Data

Tools

Indexes

Applications

Experiments

Open Source Science

Phitter

Phitter: A library designed to streamline the process of fitting and analyzing probability distributions - Published in JOSS (2025)

https://github.com/phitter-hub/phitter-kernel

Science Score: 39.0%

This score indicates how likely this project is to be science-related based on various indicators:

  • ○
    CITATION.cff file
  • ✓
    codemeta.json file
    Found codemeta.json file
  • ✓
    .zenodo.json file
    Found .zenodo.json file
  • ✓
    DOI references
    Found 2 DOI reference(s) in README
  • ○
    Academic publication links
  • ○
    Academic email domains
  • ○
    Institutional organization owner
  • ○
    JOSS paper metadata
  • ○
    Scientific vocabulary similarity
    Low similarity (15.0%) to scientific vocabulary

Keywords

operations-research probability-distribution probability-models simulation

Scientific Fields

Earth and Environmental Sciences Physical Sciences - 40% confidence
Last synced: 4 months ago · JSON representation

Repository

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.

Basic Info
  • Host: GitHub
  • Owner: phitter-hub
  • License: mit
  • Language: Jupyter Notebook
  • Default Branch: main
  • Homepage: https://phitter.io/
  • Size: 410 MB
Statistics
  • Stars: 30
  • Watchers: 1
  • Forks: 2
  • Open Issues: 0
  • Releases: 6
Topics
operations-research probability-distribution probability-models simulation
Created over 2 years ago · Last pushed 4 months ago
Metadata Files
Readme Funding License

README.md

phitter-dark-logo

PyPI Downloads License Supported Python versions DOI badge Tests

⭐⭐⭐ If you find this project useful, giving it a star on GitHub. It really helps! ⭐⭐⭐

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.

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.

This repository contains the implementation of the python library and the kernel of Phitter Web

phitter_histogram

📄 Documentation

Find the complete Phitter documentation here.

Installation

Requirements

console python: >=3.9

PyPI

console pip install phitter

Usage

1. Fit Notebook's Tutorials

| Tutorial | Notebooks | | :------------------------------: | :------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------: | | Fit Continuous | Open In Colab | | Fit Discrete | Open In Colab | | Fit Accelerate [Sample>100K] | Open In Colab | | Fit Specific Distribution | Open In Colab | | Working Distribution | Open In Colab |

2. Simulation Notebook's Tutorials

| Tutorial | Notebooks | | :-----------------------------------------------: | :----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------: | | Process Simulation | Open In Colab | | Own Distribution | Open In Colab | | Queue Simulation First-In-First-Out (FIFO) | Open In Colab | | Queue Simulation Last-In-First-Out (LIFO) | Open In Colab | | Queue Simulation Priority-Based Service (PBS) | Open In Colab |

