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Optimality Results for Coupon Collection

Part of: Special processes

Published online by Cambridge University Press:  24 October 2016

Mark Brown  and
Sheldon M. Ross
Mark Brown*
Affiliation:
Columbia University
Sheldon M. Ross*
Affiliation:
University of Southern California
*
* Postal address: Department of Statistics, Columbia University, New York, NY 10027, USA. Email address: mb2484@columbia.edu
** Postal address: Department of Industrial and Systems Engineering, University of Southern California, Los Angeles, CA 90089, USA. Email address: smross@usc.edu
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Abstract

We consider the coupon collection problem, where each coupon is one of the types 1,…,s with probabilities given by a vector 𝒑. For specified numbers r 1,…,r s , we are interested in finding 𝒑 that minimizes the expected time to obtain at least r i type-i coupons for all i=1,…,s. For example, for s=2, r 1=1, and r 2=r, we show that p 1=(logr−log(logr))∕r is close to optimal.

Keywords

Multinomial trialPoissonizationlikelihood ratio orderedincreasing failure rate

MSC classification

Primary: 60K99: None of the above, but in this section
Type
Research Papers
Information
Journal of Applied Probability , Volume 53 , Issue 3 , September 2016 , pp. 930 - 937
Copyright
Copyright © Applied Probability Trust 2016 

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References

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