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Compound Poisson Approximation for Dissociated Random Variables via Stein's Method

Published online by Cambridge University Press:  01 July 1999

PETER EICHELSBACHER
Affiliation:
Fakultät für Mathematik, Universität Bielefeld, Postfach 100131, D-33501 Bielefeld, Germany (e-mail: peter@mathematik.uni-bielefeld.de)
MAŁGORZATA ROOS
Affiliation:
Biostatistik, ISPM, Universität Zürich, Sumatrastrasse 30, CH-8006 Zürich, Switzerland (e-mail: mroos@ifspm.unizh.ch)

Abstract

In the present paper we consider compound Poisson approximation by Stein's method for dissociated random variables. We present some applications to problems in system reliability. In particular, our examples have the structure of an incomplete U-statistics. We mainly apply techniques from Barbour and Utev, who gave new bounds for the solutions of the Stein equation in compound Poisson approximation in two recent papers.

Type
Research Article
Copyright
1999 Cambridge University Press

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