Asymptotic approximations for coupon collectors

Anna Pósfai; Sándor Csörgő

doi:10.1556/sscmath.2008.1075

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Studia Scientiarum Mathematicarum Hungarica

Volume/Issue:: Volume 46: Issue 1

Asymptotic approximations for coupon collectors

Authors:

Anna Pósfai

Anna Pósfai University of Szeged Analysis and Stochastics Research Group of the Hungarian Academy of Sciences, Bolyai Institute Aradi vértanúk tere 1 H-6720 Szeged Hungary

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Sándor Csörgő

Sándor Csörgő University of Szeged Analysis and Stochastics Research Group of the Hungarian Academy of Sciences, Bolyai Institute Aradi vértanúk tere 1 H-6720 Szeged Hungary

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Pages:: 61–96

Online Publication Date:: 17 Oct 2008

Publication Date:: 01 Mar 2009

Article Category:: Journal Article

DOI:: https://doi.org/10.1556/sscmath.2008.1075

Keywords:: Primary 60F05; Coupon collector; waiting time; asymptotic approximation

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A collector samples with replacement a set of n ≧ 2 distinct coupons until he has n − m , 0 ≦ m < n , distinct coupons for the first time. We refine the limit theorems concerning the standardized random number of necessary draws if n → ∞ and m is fixed: we give a one-term asymptotic expansion of the distribution function in question, providing a better approximation of it, than the one given by the limiting distribution function, and proving in particular that the rate of convergence in these limiting theorems is of order (log n )/ n .

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Studia Scientiarum Mathematicarum Hungarica

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Frédéric MEUNIER (École des Ponts ParisTech)
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János PACH (Rényi Institute of Mathematics)
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Studia Scientiarum Mathematicarum Hungarica
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