com/phitter-hub/phitter-files/blob/main/continuous/nakagami.xlsx)                             | 🌐[gs:nakagami](https://docs.google.com/spreadsheets/d/1fY8ID5gz1R6oWFm4w91GFdQMCd0wJ5ZRgfWi-yQtGqs)               |\n| 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/phitter-hub/phitter-files/blob/main/continuous/non_central_chi_square.xlsx) | 🌐[gs:non_central_chi_square](https://docs.google.com/spreadsheets/d/17KWXPKOuMfTG0w4Gqe3lU3vWY2e9k31AX22PXTzOrFk) |\n| non_central_f             | ▶️[phitter:non_central_f](https://phitter.io/distributions/continuous/non_central_f)                   | 📊[non_central_f.xlsx](https://github.com/phitter-hub/phitter-files/blob/main/continuous/non_central_f.xlsx)                   | 🌐[gs:non_central_f](https://docs.google.com/spreadsheets/d/14mZ563hIw2vXNM89DUncpsOdGgBXEUIIxJNa3-MVNIM)          |\n| 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/phitter-hub/phitter-files/blob/main/continuous/non_central_t_student.xlsx)   | 🌐[gs:non_central_t_student](https://docs.google.com/spreadsheets/d/1u8pseBDM3brw0AXlru1cprOsfQuHMWfvfDbz2XxKoOY)  |\n| normal                    | ▶️[phitter:normal](https://phitter.io/distributions/continuous/normal)                                 | 📊[normal.xlsx](https://github.com/phitter-hub/phitter-files/blob/main/continuous/normal.xlsx)                                 | 🌐[gs:normal](https://docs.google.com/spreadsheets/d/18QTB3YYprvdFhr6PJI-DFcZOnYAuffdH8JHOtH1f83I)                 |\n| pareto_first_kind         | ▶️[phitter:pareto_first_kind](https://phitter.io/distributions/continuous/pareto_first_kind)           | 📊[pareto_first_kind.xlsx](https://github.com/phitter-hub/phitter-files/blob/main/continuous/pareto_first_kind.xlsx)           | 🌐[gs:pareto_first_kind](https://docs.google.com/spreadsheets/d/1T-Sjp0yCxbJpP9njbovOiFpbP8PrwI5jlj66odxAw5E)      |\n| pareto_second_kind        | ▶️[phitter:pareto_second_kind](https://phitter.io/distributions/continuous/pareto_second_kind)         | 📊[pareto_second_kind.xlsx](https://github.com/phitter-hub/phitter-files/blob/main/continuous/pareto_second_kind.xlsx)         | 🌐[gs:pareto_second_kind](https://docs.google.com/spreadsheets/d/1hnBOqkbcRNuyRxaLP8eHei5MRwUFDb1bgdcZYkpYKio)     |\n| pert                      | ▶️[phitter:pert](https://phitter.io/distributions/continuous/pert)                                     | 📊[pert.xlsx](https://github.com/phitter-hub/phitter-files/blob/main/continuous/pert.xlsx)                                     | 🌐[gs:pert](https://docs.google.com/spreadsheets/d/1NeKJKq4D_BB-ouefgJ35FzcORA7fH1OQwC5dCZKI_38)                   |\n| power_function            | ▶️[phitter:power_function](https://phitter.io/distributions/continuous/power_function)                 | 📊[power_function.xlsx](https://github.com/phitter-hub/phitter-files/blob/main/continuous/power_function.xlsx)                 | 🌐[gs:power_function](https://docs.google.com/spreadsheets/d/1Hbi-XZiCK--JGFnoY-8iDLmNgYclDo5L4LKYKCCxfzw)         |\n| rayleigh                  | ▶️[phitter:rayleigh](https://phitter.io/distributions/continuous/rayleigh)                             | 📊[rayleigh.xlsx](https://github.com/phitter-hub/phitter-files/blob/main/continuous/rayleigh.xlsx)                             | 🌐[gs:rayleigh](https://docs.google.com/spreadsheets/d/1UWtjOwokob4x43OcMLLFbNTYUqOo5dJWqSTfWbS-yyw)               |\n| reciprocal                | ▶️[phitter:reciprocal](https://phitter.io/distributions/continuous/reciprocal)                         | 📊[reciprocal.xlsx](https://github.com/phitter-hub/phitter-files/blob/main/continuous/reciprocal.xlsx)                         | 🌐[gs:reciprocal](https://docs.google.com/spreadsheets/d/1ghFeCj8Q_hbpWqv9xXaNl1UKUe-5kOomZPWyI1JsoGA)             |\n| rice                      | ▶️[phitter:rice](https://phitter.io/distributions/continuous/rice)                                     | 📊[rice.xlsx](https://github.com/phitter-hub/phitter-files/blob/main/continuous/rice.xlsx)                                     | 🌐[gs:rice](https://docs.google.com/spreadsheets/d/1hGVFWbF0w7D0l54t_p0vUId0rO2s61BRdrgslDYTnWc)                   |\n| semicircular              | ▶️[phitter:semicircular](https://phitter.io/distributions/continuous/semicircular)                     | 📊[semicircular.xlsx](https://github.com/phitter-hub/phitter-files/blob/main/continuous/semicircular.xlsx)                     | 🌐[gs:semicircular](https://docs.google.com/spreadsheets/d/195c9VbAKtvEndJKnFp52TrENYK2iytMzIXLMKFAGgx4)           |\n| t_student                 | ▶️[phitter:t_student](https://phitter.io/distributions/continuous/t_student)                           | 📊[t_student.xlsx](https://github.com/phitter-hub/phitter-files/blob/main/continuous/t_student.xlsx)                           | 🌐[gs:t_student](https://docs.google.com/spreadsheets/d/1fGxJfFL5eXAWk8xNI6HgCX9SQuXi-m5mR83N1dMLJrg)              |\n| t_student_3p              | ▶️[phitter:t_student_3p](https://phitter.io/distributions/continuous/t_student_3p)                     | 📊[t_student_3p.xlsx](https://github.com/phitter-hub/phitter-files/blob/main/continuous/t_student_3p.xlsx)                     | 🌐[gs:t_student_3p](https://docs.google.com/spreadsheets/d/1K8bpbc-0mwe0mvRYXUQmoE8vaTigciJWDS4CPXmJodU)           |\n| trapezoidal               | ▶️[phitter:trapezoidal](https://phitter.io/distributions/continuous/trapezoidal)                       | 📊[trapezoidal.xlsx](https://github.com/phitter-hub/phitter-files/blob/main/continuous/trapezoidal.xlsx)                       | 🌐[gs:trapezoidal](https://docs.google.com/spreadsheets/d/1Gsk5M_R2q9Or8RTggKtTkqEk-cN6IuDgYqbmhFm5Xlw)            |\n| triangular                | ▶️[phitter:triangular](https://phitter.io/distributions/continuous/triangular)                         | 📊[triangular.xlsx](https://github.com/phitter-hub/phitter-files/blob/main/continuous/triangular.xlsx)                         | 🌐[gs:triangular](https://docs.google.com/spreadsheets/d/1nirKOt7O7rUf2nlYu61cnNYT91GKSzb6pVlc1-pzzGw)             |\n| uniform                   | ▶️[phitter:uniform](https://phitter.io/distributions/continuous/uniform)                               | 📊[uniform.xlsx](https://github.com/phitter-hub/phitter-files/blob/main/continuous/uniform.xlsx)                               | 🌐[gs:uniform](https://docs.google.com/spreadsheets/d/1TSaKNHOsVLYUobyKTpHR6qCuCAgfkKmRSETvdeZLcw4)                |\n| weibull                   | ▶️[phitter:weibull](https://phitter.io/distributions/continuous/weibull)                               | 📊[weibull.xlsx](https://github.com/phitter-hub/phitter-files/blob/main/continuous/weibull.xlsx)                               | 