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September 2016 Optimality results for coupon collection
Mark Brown, Sheldon M. Ross
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J. Appl. Probab. 53(3): 930-937 (September 2016).

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 r1,…,rs, we are interested in finding 𝒑 that minimizes the expected time to obtain at least ri type-i coupons for all i=1,…,s. For example, for s=2, r1=1, and r2=r, we show that p1=(logr−log(logr))∕r is close to optimal.

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Mark Brown. Sheldon M. Ross. "Optimality results for coupon collection." J. Appl. Probab. 53 (3) 930 - 937, September 2016.

Information

Published: September 2016
First available in Project Euclid: 13 October 2016

zbMATH: 1353.60089
MathSciNet: MR3570105

Subjects:
Primary: 60K99

Keywords: increasing failure rate , likelihood ratio ordered , Multinomial trial , poissonization

Rights: Copyright © 2016 Applied Probability Trust

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Vol.53 • No. 3 • September 2016
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