Journal of Applied Probability

A generalized coupon collector problem

Weiyu Xu and A. Kevin Tang

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This paper presents an analysis of a generalized version of the coupon collector problem, in which the collector receives d coupons each run and chooses the least-collected coupon so far. In the asymptotic case when the number of coupons n goes to infinity, we show that, on average, (nlogn) / d + (n / d)(m - 1)log logn + O(mn) runs are needed to collect m sets of coupons. An exact algorithm is also developed for any finite case to compute the exact mean number of runs. Numerical examples are provided to verify our theoretical predictions.

Article information

J. Appl. Probab., Volume 48, Number 4 (2011), 1081-1094.

First available in Project Euclid: 16 December 2011

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 60G70: Extreme value theory; extremal processes
Secondary: 60C05: Combinatorial probability

Coupon collector problem expected run state-space representation wireless communication opportunistic scheduling


Xu, Weiyu; Tang, A. Kevin. A generalized coupon collector problem. J. Appl. Probab. 48 (2011), no. 4, 1081--1094. doi:10.1239/jap/1324046020.

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