bernmix 1.11.31

Methods to compute PMF and CDF values of a weighted sum of i.ni.d. BRVs

BernMix

Computation of PMF and CDF for a weighted sum of i.ni.d. Bernoulli random variables

Abbreviations

BRV - Bernoulli Random variable
PMF - Probability mass function
CDF - Cumulative distribution function
i.ni.d. - independent non-identically distributed

Description

The BernMix package includes two efficient algorithms to calculate the exact distribution of a weighted sum of i.ni.d. BRV – the first is for integer weights and the second is for non-integer weights. The discussed distribution includes, as particular cases, Binomial and Poisson Binomial distributions together with their linear combinations. For integer weights we present the algorithm to calculate a PMF and a CDF of a weighted sum of BRVs utilising the Discrete Fourier transform of the characteristic function. For non-integer weights we suggest the heuristic approach to compute pointwise CDF using rounding and integer linear programming.

The BernMix package provides a Python implementation of the algorithms to calculate PMFs and CDFs for both cases (integer and non-integer weights); C++ library for using Fast Fourier transform is wrapped with Cython. We analyse the time complexity of the algorithms and demonstrate their performance and accuracy.

Implemented methods

• bernmix_pmf_int - computation of the PMF for a integer-weighted sum of BRVs by the developed method
• bernmix_cdf_int - computation of the CDF for a integer-weighted sum of BRVs by the developed method
• bernmix_cdf_double - computation of the CDF for a weighted sum of BRVs with real weights by the developed method
• conv_pmf_int - computation of the PMF for a integer-weighted sum of BRVs by the convolution
• permut_cdf - computation of the CDF for a weighted sum of BRVs by the permutation

Requirements

To run BernMix methods you need Python 3.4 or later. A list of required Python packages that the BernMix depends on, are in requirements.txt.
The BernMix also required the FFTW3 library (a C library for computing the discrete Fourier transform) and Cython.

Installation

To install the BernMix package, run the following commands:

git clone https://github.com/iganna/bernmix.git
cd bernmix
python setup.py sdist bdist_wheel
cd dist
pip install *.whl

Running the tests

To demonstrate the use of methods we created a Python notebook tests/bernmix_demo.ipynb.
All tests that were used in the below article, are presented in a Python notebook tests/bernmix_test.ipynb and in a R notebook tests/gpb_test.ipynb

References

The mathematical inference of the algorithm implemented in the BernMix package is described in A.A.Igolkina et al., BernMix: the distribution of a weighted sum of independent Bernoulli random variables with different success probabilities

Authors

Anna Igolkina developed the BernMix package, e-mail.
Max Kovalev contributed in bernmix_int/bernmix_fourier.c.

License information

The BernMix package is open-sourced software licensed under the MIT license.