Documentation

Documentation Fit Module ### General Fit ```python import phitter ## Define your dataset data: list[int | float] = [...] ## Make a continuous fit using Phitter phi = phitter.Phitter(data=data) phi.fit() ``` ### Full continuous implementation ```python import phitter ## Define your dataset data: list[int | float] = [...] ## Make a continuous fit using Phitter phi = 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"], ) phi.fit(n_workers=6) ``` ### Full discrete implementation ```python import phitter ## Define your dataset data: list[int | float] = [...] ## Make a discrete fit using Phitter phi = phitter.Phitter( data=data, fit_type="discrete", confidence_level=0.95, minimum_sse=1e-2, distributions_to_fit=["binomial", "geometric"], ) phi.fit(n_workers=2) ``` ### Phitter: properties and methods ```python import phitter ## Define your dataset data: list[int | float] = [...] ## Make a fit using Phitter phi = phitter.Phitter(data=data) phi.fit(n_workers=2) ## Global methods and properties phi.summarize(k: int) -> pandas.DataFrame phi.summarize_info(k: int) -> pandas.DataFrame phi.best_distribution -> dict phi.sorted_distributions_sse -> dict phi.not_rejected_distributions -> dict phi.df_sorted_distributions_sse -> pandas.DataFrame phi.df_not_rejected_distributions -> pandas.DataFrame ## Specific distribution methods and properties phi.get_parameters(id_distribution: str) -> dict phi.get_test_chi_square(id_distribution: str) -> dict phi.get_test_kolmmogorov_smirnov(id_distribution: str) -> dict phi.get_test_anderson_darling(id_distribution: str) -> dict phi.get_sse(id_distribution: str) -> float phi.get_n_test_passed(id_distribution: str) -> int phi.get_n_test_null(id_distribution: str) -> int ``` ### Histogram Plot ```python import phitter data: list[int | float] = [...] phi = phitter.Phitter(data=data) phi.fit() phi.plot_histogram() ``` phitter_histogram ### Histogram PDF Dsitributions Plot ```python import phitter data: list[int | float] = [...] phi = phitter.Phitter(data=data) phi.fit() phi.plot_histogram_distributions() ``` phitter_histogram ### Histogram PDF Dsitribution Plot ```python import phitter data: list[int | float] = [...] phi = phitter.Phitter(data=data) phi.fit() phi.plot_distribution("beta") ``` phitter_histogram ### ECDF Plot ```python import phitter data: list[int | float] = [...] phi = phitter.Phitter(data=data) phi.fit() phi.plot_ecdf() ``` phitter_histogram ### ECDF Distribution Plot ```python import phitter data: list[int | float] = [...] phi = phitter.Phitter(data=data) phi.fit() phi.plot_ecdf_distribution("beta") ``` phitter_histogram ### QQ Plot ```python import phitter data: list[int | float] = [...] phi = phitter.Phitter(data=data) phi.fit() phi.qq_plot("beta") ``` phitter_histogram ### QQ - Regression Plot ```python import phitter data: list[int | float] = [...] phi = phitter.Phitter(data=data) phi.fit() phi.qq_plot_regression("beta") ``` phitter_histogram ### Working with 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/phitter-hub/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/phitter-hub/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/phitter-hub/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/phitter-hub/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/phitter-hub/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/phitter-hub/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/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) | | 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) | | 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) | | 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) | | 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) | | 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) | | 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) | | 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) | | 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) | | 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) | | 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) | | 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) | | 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) | | 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) | | 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) | | 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) | | 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) | | 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) | | 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) | | 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) | | 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) | | 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) | | 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) | | 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) | | 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) | | 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) | | 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) | | 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) | | 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) | | 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) | | 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) | | 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) | | 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) | | 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) | | 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) | | 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) | | 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) | | 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) | | 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) | | 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) | | 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) | | 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) | | 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) | | 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) | | 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) | | 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) | | 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) | | 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) | | 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) | | 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) | | 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) | | 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) | | 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) | | 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) | | 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) | | 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) | | 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) | | 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) | | 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) | | 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) | | 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) | | 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) | | 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) | | 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) | | 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) | | 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) | | 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) | | 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) | ## Discrete Distributions #### [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) #### 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/phitter-hub/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/phitter-hub/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/phitter-hub/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/phitter-hub/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/phitter-hub/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/phitter-hub/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/phitter-hub/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/phitter-hub/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 |
Documentation Simulation Module ## Process Simulation This will help you to understand your processes. To use it, run the following line ```python from phitter import simulation # Create a simulation process instance simulation = simulation.ProcessSimulation() ``` ### Add processes to your simulation instance There are two ways to add processes to your simulation instance: - Adding a **process _without_ preceding process (new branch)** - Adding a **process _with_ preceding process (with previous ids)** #### Process _without_ preceding process (new branch) ```python # Add a new process without preceding process simulation.add_process( prob_distribution="normal", parameters={"mu": 5, "sigma": 2}, process_id="first_process", number_of_products=10, number_of_servers=3, new_branch=True, ) ``` #### Process _with_ preceding process (with previous ids) ```python # Add a new process with preceding process simulation.add_process( prob_distribution="exponential", parameters={"lambda": 4}, process_id="second_process", previous_ids=["first_process"], ) ``` #### All together and adding some new process The order in which you add each process **_matters_**. You can add as many processes as you need. ```python # Add a new process without preceding process simulation.add_process( prob_distribution="normal", parameters={"mu": 5, "sigma": 2}, process_id="first_process", number_of_products=10, number_of_servers=3, new_branch=True, ) # Add a new process with preceding process simulation.add_process( prob_distribution="exponential", parameters={"lambda": 4}, process_id="second_process", previous_ids=["first_process"], ) # Add a new process with preceding process simulation.add_process( prob_distribution="gamma", parameters={"alpha": 15, "beta": 3}, process_id="third_process", previous_ids=["first_process"], ) # Add a new process without preceding process simulation.add_process( prob_distribution="exponential", parameters={"lambda": 4.3}, process_id="fourth_process", new_branch=True, ) # Add a new process with preceding process simulation.add_process( prob_distribution="beta", parameters={"alpha": 1, "beta": 1, "A": 2, "B": 3}, process_id="fifth_process", previous_ids=["second_process", "fourth_process"], ) # Add a new process with preceding process simulation.add_process( prob_distribution="normal", parameters={"mu": 15, "sigma": 2}, process_id="sixth_process", previous_ids=["third_process", "fifth_process"], ) ``` ### Visualize your processes You can visualize your processes to see if what you're trying to simulate is your actual process. ```python # Graph your process simulation.process_graph() ``` ![Simulation](./multimedia/simulation_process_graph.png) ### Start Simulation You can simulate and have different simulation time values or you can create a confidence interval for your process #### Run Simulation Simulate several scenarios of your complete process ```python # Run Simulation simulation.run(number_of_simulations=100) # After run simulation: pandas.Dataframe ``` ### Review Simulation Metrics by Stage If you want to review average time and standard deviation by stage run this line of code ```python # Review simulation metrics simulation.simulation_metrics() -> pandas.Dataframe ``` #### Run confidence interval If you want to have a confidence interval for the simulation metrics, run the following line of code ```python # Confidence interval for Simulation metrics simulation.run_confidence_interval( confidence_level=0.99, number_of_simulations=100, replications=10, ) -> pandas.Dataframe ``` ## Queue Simulation If you need to simulate queues run the following code: ```python from phitter import simulation # Create a simulation process instance simulation = simulation.QueueingSimulation( a="exponential", a_parameters={"lambda": 5}, s="exponential", s_parameters={"lambda": 20}, c=3, ) ``` In 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. By 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** ### Run the simulation If you want to have the simulation results ```python # Run simulation simulation.run(simulation_time = 2000) ``` If you want to see some metrics and probabilities from this simulation you should use:: ```python # Calculate metrics simulation.metrics_summary() -> pandas.Dataframe # Calculate probabilities simulation.number_probability_summary() -> pandas.Dataframe ``` ### Run Confidence Interval for metrics and probabilities If you want to have a confidence interval for your metrics and probabilities you should run the following line ```python # Calculate confidence interval for metrics and probabilities probabilities, metrics = simulation.confidence_interval_metrics( simulation_time=2000, confidence_level=0.99, replications=10, ) probabilities -> pandas.Dataframe metrics -> pandas.Dataframe ```

