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The Poisson-binomial distribution is useful in many applied problems inengineering, actuarial science, and data mining. The Poisson-binomialdistribution models the distribution of the sum of independent but notidentically distributed Bernoulli random variables whose success probabilitiesvary. In this paper, we extend the Poisson-binomial distribution to thegeneralized Poisson-binomial (GPB) distribution. The GPB distribution isdefined in cases where the Bernoulli variables can take any two arbitraryvalues instead of 0 and~1. The GPB distribution is useful in many areas such asvoting theory, actuarial science, warranty prediction, and probability theory.With few previous works studying the GPB distribution, we derive theprobability distribution via the discrete Fourier transform of thecharacteristic function of the distribution. We develop an efficient algorithmfor computing the distribution function, which uses the fast Fourier transform.We test the accuracy of the developed algorithm upon comparing it withenumeration-based exact method and the results from the binomial distribution.We also study the computational time of the algorithm in various parametersettings. Finally, we discus the factors affecting the computational efficiencyof this algorithm, and illustrate the use of the software package.

An Algorithm for Computing the Distribution Function of the Generalized Poisson-Binomial Distribution