Poisson Binomial Distribution for Python

This Version

This is a fork from the original project by @tsakim This version adds these Features:

Adds mean, var, std, skew, amax and argmax methods
Solves FFT instability issues, as proposed here by @zeeshansayyed

About

The module contains a Python implementation of functions related to the Poisson Binomial probability distribution [1], which describes the probability distribution of the sum of independent Bernoulli random variables with non-uniform success probabilities. For further information, see reference [1].

The implemented methods are:

pmf: probability mass function
cdf: cumulative distribution function
pval: p-value for right tailed tests
mean: mean of the distribution
var: variance of the distribution
std: standard deviation of the distribution
skew: skewness of the distribution
amax: max value of the probability mass function
argmax: index of the max value of the probability mass function

Authors

Mika Straka, Maxi Marufo, Zeeshan Sayyed

Dependencies

NumPy
pytest For testing

Usage

Consider n independent and non-identically distributed random variables and be p a list/NumPy array of the corresponding Bernoulli success probabilities. In order to create the Poisson Binomial distributions, use

from poibin import PoiBin
pb = PoiBin(p)

Mean

pb.mean()

Variance

pb.var()

Standard Deviation

pb.std()

Skewness

pb.skew()

Max value

pb.amax()

Index of the max value

pb.argmax()

Be x a list/NumPy array of different numbers of success. Use the following methods to obtain the corresponding quantities:

Probability mass function

pb.pmf(x)

Cumulative distribution function

pb.cdf(x)

P-values for right tailed tests

pb.pval(x)

All three methods accept single integers as well as lists/NumPy arrays of integers. Note that x[i] must be smaller than len(p).

Testing

The methods have been implemented using the pytest module. To run the tests, execute

$ pytest test_poibin.py

in the command line. For verbose mode, use

$ pytest -v test_poibin.py

Reference

Yili Hong, On computing the distribution function for the Poisson binomial distribution, Computational Statistics & Data Analysis, Volume 59, March 2013, pages 41-51, ISSN 0167-9473

maxi-marufo/my-poibin