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January, 1989 Two Moments Suffice for Poisson Approximations: The Chen-Stein Method
R. Arratia, L. Goldstein, L. Gordon
Ann. Probab. 17(1): 9-25 (January, 1989). DOI: 10.1214/aop/1176991491

Abstract

Convergence to the Poisson distribution, for the number of occurrences of dependent events, can often be established by computing only first and second moments, but not higher ones. This remarkable result is due to Chen (1975). The method also provides an upper bound on the total variation distance to the Poisson distribution, and succeeds in cases where third and higher moments blow up. This paper presents Chen's results in a form that is easy to use and gives a multivariable extension, which gives an upper bound on the total variation distance between a sequence of dependent indicator functions and a Poisson process with the same intensity. A corollary of this is an upper bound on the total variation distance between a sequence of dependent indicator variables and the process having the same marginals but independent coordinates.

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R. Arratia. L. Goldstein. L. Gordon. "Two Moments Suffice for Poisson Approximations: The Chen-Stein Method." Ann. Probab. 17 (1) 9 - 25, January, 1989. https://doi.org/10.1214/aop/1176991491

Information

Published: January, 1989
First available in Project Euclid: 19 April 2007

zbMATH: 0675.60017
MathSciNet: MR972770
Digital Object Identifier: 10.1214/aop/1176991491

Subjects:
Primary: 60F05
Secondary: 60F17

Keywords: coupling , inclusion-exclusion , invariance principle , method of moments , Poisson approximation , Poisson process

Rights: Copyright © 1989 Institute of Mathematical Statistics

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Vol.17 • No. 1 • January, 1989
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