No. 949

Title:

On generating functions of waiting times and numbers of occurrences of compound patterns in a sequence of multi-state trials

Author(s):

Kiyoshi, Inoue (Seikei University);
Sigeo, Aki (Kansai University)

Key words:

Compound pattern, multi-state trials, sooner/later waiting time, runs, enumeration schemes, probability function, probability generating function, double generating function.

Abstract:

    In this paper, we study two distributions, i.e., the distribution of the waiting time until given numbers of occurrences of compound patterns and the distribution of the numbers of occurrences of compound patterns in a fixed number of trials. We elucidate the interrelation between the aforementioned two distributions in terms of the generating functions. We provide the perspectives on the problems related to the compound patterns in statistics and probability. As an application, the waiting time problems of runs of specified length is considered in order to illustrate how the distributions of waiting times can be derived through our theoretical results. \par