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The coupon subset collection problem

Part of: Combinatorial probability Probabilistic methods, simulation and stochastic differential equations

Published online by Cambridge University Press:  14 July 2016

Ilan Adler  and
Sheldon M. Ross
Ilan Adler*
Affiliation:
University of California, Berkeley
Sheldon M. Ross*
Affiliation:
University of California, Berkeley
*
∗ Postal address: Department of Industrial Engineering and Operations Research, University of California, Berkeley, 94720, USA.
∗ Postal address: Department of Industrial Engineering and Operations Research, University of California, Berkeley, 94720, USA.
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Abstract

The coupon subset collection problem is a generalization of the classical coupon collecting problem, in that rather than collecting individual coupons we obtain, at each time point, a random subset of coupons. The problem of interest is to determine the expected number of subsets needed until each coupon is contained in at least one of these subsets. We provide bounds on this number, give efficient simulation procedures for estimating it, and then apply our results to a reliability problem.

Keywords

Coupon collecting simulationcombinatorial probabilityboundsexchangeable caserandomly chosen subsetsreliability application

MSC classification

Primary: 60C05: Combinatorial probability
Secondary: 65C05: Monte Carlo methods
Type
Short Communications
Information
Journal of Applied Probability , Volume 38 , Issue 3 , September 2001 , pp. 737 - 746
Copyright
Copyright © by the Applied Probability Trust 2001 

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