No. 1012

Title:

On generalized birthday and coupon collection problems

Author(s):

Kiyoshi, Inoue (Faculty of Economics, Seikei University);
Sigeo, Aki (Faculty of Engineering, Kansai University)

Key words:

Birthday problem, coupon collector's problem, urn model, generating function, waiting time problem

Abstract:

    In this paper, we consider generalizations of two classical probability problems: the birthday problem and the coupon collector's problem. These problems are discussed in terms of urn models and captured through generating functions. Some methods for the study of the problems are presented. Furthermore, we also formulate the generalized birthday and coupon collector's problems as the waiting time problems. In each case, numerical examples are given in order to illustrate the feasibility of our methods.