Stein's method for compound Poisson approximation: The local approach
type: Item
instance of: scholarly article
title: Stein's method for compound Poisson approximation: The local approach
zbMATH Open document ID: 0816.60021
author: Małgorzata Roos
published in: The Annals of Applied Probability
publication date: 1995-07-06T00:00:00Z
review text: The author considers compound Poisson approximation by Stein's method. Exploiting existence of a natural dependence structure which is appropriate for example in stationary \(m\)-mixing [\textit{M. R. Leadbetter}, \textit{G. Lindgren} and \textit{H. Rootzén}, Extremes and related properties of random sequences and processes (1983; Zbl 0518.60021)] or local dependence [\textit{A. D. Barbour}, \textit{L. H. Y. Chen} and \textit{W.-L. Loh}, Ann. Probab. 20, No. 4, 1843-1866 (1992; Zbl 0765.60015)], the author gives a bound on the total variation distance between sums of dependent 0-1 valued random variables and the Poisson distribution. An analogue of this result for compound Poisson approximation is given and later it is applied to a reliability problem involving the number of isolated vertices in the rectangular lattice on the torus.
Mathematics Subject Classification ID: 60F05
Mathematics Subject Classification ID: 05C90
Mathematics Subject Classification ID: 60C05
Mathematics Subject Classification ID: 90B25
zbMATH DE Number: 731972
zbMATH Keywords: Stein-Chen method
zbMATH Keywords: compound Poisson approximation
zbMATH Keywords: reliability problem
zbMATH Keywords: isolated vertices
reviewed by: Adhir K. Basu
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1214/aoap/1177004910
OpenAlex ID: W2000855002
DOI: 10.1214/AOAP/1177004910
description: scientific article; zbMATH DE number 731972