🌐[gs:weibull](https://docs.google.com/spreadsheets/d/1DdNwWHmu0PZAhMYf475EMU3scTMXok3wOhzsg7gn8Ek)                |\n| weibull_3p                | ▶️[phitter:weibull_3p](https://phitter.io/distributions/continuous/weibull_3p)                         | 📊[weibull_3p.xlsx](https://github.com/phitter-hub/phitter-files/blob/main/continuous/weibull_3p.xlsx)                         | 🌐[gs:weibull_3p](https://docs.google.com/spreadsheets/d/1agwpFGpXm62srDxgPOoDQGN8nGd8zaoztXg84Bgedlo)             |\n\n## Discrete Distributions\n\n#### [1. PDF File Documentation Discrete Distributions](https://github.com/phitter-hub/phitter-kernel/blob/main/distributions_documentation/discrete/document_discrete_distributions/phitter_discrete_distributions.pdf)\n\n#### 2. Resources Discrete Distributions\n\n| Distribution      | Phitter Playground                                                                           | Excel File                                                                                                          | Google Sheets Files                                                                                           |\n| :---------------- | :------------------------------------------------------------------------------------------- | :------------------------------------------------------------------------------------------------------------------ | :------------------------------------------------------------------------------------------------------------ |\n| bernoulli         | ▶️[phitter:bernoulli](https://phitter.io/distributions/continuous/bernoulli)                 | 📊[bernoulli.xlsx](https://github.com/phitter-hub/phitter-files/blob/main/discrete/bernoulli.xlsx)                 | 🌐[gs:bernoulli](https://docs.google.com/spreadsheets/d/1sWJZYZWW8cVLFXYV-fb3Lq4y2YgWzgTGWHfhIJ0zM5c)         |\n| binomial          | ▶️[phitter:binomial](https://phitter.io/distributions/continuous/binomial)                   | 📊[binomial.xlsx](https://github.com/phitter-hub/phitter-files/blob/main/discrete/binomial.xlsx)                   | 🌐[gs:binomial](https://docs.google.com/spreadsheets/d/1bPOiZVUhjLMmbFqVjWMqg1NzTvsZxVIw95fi5hIhkn0)          |\n| geometric         | ▶️[phitter:geometric](https://phitter.io/distributions/continuous/geometric)                 | 📊[geometric.xlsx](https://github.com/phitter-hub/phitter-files/blob/main/discrete/geometric.xlsx)                 | 🌐[gs:geometric](https://docs.google.com/spreadsheets/d/1cEU6n8UxpJ_Had6WfFnAXZ2FcaLGYu8g5srQ_iEfjgg)         |\n| hypergeometric    | ▶️[phitter:hypergeometric](https://phitter.io/distributions/continuous/hypergeometric)       | 📊[hypergeometric.xlsx](https://github.com/phitter-hub/phitter-files/blob/main/discrete/hypergeometric.xlsx)       | 🌐[gs:hypergeometric](https://docs.google.com/spreadsheets/d/10xUqKVoFzUiukuYt6VFwlaetMDTdGulHQPEWl1rJiMA)    |\n| logarithmic       | ▶️[phitter:logarithmic](https://phitter.io/distributions/continuous/logarithmic)             | 📊[logarithmic.xlsx](https://github.com/phitter-hub/phitter-files/blob/main/discrete/logarithmic.xlsx)             | 🌐[gs:logarithmic](https://docs.google.com/spreadsheets/d/1N-YXrSfOYkPKwerL5I1QmfxuwbZzVUzgBWTcKzcmLhE)       |\n| negative_binomial | ▶️[phitter:negative_binomial](https://phitter.io/distributions/continuous/negative_binomial) | 📊[negative_binomial.xlsx](https://github.com/phitter-hub/phitter-files/blob/main/discrete/negative_binomial.xlsx) | 