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A unification of some approaches to Poisson approximation

Published online by Cambridge University Press:  14 July 2016

Hans-Jürgen Witte
Hans-Jürgen Witte*
Affiliation:
University of Oldenburg
*
∗ Postal address: Universität Oldenburg, Fachbereich 6 Mathematik, Postfach 2503, D-2900 Oldenburg, W. Germany.
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Abstract

Let Sn be a sum of independent random variables. For the approximation of Sn by a Poisson random variable Y with the same mean, the complex analysis approaches based on generating functions and the semigroup approach are presented in a unified setting which permits us to refine Kerstan's complex analysis approach obtaining considerably sharper upper bounds for some metric distances of Sn and Y. These results are applied to some special Sn counting the records of an i.i.d. sequence of random variables which is important to various applied problems, for instance the secretary problem.

Keywords

TOTAL VARIATION DISTANCEKOLMOGOROV METRICFORTET–MOURIER METRICGENERATING FUNCTIONSSEMIGROUPS

Information

Type
Research Papers
Information
Journal of Applied Probability , Volume 27 , Issue 3 , September 1990 , pp. 611 - 621
Copyright
Copyright © Applied Probability Trust 1990 

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