## Journal of Applied Probability

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

### Optimality results for coupon collection

Mark Brown and Sheldon M. Ross

#### 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}=(log*r*−log(log*r*))∕*r* is close to optimal.

#### Article information

**Source**

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

**Dates**

First available in Project Euclid: 13 October 2016

**Permanent link to this document**

https://projecteuclid.org/euclid.jap/1476370787

**Mathematical Reviews number (MathSciNet)**

MR3570105

**Zentralblatt MATH identifier**

1353.60089

**Subjects**

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

**Keywords**

Multinomial trial Poissonization likelihood ratio ordered increasing failure rate

#### Citation

Brown, Mark; Ross, Sheldon M. Optimality results for coupon collection. J. Appl. Probab. 53 (2016), no. 3, 930--937. https://projecteuclid.org/euclid.jap/1476370787