🌐[gs:negative_binomial](https://docs.google.com/spreadsheets/d/1xmCWBiswdW5s7SIhwT2nrdQxLFAb6hw73iy52_nvjQE) |\n| poisson           | ▶️[phitter:poisson](https://phitter.io/distributions/continuous/poisson)                     | 📊[poisson.xlsx](https://github.com/phitter-hub/phitter-files/blob/main/discrete/poisson.xlsx)                     | 🌐[gs:poisson](https://docs.google.com/spreadsheets/d/1fwoe70JH5Ve6sETb7AwBdb4eep_h2DeGlpHIWcHeZA8)           |\n| uniform           | ▶️[phitter:uniform](https://phitter.io/distributions/continuous/uniform)                     | 📊[uniform.xlsx](https://github.com/phitter-hub/phitter-files/blob/main/discrete/uniform.xlsx)                     | 🌐[gs:uniform](https://docs.google.com/spreadsheets/d/1Ahl2ugOKkUCVWzzc_aNHwlA5Af4sHpTwqSiFIyYPsfM)           |\n\n## Benchmarks\n\n### _Fit time continuous distributions_\n\n| Sample Size / Workers |     1     |    2     |    6     |    10    |    20    |\n| :-------------------: | :-------: | :------: | :------: | :------: | :------: |\n|        **1K**         |  8.2981   |  7.1242  |  8.9667  |  9.9287  | 16.2246  |\n|        **10K**        |  20.8711  | 14.2647  | 10.5612  | 11.6004  | 17.8562  |\n|       **100K**        | 152.6296  | 97.2359  | 57.7310  | 51.6182  | 53.2313  |\n|       **500K**        | 914.9291  | 640.8153 | 370.0323 | 267.4597 | 257.7534 |\n|        **1M**         | 1580.8501 | 972.3985 | 573.5429 | 496.5569 | 425.7809 |\n\n### _Estimation time parameters discrete distributions_\n\n| Sample Size / Workers |    1    |    2    |    4    |\n| :-------------------: | :-----: | :-----: | :-----: |\n|        **1K**         | 0.1688  | 2.6402  | 2.8719  |\n|        **10K**        | 0.4462  | 2.4452  | 3.0471  |\n|       **100K**        | 4.5598  | 6.3246  | 7.5869  |\n|       **500K**        | 19.0172 | 21.8047 | 19.8420 |\n|        **1M**         | 39.8065 | 29.8360 | 30.2334 |\n\n### _Estimation time parameters continuous distributions_\n\n| Distribution / Sample Size |   1K   |  10K   |  100K   |  500K   |    1M    |    10M    |\n| :------------------------: | :----: | :----: | :-----: | :-----: | :------: | :-------: |\n|           alpha            | 0.3345 | 0.4625 | 2.5933  | 18.3856 | 39.6533  | 362.2951  |\n|          arcsine           | 0.0000 | 0.0000 | 0.0000  | 0.0000  |  0.0000  |  0.0000   |\n|           argus            | 0.0559 | 0.2050 | 2.2472  | 13.3928 | 41.5198  | 362.2472  |\n|            beta            | 0.1880 | 0.1790 | 0.1940  | 0.2110  |  0.1800  |  0.3134   |\n|         beta_prime         | 0.1766 | 0.7506 | 7.6039  | 40.4264 | 85.0677  | 812.1323  |\n|       beta_prime_4p        | 0.0720 | 0.3630 | 3.9478  | 20.2703 | 40.2709  | 413.5239  |\n|          bradford          | 0.0110 | 0.0000 | 0.0000  | 0.0000  |  0.0000  |  0.0010   |\n|            burr            | 0.0733 | 0.6931 | 5.5425  | 36.7684 | 79.8269  | 668.2016  |\n|          burr_4p           | 0.1552 | 0.7981 | 8.4716  | 44.4549 | 87.7292  | 858.0035  |\n|           cauchy           | 0.0090 | 0.0160 | 0.1581  | 1.1052  |  2.1090  |  21.5244  |\n|         chi_square         | 0.0000 | 0.0000 | 0.0000  | 0.0000  |  0.0000  |  0.0000   |\n|       chi_square_3p        | 0.0000 | 0.0000 | 0.0000  | 0.0000  |  0.0000  |  0.0000   |\n|           dagum            | 0.3381 | 0.8278 | 9.6907  | 45.5855 | 98.6691  | 917.6713  |\n|          dagum_4p          | 0.3646 | 1.3307 | 13.3437 | 70.9462 | 140.9371 | 1396.3368 |\n|           erlang           | 0.0010 | 0.0000 | 0.0000  | 0.0000  |  0.0000  |  0.0000   |\n|         erlang_3p          | 0.0000 | 0.0000 | 0.0000  | 0.0000  |  0.0000  |  0.0000   |\n|       error_function       | 0.0000 | 0.0000 | 0.0000  | 0.0000  |  0.0000  |  0.0000   |\n|        exponential         | 0.0000 | 0.0000 | 0.0000  | 0.0000  |  0.0000  |  0.0000   |\n|       exponential_2p       | 0.0000 | 0.0000 | 0.0000  | 0.0000  |  0.0000  |  0.0000   |\n|             f              | 0.0592 | 0.2948 | 2.6920  | 18.9458 | 29.9547  | 402.2248  |\n|        fatigue_life        | 0.0352 | 0.1101 | 1.7085  | 9.0090  | 20.4702  | 186.9631  |\n|       folded_normal        | 0.0020 | 0.0020 | 0.0020  | 0.0022  |  0.0033  |  0.0040   |\n|          frechet           | 0.1313 | 0.4359 | 5.7031  | 39.4202 | 43.2469  | 671.3343  |\n|            f_4p            | 0.3269 | 0.7517 | 0.6183  | 0.6037  |  0.5809  |  0.2073   |\n|           gamma            | 0.0000 | 0.0000 | 0.0000  | 0.0000  |  0.0000  |  0.0000   |\n|          gamma_3p          | 0.0000 | 0.0000 | 0.0000  | 0.0000  |  0.0000  |  0.0000   |\n| generalized_extreme_value  | 0.0833 | 0.2054 | 2.0337  | 10.3301 | 22.1340  | 243.3120  |\n|     generalized_gamma      | 0.0298 | 0.0178 | 0.0227  | 0.0236  |  0.0170  |  0.0241   |\n|    generalized_gamma_4p    | 0.0371 | 0.0116 | 0.0732  | 0.0725  |  0.0707  |  0.0730   |\n|    generalized_logistic    | 0.1040 | 0.1073 | 0.1037  | 0.0819  |  0.0989  |  0.0836   |\n|     generalized_normal     | 0.0154 | 0.0736 | 0.7367  | 2.4831  |  5.9752  |  55.2417  |\n|     generalized_pareto     | 0.3189 | 0.8978 | 8.9370  | 51.3813 | 101.6832 | 1015.2933 |\n|           gibrat           | 0.0328 | 0.0432 | 0.4287  | 2.7159  |  5.5721  |  54.1702  |\n|        gumbel_left         | 0.0000 | 0.0000 | 0.0000  | 0.0000  |  0.0010  |  0.0010   |\n|        gumbel_right        | 0.0000 | 0.0000 | 0.0000  | 0.0000  |  0.0000  |  0.0000   |\n|        half_normal         | 0.0010 | 0.0000 | 0.0000  | 0.0010  |  0.0000  |  0.0000   |\n|     hyperbolic_secant      | 0.0000 | 0.0000 | 0.0000  | 0.0000  |  0.0000  |  0.0000   |\n|       inverse_gamma        | 0.0308 | 0.0632 | 0.7233  | 5.0127  | 10.7885  |  99.1316  |\n|      inverse_gamma_3p      | 0.0787 | 0.1472 | 1.6513  | 11.1161 | 23.4587  | 227.6125  |\n|      inverse_gaussian      | 0.0000 | 0.0000 | 0.0000  | 0.0000  |  0.0000  |  0.0000   |\n|    inverse_gaussian_3p     | 0.0000 | 0.0000 | 0.0000  | 0.0000  |  0.0000  |  0.0000   |\n|         johnson_sb         | 0.2966 | 0.7466 | 4.0707  | 40.2028 | 56.2130  | 728.2447  |\n|         johnson_su         | 0.0070 | 0.0010 | 0.0010  | 0.0143  |  0.0010  |  0.0010   |\n|        kumaraswamy         | 0.0164 | 0.0120 | 0.0130  | 0.0123  |  0.0125  |  0.0150   |\n|          laplace           | 0.0000 | 0.0000 | 0.0000  | 0.0000  |  0.0000  |  0.0000   |\n|            levy            | 0.0100 | 0.0314 | 0.2296  | 1.1365  |  2.7211  |  26.4966  |\n|          loggamma          | 0.0085 | 0.0050 | 0.0050  | 0.0070  |  0.0062  |  0.0080   |\n|          logistic          | 0.0000 | 0.0000 | 0.0000  | 0.0000  |  0.0000  |  0.0000   |\n|        loglogistic         | 0.0000 | 0.0000 | 0.0000  | 