The module contains a Python implementation of functions related to the Poisson Binomial probability distribution, which describes the probability distribution of the sum of independent Bernoulli random variables with non-uniform success probabilities. For further information, see reference.
The implemented methods are:
pmf: probability mass functioncdf: cumulative distribution functionpval: p-value for right tailed tests
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)
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).
The methods have been implemented using the doctest module. To run the tests, execute
$ python -m doctest poibin_tests.txt
in the command line. For verbose mode, use
$ python -m doctest -v poibin_tests.txt
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,