A non-uniform bound on binomial approximation with w-functions

K. Teerapabolarn

Communications in Statistics - Theory and Methods, 2022, vol. 51, issue 23, 8391-8405

Abstract: We use Stein’s method and w-functions to determine a non-uniform bound for approximating the distribution of a non-negative integer-valued random variable X by a binomial distribution with parameters n∈N and p=1−q∈(0,1), where np=E(X). Additionally, we also give a new improvement of non-uniform bound for the distance between the cumulative distribution function of X and a binomial cumulative distribution function. For applications, we use the obtained result to approximate the hypergeometric, negative hypergeometric, Pólya and beta binomial distributions.

Date: 2022
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DOI: 10.1080/03610926.2021.1896733

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