0.0000  |  0.0000  |  0.0000   |\n|       loglogistic_3p       | 0.0000 | 0.0000 | 0.0000  | 0.0000  |  0.0000  |  0.0000   |\n|         lognormal          | 0.0000 | 0.0000 | 0.0000  | 0.0000  |  0.0010  |  0.0000   |\n|          maxwell           | 0.0000 | 0.0000 | 0.0000  | 0.0000  |  0.0000  |  0.0010   |\n|           moyal            | 0.0000 | 0.0000 | 0.0000  | 0.0000  |  0.0000  |  0.0000   |\n|          nakagami          | 0.0000 | 0.0030 | 0.0213  | 0.1215  |  0.2649  |  2.2457   |\n|   non_central_chi_square   | 0.0000 | 0.0000 | 0.0000  | 0.0000  |  0.0000  |  0.0000   |\n|       non_central_f        | 0.0190 | 0.0182 | 0.0210  | 0.0192  |  0.0190  |  0.0200   |\n|   non_central_t_student    | 0.0874 | 0.0822 | 0.0862  | 0.1314  |  0.2516  |  0.1781   |\n|           normal           | 0.0000 | 0.0000 | 0.0000  | 0.0000  |  0.0000  |  0.0000   |\n|     pareto_first_kind      | 0.0010 | 0.0030 | 0.0390  | 0.2494  |  0.5226  |  5.5246   |\n|     pareto_second_kind     | 0.0643 | 0.1522 | 1.1722  | 10.9871 | 23.6534  | 201.1626  |\n|            pert            | 0.0052 | 0.0030 | 0.0030  | 0.0040  |  0.0040  |  0.0092   |\n|       power_function       | 0.0075 | 0.0040 | 0.0040  | 0.0030  |  0.0040  |  0.0040   |\n|          rayleigh          | 0.0000 | 0.0000 | 0.0000  | 0.0000  |  0.0000  |  0.0000   |\n|         reciprocal         | 0.0000 | 0.0000 | 0.0000  | 0.0000  |  0.0000  |  0.0000   |\n|            rice            | 0.0182 | 0.0030 | 0.0040  | 0.0060  |  0.0030  |  0.0050   |\n|        semicircular        | 0.0000 | 0.0000 | 0.0000  | 0.0000  |  0.0000  |  0.0000   |\n|        trapezoidal         | 0.0083 | 0.0072 | 0.0073  | 0.0060  |  0.0070  |  0.0060   |\n|         triangular         | 0.0000 | 0.0000 | 0.0000  | 0.0000  |  0.0000  |  0.0000   |\n|         t_student          | 0.0000 | 0.0000 | 0.0000  | 0.0000  |  0.0000  |  0.0000   |\n|        t_student_3p        | 0.3892 | 1.1860 | 11.2759 | 71.1156 | 143.1939 | 1409.8578 |\n|          uniform           | 0.0000 | 0.0000 | 0.0000  | 0.0000  |  0.0000  |  0.0000   |\n|          weibull           | 0.0010 | 0.0000 | 0.0000  | 0.0000  |  0.0010  |  0.0010   |\n|         weibull_3p         | 0.0061 | 0.0040 | 0.0030  | 0.0040  |  0.0050  |  0.0050   |\n\n### _Estimation time parameters discrete distributions_\n\n| Distribution / Sample Size |   1K   |  10K   |  100K  |  500K  |   1M   |  10M   |\n| :------------------------: | :----: | :----: | :----: | :----: | :----: | :----: |\n|         bernoulli          | 0.0000 | 0.0000 | 0.0000 | 0.0000 | 0.0000 | 0.0000 |\n|          binomial          | 0.0000 | 0.0000 | 0.0000 | 0.0000 | 0.0000 | 0.0000 |\n|         geometric          | 0.0000 | 0.0000 | 0.0000 | 0.0000 | 0.0000 | 0.0000 |\n|       hypergeometric       | 0.0773 | 0.0061 | 0.0030 | 0.0020 | 0.0030 | 0.0051 |\n|        logarithmic         | 0.0210 | 0.0035 | 0.0171 | 0.0050 | 0.0030 | 0.0756 |\n|     negative_binomial      | 0.0293 | 0.0000 | 0.0000 | 0.0000 | 0.0000 | 0.0000 |\n|          poisson           | 0.0000 | 0.0000 | 0.0000 | 0.0000 | 0.0000 | 0.0000 |\n|          uniform           | 0.0000 | 0.0000 | 0.0000 | 0.0000 | 0.0000 | 0.0000 |\n\n\u003c/details\u003e\n\n\u003cdetails\u003e\n\u003csummary style=\"font-size: 16px; font-weight: bold;\"\u003eDocumentation Simulation Module\u003c/summary\u003e\n\n## Process