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Poisson Approximation in a Poisson Limit Theorem Inspired by Coupon Collecting

Part of: Limit theorems Distribution theory

Published online by Cambridge University Press:  14 July 2016

Anna Pósfai
Anna Pósfai*
Affiliation:
University of Szeged
*
∗Postal address: Analysis and Stochastics Research Group of the Hungarian Academy of Sciences, Bolyai Institute, University of Szeged, Aradi vértanúuk tere 1, Szeged 6720, Hungary. Email address: posfai@math.u-szeged.hu
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Abstract

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In this paper we refine a Poisson limit theorem of Gnedenko and Kolmogorov (1954): we determine the error order of a Poisson approximation for sums of asymptotically negligible integer-valued random variables that converge in distribution to the Poisson law. As an application of our results, we investigate the case of the coupon collector's problem when the distribution of the collector's waiting time is asymptotically Poisson.

Keywords

Poisson limit theoremPoisson approximationtotal variation distancecoupon collecting

MSC classification

Secondary: 60F05: Central limit and other weak theorems 62E17: Approximations to distributions (nonasymptotic) 62E20: Asymptotic distribution theory
Type
Research Article
Information
Journal of Applied Probability , Volume 46 , Issue 2 , June 2009 , pp. 585 - 592
Copyright
Copyright © Applied Probability Trust 2009 

References

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