On Probability Generating Functions for Waiting Time Distributions of Compound Patterns in a Sequence of Multistate Trials

Abstract

Probability generation functions of waiting time distributions of runs and patterns have been used successfully in various areas of statistics and applied probability. Usually, finding the probability generating function for the waiting time entails tedious mathematics and heavy probability theory, even for the case of simple pattern in a sequence of Bernoulli trials. In this talk, we will introduce a simple and general method of obtaining the probability generating functions for waiting time distributions of compound patterns by using the finite Markov chain imbedding techniques. Examples are given for illustrating our results.