Journal of Applied Probability

A generalized coupon collector problem

Weiyu Xu and A. Kevin Tang

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Abstract

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

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

Dates
First available in Project Euclid: 16 December 2011

Permanent link to this document
https://projecteuclid.org/euclid.jap/1324046020

Digital Object Identifier
doi:10.1239/jap/1324046020

Mathematical Reviews number (MathSciNet)
MR2896669

Zentralblatt MATH identifier
1239.60030

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

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

Citation

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


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