Open Access
November, 1990 Poisson Approximation and the Chen-Stein Method
Richard Arratia, Larry Goldstein, Louis Gordon
Statist. Sci. 5(4): 403-424 (November, 1990). DOI: 10.1214/ss/1177012015


The Chen-Stein method of Poisson approximation is a powerful tool for computing an error bound when approximating probabilities using the Poisson distribution. In many cases, this bound may be given in terms of first and second moments alone. We present a background of the method and state some fundamental Poisson approximation theorems. The body of this paper is an illustration, through varied examples, of the wide applicability and utility of the Chen-Stein method. These examples include birthday coincidences, head runs in coin tosses, random graphs, maxima of normal variates and random permutations and mappings. We conclude with an application to molecular biology. The variety of examples presented here does not exhaust the range of possible applications of the Chen-Stein method.


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Richard Arratia. Larry Goldstein. Louis Gordon. "Poisson Approximation and the Chen-Stein Method." Statist. Sci. 5 (4) 403 - 424, November, 1990.


Published: November, 1990
First available in Project Euclid: 19 April 2007

zbMATH: 0955.62542
MathSciNet: MR1092983
Digital Object Identifier: 10.1214/ss/1177012015

Keywords: invariance principle , Poisson approximation , Stein's method

Rights: Copyright © 1990 Institute of Mathematical Statistics

Vol.5 • No. 4 • November, 1990
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