The Poisson Binomial Distribution— Old & New
Wenpin Tang, Fengmin Tang
Abstract
This is an expository article on the Poisson binomial distribution. We review lesser known results and recent progress on this topic, including geometry of polynomials and distribution learning. We also provide examples to illustrate the use of the Poisson binomial machinery. Some open questions of approximating rational fractions of the Poisson binomial are presented.
Topics & Concepts
Poisson binomial distributionPoisson distributionBinomial distributionNegative binomial distributionCount dataBinomial (polynomial)MathematicsCompound Poisson distributionZero-inflated modelDistribution (mathematics)Negative multinomial distributionApplied mathematicsContinuity correctionBeta-binomial distributionStatisticsPoisson regressionMathematical analysisMedicineEnvironmental healthPopulationAdvanced Combinatorial MathematicsAdvanced Mathematical IdentitiesBayesian Methods and Mixture Models