Simulation\n\nThis will help you to understand your processes. To use it, run the following line\n\n```python\nfrom phitter import simulation\n\n# Create a simulation process instance\nsimulation = simulation.ProcessSimulation()\n\n```\n\n### Add processes to your simulation instance\n\nThere are two ways to add processes to your simulation instance:\n\n-   Adding a **process _without_ preceding process (new branch)**\n-   Adding a **process _with_ preceding process (with previous ids)**\n\n#### Process _without_ preceding process (new branch)\n\n```python\n# Add a new process without preceding process\nsimulation.add_process(\n    prob_distribution=\"normal\",\n    parameters={\"mu\": 5, \"sigma\": 2},\n    process_id=\"first_process\",\n    number_of_products=10,\n    number_of_servers=3,\n    new_branch=True,\n)\n\n```\n\n#### Process _with_ preceding process (with previous ids)\n\n```python\n# Add a new process with preceding process\nsimulation.add_process(\n    prob_distribution=\"exponential\",\n    parameters={\"lambda\": 4},\n    process_id=\"second_process\",\n    previous_ids=[\"first_process\"],\n)\n\n```\n\n#### All together and adding some new process\n\nThe order in which you add each process **_matters_**. You can add as many processes as you need.\n\n```python\n# Add a new process without preceding process\nsimulation.add_process(\n    prob_distribution=\"normal\",\n    parameters={\"mu\": 5, \"sigma\": 2},\n    process_id=\"first_process\",\n    number_of_products=10,\n    number_of_servers=3,\n    new_branch=True,\n)\n\n# Add a new process with preceding process\nsimulation.add_process(\n    prob_distribution=\"exponential\",\n    parameters={\"lambda\": 4},\n    process_id=\"second_process\",\n    previous_ids=[\"first_process\"],\n)\n\n# Add a new process with preceding process\nsimulation.add_process(\n    prob_distribution=\"gamma\",\n    parameters={\"alpha\": 15, \"beta\": 3},\n    process_id=\"third_process\",\n    previous_ids=[\"first_process\"],\n)\n\n# Add a new process without preceding process\nsimulation.add_process(\n    prob_distribution=\"exponential\",\n    parameters={\"lambda\": 4.3},\n    process_id=\"fourth_process\",\n    new_branch=True,\n)\n\n\n# Add a new process with preceding process\nsimulation.add_process(\n    prob_distribution=\"beta\",\n    parameters={\"alpha\": 1, \"beta\": 1, \"A\": 2, \"B\": 3},\n    process_id=\"fifth_process\",\n    previous_ids=[\"second_process\", \"fourth_process\"],\n)\n\n# Add a new process with preceding process\nsimulation.add_process(\n    prob_distribution=\"normal\",\n    parameters={\"mu\": 15, \"sigma\": 2},\n    process_id=\"sixth_process\",\n    previous_ids=[\"third_process\", \"fifth_process\"],\n)\n```\n\n### Visualize your processes\n\nYou can visualize your processes to see if what you're trying to simulate is your actual process.