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Zbl 1173.60008
Pósfai, Anna
Poisson approximation in a Poisson limit theorem inspired by coupon collecting. (English)
[J] J. Appl. Probab. 46, No. 2, 585-592 (2009). ISSN 0021-9002

This paper is concerned with a Poisson approximation for the distribution of sums of asymptotically negligible integer-valued random variables in the setting of row-wise independent triangular arrays. The author refines the classical Poisson convergence theorem of {\it B. V. Gnedenko} and {\it A. N. Kolmogorov} [Limit distributions for sums of independent random variables. Translated from the Russian by K. L. Chung. Cambridge: Addison-Wesley Publishing Company (1954; Zbl 0056.36001)]. The upper and lower error bounds are expressed in terms of the total variation distance. \par The results are applied to the case of the coupon collector's problem when the distribution of the collector's waiting time is asymptotically Poisson.
[Wiesław Dziubdziela (Kielce)]

MSC 2000:: *60F05 Weak limit theorems
62E17 Approximations to statistical distributions (nonasymptotic)
62E20 Asymptotic distribution theory in statistics

Keywords: Poisson limit theorem; Poisson approximation; total variation distance; coupon collecting

Citations: Zbl 0056.36001

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