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Poisson perturbations

Published online by Cambridge University Press:  15 August 2002

Andrew D. Barbour
Abteilung für Angewandte Mathematik, Universität Zürich, Winterthurerstrasse 190, 8057 Zürich, Switzerland;
Aihua Xia
Department of Statistics, School of Mathematics, The University of New South Wales, Sydney 2052, Australia.
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Stein's method is used to prove approximations in total variation to the distributions 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 earlier work of Kruopis (1983) and Čekanavičius (1997); coupling methods are used to derive concrete expressions for the error bounds. An example is given to illustrate the potential for application to sums of dependent random variables.

Research Article
© EDP Sciences, SMAI, 1999

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