Approximating the number of successes in independent trials: binomial versus Poisson
type: Item
instance of: scholarly article
title: Approximating the number of successes in independent trials: binomial versus Poisson
zbMATH Open document ID: 1019.60018
author: Aihua Xia
author: Kwok Pui Choi
published in: The Annals of Applied Probability
publication date: 2003-05-06T00:00:00Z
review text: The authors consider approximations to the distribution of a sum \(\sum^n_{i=1}\) of independent Bernoulli random variables \(X_i\sim \text{Be}(p_i)\) by binomial and Poisson random distributions with the same mean \(\lambda= \sum^n_{i=1} p_i\). They show that total variation approximation is better using the binomial distribution \(\text{Bi}(k,\lambda/k)\) than that using \(\text{Bi}(m,\lambda/m)\) for any \(m> k\), including the Poisson case corresponding to \(m=\infty\), for \(k\) given explicitly in terms of the parameters of the problem; frequently, \(k=n\). They conjecture that the result is actually true for another, smaller value of \(k\).
Mathematics Subject Classification ID: 60F05
Mathematics Subject Classification ID: 60E15
zbMATH DE Number: 1906159
zbMATH Keywords: total variation approximation
reviewed by: A. D. Barbour
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1214/aoap/1037125856
OpenAlex ID: W2007533680
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DOI: 10.1214/AOAP/1037125856
description: scientific article; zbMATH DE number 1906159