\n\n```python\n# Graph your process\nsimulation.process_graph()\n```\n\n![Simulation](./multimedia/simulation_process_graph.png)\n\n### Start Simulation\n\nYou can simulate and have different simulation time values or you can create a confidence interval for your process\n\n#### Run Simulation\n\nSimulate several scenarios of your complete process\n\n```python\n# Run Simulation\nsimulation.run(number_of_simulations=100)\n\n# After run\nsimulation: pandas.Dataframe\n```\n\n### Review Simulation Metrics by Stage\n\nIf you want to review average time and standard deviation by stage run this line of code\n\n```python\n# Review simulation metrics\nsimulation.simulation_metrics() -\u003e pandas.Dataframe\n```\n\n#### Run confidence interval\n\nIf you want to have a confidence interval for the simulation metrics, run the following line of code\n\n```python\n# Confidence interval for Simulation metrics\nsimulation.run_confidence_interval(\n    confidence_level=0.99,\n    number_of_simulations=100,\n    replications=10,\n) -\u003e pandas.Dataframe\n```\n\n## Queue Simulation\n\nIf you need to simulate queues run the following code:\n\n```python\nfrom phitter import simulation\n\n# Create a simulation process instance\nsimulation = simulation.QueueingSimulation(\n    a=\"exponential\",\n    a_parameters={\"lambda\": 5},\n    s=\"exponential\",\n    s_parameters={\"lambda\": 20},\n    c=3,\n)\n```\n\nIn this case we are going to simulate **a** (arrivals) with _exponential distribution_ and **s** (service) as _exponential distribution_ with **c** equals to 3 different servers.\n\nBy default Maximum Capacity **k** is _infinity_, total population **n** is _infinity_ and the queue discipline **d** is _FIFO_. As we are not selecting **d** equals to \"PBS\" we don't have any information to add for **pbs_distribution** nor **pbs_parameters**\n\n### Run the simulation\n\nIf you want to have the simulation results\n\n```python\n# Run simulation\nsimulation.run(simulation_time = 2000)\n```\n\nIf you want to see some metrics and probabilities from this simulation you should use::\n\n```python\n# Calculate metrics\nsimulation.metrics_summary() -\u003e pandas.Dataframe\n\n# Calculate probabilities\nsimulation.number_probability_summary() -\u003e pandas.Dataframe\n```\n\n### Run Confidence Interval for metrics and probabilities\n\nIf you want to have a confidence interval for your metrics and probabilities you should run the following line\n\n```python\n# Calculate confidence interval for metrics and probabilities\nprobabilities, metrics = simulation.confidence_interval_metrics(\n    simulation_time=2000,\n    confidence_level=0.99,\n    replications=10,\n)\n\nprobabilities -\u003e pandas.Dataframe\nmetrics -\u003e pandas.Dataframe\n```\n\n\u003c/details\u003e\n\n\n## Sponsor Phitter\n\n[![Buy Me A Coffee](https://img.shields.io/badge/Buy%20me%20a%20coffee-donate-yellow?style=for-the-badge\u0026logo=buy-me-a-coffee)](https://buymeacoffee.com/sebastianjhm)\n\n\n## Contribution\n\nAll contributions and collaborations are welcome!\n\nFor bugs, feature requests, and clear suggestions for improvement please\n[open an issue](https://github.com/phitter-hub/phitter-kernel/issues).\n\nIf you have built something upon _Phitter-Kernel_ that would be useful to others, or can\naddress an [open issue](https://github.com/phitter-hub/phitter-kernel/issues), please\n[fork the repository](https://github.com/phitter-hub/phitter-kernel/fork) and open a\n[pull request](https://github.com/phitter-hub/phitter-kernel/pulls).\n","project_url":"https://awesome.ecosyste.ms/api/v1/projects/github.com%2Fphitter-hub%2Fphitter-kernel","html_url":"https://awesome.ecosyste.ms/projects/github.com%2Fphitter-hub%2Fphitter-kernel","lists_url":"https://awesome.ecosyste.ms/api/v1/projects/github.com%2Fphitter-hub%2Fphitter-kernel/lists"}