A new method for obtaining sharp compound Poisson approximation error estimates for sums of locally dependent random variables
type: Item
instance of: scholarly article
title: A new method for obtaining sharp compound Poisson approximation error estimates for sums of locally dependent random variables
zbMATH Open document ID: 1266.60039
DOI: 10.3150/09-BEJ201
author: Michael V. Boutsikas
author: Eutichia Vaggelatou
published in: Bernoulli
publication date: 2012-09-19T00:00:00Z
full work available at URL: https://arxiv.org/abs/1010.1625
full work available at URL: https://projecteuclid.org/euclid.bj/1274821072
review text: The authors develop probabilistic techniques (the employment of ideal probability metrics, stochastic orders and the coupling method) to establish sharp bounds for the total variation distance between the distribution of the sum of integer-valued independent or \(k\)-dependent random variables and appropriate Poisson or compound Poisson law. These bounds contain the smoothness factor, i.e., the \(L_1\)-norm of the second-order difference of the probability distribution function of the approximating law. The obtained results are compared with well-known ones proven by the Stein-Chen method. Some examples concerning the appearances of rare runs in a sequence of Bernoulli trials are provided to illustrate the effectiveness of the paper's main results.
reviewed by: Alexander V. Bulinski
Mathematics Subject Classification ID: 60F05
Mathematics Subject Classification ID: 60G50
zbMATH DE Number: 6083965
zbMATH Keywords: sums of independent integer-valued random variables
zbMATH Keywords: \(k\)-dependence
zbMATH Keywords: Poisson (compound) approximation
zbMATH Keywords: convergence rate
zbMATH Keywords: total variation distance
zbMATH Keywords: ideal metric
MaRDI profile type: Publication
arXiv ID: 1010.1625
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OpenAlex ID: W3100253441
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description: scientific article; zbMATH DE number 6083965