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Poisson perturbations

Published online by Cambridge University Press:  15 August 2002

Andrew D. Barbour  and
Aihua Xia
Andrew D. Barbour
Affiliation:
Abteilung für Angewandte Mathematik, Universität Zürich, Winterthurerstrasse 190, 8057 Zürich, Switzerland; [email protected].
Aihua Xia
Affiliation:
Department of Statistics, School of Mathematics, The University of New South Wales, Sydney 2052, Australia.
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Abstract

Stein's method is used to prove approximations in total variation to thedistributions of integer valued random variables by (possibly signed)compound Poisson measures. For sums of independent random variables,the results obtained are very explicit, and improve upon earlierwork of Kruopis (1983) and Čekanavičius (1997);coupling methods are used to derive concrete expressions for the errorbounds. An example is given to illustrate the potential for applicationto sums of dependent random variables.

Keywords

Stein's methodsigned compound Poisson measuretotal variationcoupling.
Type
Research Article
Information
ESAIM: Probability and Statistics , Volume 3 , 1999 , pp. 131 - 150
Copyright
© EDP Sciences, SMAI, 1999

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