Sponsor Phitter

Buy Me A Coffee

Contribution

All contributions and collaborations are welcome!

For bugs, feature requests, and clear suggestions for improvement please open an issue.

If you have built something upon Phitter-Kernel that would be useful to others, or can address an open issue, please fork the repository and open a pull request.

Owner

  • Name: Phitter
  • Login: phitter-hub
  • Kind: user

Phitter helps you find the best theoretical probability distribution online for free. Also is a python package

GitHub Events

Total
  • Push event: 1
Last Year
  • Push event: 1

Issues and Pull Requests

Last synced: 4 months ago

All Time
  • Total issues: 0
  • Total pull requests: 0
  • Average time to close issues: N/A
  • Average time to close pull requests: N/A
  • Total issue authors: 0
  • Total pull request authors: 0
  • Average comments per issue: 0
  • Average comments per pull request: 0
  • Merged pull requests: 0
  • Bot issues: 0
  • Bot pull requests: 0
Past Year
  • Issues: 0
  • Pull requests: 0
  • Average time to close issues: N/A
  • Average time to close pull requests: N/A
  • Issue authors: 0
  • Pull request authors: 0
  • Average comments per issue: 0
  • Average comments per pull request: 0
  • Merged pull requests: 0
  • Bot issues: 0
  • Bot pull requests: 0
View more stats
Top Authors
Issue Authors
Pull Request Authors
Top Labels
Issue Labels
Pull Request Labels

Dependencies

pyproject.toml pypi
  • plotly >=5.14.0
  • scipy >=1.1.0