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2013 Asymptotics of the rising moments for the coupon collector's problem
Aristides Doumas, Vassilis Papanicolaou
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Electron. J. Probab. 18: 1-15 (2013). DOI: 10.1214/EJP.v18-1746


We develop techniques of computing the asymptotics of the moments of the number $T_N$ of coupons that a collector has to buy in order to find all $N$ existing different coupons as $N\rightarrow \infty.$ The probabilities (occurring frequencies) of the coupons can be quite arbitrary. After mentioning the case where the coupon probabilities are equal we consider the general case (of unequal probabilities). For a large class of distributions (after adopting a dichotomy) we arrive at the leading behavior of the moments of $T_N$ as $N\rightarrow \infty.$ We also present various illustrative examples.


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Aristides Doumas. Vassilis Papanicolaou. "Asymptotics of the rising moments for the coupon collector's problem." Electron. J. Probab. 18 1 - 15, 2013.


Accepted: 22 March 2013; Published: 2013
First available in Project Euclid: 4 June 2016

zbMATH: 1283.60035
MathSciNet: MR3040551
Digital Object Identifier: 10.1214/EJP.v18-1746

Primary: 60F05
Secondary: 60F99

Keywords: Coupon collector's problem , higher asymptotics

Vol.18 • 2013
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