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Some applications of the Stein-Chen method for proving Poisson convergence

Published online by Cambridge University Press:  01 July 2016

A. D. Barbour  and
Lars Holst
A. D. Barbour*
Affiliation:
Universität Zürich
Lars Holst*
Affiliation:
Uppsala University
*
∗Postal address: Institut für Angewandte Mathematik, Universität Zürich, Rämistrasse 74, CH-8001 Zürich, Switzerland.
∗∗ Postal address: Uppsala University, Department of Mathematics, Thunbergsv. 3, S-752 38 Uppsala, Sweden.
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Abstract

Let W be a sum of Bernoulli random variables and Uλ a Poisson random variable having the same mean λ = EW. Using the Stein-Chen method and suitable couplings, general upper bounds for the variational distance between W and Uλ are given. These bounds are applied to problems of occupancy, using sampling with and without replacement and Pólya sampling, of capture-recapture, of spacings and of matching and ménage.

Keywords

VARIATIONAL DISTANCECOUPLINGOCCUPANCYCAPTURE–RECAPTURESPACINGSMATCHING
Type
Research Article
Information
Advances in Applied Probability , Volume 21 , Issue 1 , March 1989 , pp. 74 - 90
Copyright
Copyright © Applied Probability Trust 1989 

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