Award Date

5-2010

Degree Type

Thesis

Degree Name

Master of Science in Mathematical Science

Department

Mathematical Sciences

First Committee Member

Hokwon Cho, Chair

Second Committee Member

Malwane Ananda

Third Committee Member

Sandra Catlin

Graduate Faculty Representative

Evangelos Yfantis

Number of Pages

40

Abstract

The coupon collection problem is one of the most studied problems in statistics. It is the problem of collecting r (r<∞) distinct coupons one by one from k different kinds (k<∞) of coupons. We note that this is equivalent to the classical occupancy problem which involves the random allocation of r distinct balls into k distinct cells. Although the problem was first introduced centuries ago, it is still actively investigated today. Perhaps its greatest feature is its versatility, numerous approaches, and countless variations. For this reason, we are particularly interested in creating a classification system for the many generalizations of the coupon collection problem. In this thesis, we will introduce models that will be able to categorize these generalizations. In addition, we calculate the waiting time for the models under consideration. Our approach is to use the Dirichlet Type II integral. We compare our calculations to the ones obtained through Monte Carlo simulation. Our results will show that our models and the method used to find the waiting times are ideal for solving problems of this type.

Keywords

Collection; Coupon; Dirichlet; Integrals; Dirichlet; Monte Carlo method; Probabilities

Disciplines

Probability | Statistics and Probability

Language

English


Included in

Probability Commons

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