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A Pólya Approximation to the Poisson-Binomial Law

Part of: Distribution theory Combinatorial probability Limit theorems

Published online by Cambridge University Press:  04 February 2016

Max Skipper
Max Skipper*
Affiliation:
University of Oxford and The University of Sydney
*
∗ Postal address: School of Mathematics and Statistics, The University of Sydney, Sydney, 2006, Australia. Email address: [email protected]
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Abstract

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Using Stein's method, we derive explicit upper bounds on the total variation distance between a Poisson-binomial law (the distribution of a sum of independent but not necessarily identically distributed Bernoulli random variables) and a Pólya distribution with the same support, mean, and variance; a nonuniform bound on the pointwise distance between the probability mass functions is also given. A numerical comparison of alternative distributional approximations on a somewhat representative collection of case studies is also exhibited. The evidence proves that no single one is uniformly most accurate, though it suggests that the Pólya approximation might be preferred in several parameter domains encountered in practice.

Keywords

Stein's methodPoisson-binomial approximationBernoulli variable

MSC classification

Primary: 62E17: Approximations to distributions (nonasymptotic)
Secondary: 60F05: Central limit and other weak theorems 60C99: None of the above, but in this section
Type
Research Article
Information
Journal of Applied Probability , Volume 49 , Issue 3 , September 2012 , pp. 745 - 757
Copyright
© Applied Probability Trust 

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