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On ordered series and later waiting time distributions in a sequence of Markov dependent multistate trials

Part of: Distribution theory - Probability Markov processes

Published online by Cambridge University Press:  14 July 2016

James C. Fu  and
Yung-Ming Chang
James C. Fu*
Affiliation:
University of Manitoba
Yung-Ming Chang*
Affiliation:
National University of Kaohsiung
*
∗Postal address: Department of Statistics, University of Manitoba, Winnipeg, Manitoba R3T 2N2, Canada. Email address: james_fu@umanitoba.ca
∗Postal address: Department of Applied Mathematics, National University of Kaohsiung, Kaohsiung 811, Taiwan
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Abstract

The sooner and later waiting time problems have been extensively studied and applied in various areas of statistics and applied probability. In this paper, we give a comprehensive study of ordered series and later waiting time distributions of a number of simple patterns with respect to nonoverlapping and overlapping counting schemes in a sequence of Markov dependent multistate trials. Exact distributions and probability generating functions are derived by using the finite Markov chain imbedding technique. Examples are given to illustrate our results.

Keywords

Compound patternordered series patternlater waiting timeMarkov chain imbeddingtransition probability matrixprobability generating function

MSC classification

Primary: 60E05: Distributions
Secondary: 60J10: Markov chains (discrete-time Markov processes on discrete state spaces)
Type
Research Papers
Information
Journal of Applied Probability , Volume 40 , Issue 3 , September 2003 , pp. 623 - 642
Copyright
Copyright © Applied Probability Trust 2003 

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