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distfit is a python package for probability density fitting of univariate distributions for random variables. With the random variable as an input, distfit can find the best fit for parametric, non-parametric, and discrete distributions.

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.

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Installation

Install distfit from PyPI

pip install distfit

Install from github source (beta version)

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

Check version

import distfit
print(distfit.__version__)

The following functions are available after installation:

# Import library
from distfit import distfit

dfit = distfit()        # Initialize 
dfit.fit_transform(X)   # Fit distributions on empirical data X
dfit.predict(y)         # Predict the probability of the resonse variables
dfit.plot()             # Plot the best fitted distribution (y is included if prediction is made)

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]

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.

Example: Make predictions using the fitted distribution

Example: Test for one specific distributions

The full list of distributions is listed here: https://erdogant.github.io/distfit/pages/html/Parametric.html

Example: Test for multiple distributions

The full list of distributions is listed here: https://erdogant.github.io/distfit/pages/html/Parametric.html

Example: Fit discrete distribution

from scipy.stats import binom
# Generate random numbers

# Set parameters for the test-case
n = 8
p = 0.5

# Generate 10000 samples of the distribution of (n, p)
X = binom(n, p).rvs(10000)
print(X)

# [5 1 4 5 5 6 2 4 6 5 4 4 4 7 3 4 4 2 3 3 4 4 5 1 3 2 7 4 5 2 3 4 3 3 2 3 5
#  4 6 7 6 2 4 3 3 5 3 5 3 4 4 4 7 5 4 5 3 4 3 3 4 3 3 6 3 3 5 4 4 2 3 2 5 7
#  5 4 8 3 4 3 5 4 3 5 5 2 5 6 7 4 5 5 5 4 4 3 4 5 6 2...]

# Import distfit
from distfit import distfit

# Initialize for discrete distribution fitting
dfit = distfit(method='discrete')

# Run distfit to and determine whether we can find the parameters from the data.
dfit.fit_transform(X)

# [distfit] >fit..
# [distfit] >transform..
# [distfit] >Fit using binomial distribution..
# [distfit] >[binomial] [SSE: 7.79] [n: 8] [p: 0.499959] [chi^2: 1.11]
# [distfit] >Compute confidence interval [discrete]