<div> <a href="https://erdogant.github.io/distfit/"><img src="https://github.com/erdogant/distfit/blob/master/docs/figs/logo.png" width="250" align="left" /></a> distfit is a Python package for probability density fitting of univariate distributions for random variables. The distfit library can determine the best fit for over 90 theoretical distributions. The goodness-of-fit test is used to score for the best fit and after finding the best-fitted theoretical distribution, the loc, scale, and arg parameters are returned. It can be used for parametric, non-parametric, and discrete distributions. ⭐️Star it if you like it⭐️ </div>

---

Key Features

| Feature | Description | Medium | Gumroad+Podcast | |---------|-------------|--------|-----------------| | Parametric Fitting | Fit distributions on empirical data X. | Link | Link | | Non-Parametric Fitting | Fit distributions on empirical data X using non-parametric approaches (quantile, percentiles). | - | - | | Multivariate Fitting | Fit multivariate distributions on empirical data X that contains multiple columns. | - | - | | Discrete Fitting | Fit distributions on empirical data X using binomial distribution. | - | - | | Predict | Compute probabilities for response variables y. | - | - | | Outlier Detection | Detect anomalies using fitted distributions. | Link | Link | | Synthetic Data | Generate synthetic data. | Link | Link | | Plots | Various plotting functionalities. | - | - |

---

Resources and Links

• Example Notebooks: Examples
• Medium Blogs Medium
• Gumroad Blogs with podcast: GumRoad
• Documentation: Website
• Bug Reports and Feature Requests: GitHub Issues

---

Background

• For the parametric approach, The distfit library can determine the best fit across 89 theoretical distributions. To score the fit, one of the scoring statistics for the good-of-fitness test can be used used, such as RSS/SSE, Wasserstein, Kolmogorov-Smirnov (KS), or Energy. After finding the best-fitted theoretical distribution, the loc, scale, and arg parameters are returned, such as mean and standard deviation for normal distribution.

• For the non-parametric approach, the distfit library contains two methods, the quantile and percentile method. Both methods assume that the data does not follow a specific probability distribution. In the case of the quantile method, the quantiles of the data are modeled whereas for the percentile method, the percentiles are modeled.

• In case the dataset contains discrete values, the distift library contains the option for discrete fitting. The best fit is then derived using the binomial distribution.

---

Installation

Install distfit from PyPI

pip install distfit

Install from Github source

pip install git+https://github.com/erdogant/distfit

Imort Library

import distfit
print(distfit.__version__)

# Import library
from distfit import distfit

<hr>

Examples

Example: Quick start to find best fit for your input data

# [distfit] >INFO> fit
# [distfit] >INFO> transform
# [distfit] >INFO> [norm      ] [0.00 sec] [RSS: 0.00108326] [loc=-0.048 scale=1.997]
# [distfit] >INFO> [expon     ] [0.00 sec] [RSS: 0.404237] [loc=-6.897 scale=6.849]
# [distfit] >INFO> [pareto    ] [0.00 sec] [RSS: 0.404237] [loc=-536870918.897 scale=536870912.000]
# [distfit] >INFO> [dweibull  ] [0.06 sec] [RSS: 0.0115552] [loc=-0.031 scale=1.722]
# [distfit] >INFO> [t         ] [0.59 sec] [RSS: 0.00108349] [loc=-0.048 scale=1.997]
# [distfit] >INFO> [genextreme] [0.17 sec] [RSS: 0.00300806] [loc=-0.806 scale=1.979]
# [distfit] >INFO> [gamma     ] [0.05 sec] [RSS: 0.00108459] [loc=-1862.903 scale=0.002]
# [distfit] >INFO> [lognorm   ] [0.32 sec] [RSS: 0.00121597] [loc=-110.597 scale=110.530]
# [distfit] >INFO> [beta      ] [0.10 sec] [RSS: 0.00105629] [loc=-16.364 scale=32.869]
# [distfit] >INFO> [uniform   ] [0.00 sec] [RSS: 0.287339] [loc=-6.897 scale=14.437]
# [distfit] >INFO> [loggamma  ] [0.12 sec] [RSS: 0.00109042] [loc=-370.746 scale=55.722]
# [distfit] >INFO> Compute confidence intervals [parametric]
# [distfit] >INFO> Compute significance for 9 samples.
# [distfit] >INFO> Multiple test correction method applied: [fdr_bh].
# [distfit] >INFO> Create PDF plot for the parametric method.
# [distfit] >INFO> Mark 5 significant regions
# [distfit] >INFO> Estimated distribution: beta [loc:-16.364265, scale:32.868811]

<p align="left"> <a href="https://erdogant.github.io/distfit/pages/html/Examples.html#make-predictions"> <img src="https://github.com/erdogant/distfit/blob/master/docs/figs/example_figP4c.png" width="450" /> </a> </p>

Example: Plot summary of the tested distributions

The distfit library provides multivariate distribution fitting that enables modeling complex dependencies between multiple variables using copula-based methods.

  from distfit import distfit
  
  # Initialize with multivariate mode
  dfit = distfit(multivariate=True)
  
  # Load example data
  X = dfit.import_example(data='multi_normal')
  # X = dfit.import_example(data='multi_t')
  
  # Fit model
  dfit.fit_transform(X)
  
  # Access estimated correlation matrix (Gaussian copula)
  print(dfit.model.corr)
  
  # Evaluate joint density
  results = dfit.evaluate_pdf(X)
  print(results['score'])
  print(results['copula_density'])
  
  # Generate synthetic samples
  Xnew = dfit.generate(n=10)
  
  # Detect multivariate outliers
  bool_outliers = dfit.predict_outliers(X)

<p align="left"> <a href="https://erdogant.github.io/distfit/pages/html/multivariate.html"> <img src="https://github.com/erdogant/distfit/blob/master/docs/figs/copulaDensity_uniformB.png" width="800" /> </a> </p <p align="left"> <a href="https://erdogant.github.io/distfit/pages/html/multivariate.html"> <img src="https://github.com/erdogant/distfit/blob/master/docs/figs/jointDensity.png" width="800" /> </a> </p

Example: Plot summary of the tested distributions

After we have a fitted model, we can make some predictions using the theoretical distributions. After making some predictions, we can plot again but now the predictions are automatically included.

<p align="left"> <a href="https://erdogant.github.