Journal of Applied Probability

Optimality results for coupon collection

Mark Brown and Sheldon M. Ross

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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.

Article information

J. Appl. Probab., Volume 53, Number 3 (2016), 930-937.

First available in Project Euclid: 13 October 2016

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Mathematical Reviews number (MathSciNet)

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Primary: 60K99: None of the above, but in this section

Multinomial trial Poissonization likelihood ratio ordered increasing failure rate


Brown, Mark; Ross, Sheldon M. Optimality results for coupon collection. J. Appl. Probab. 53 (2016), no. 3, 930--937.

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