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Waiting time distributions of competing patterns in higher-order Markovian sequences

Part of: Distribution theory - Probability Markov processes

Published online by Cambridge University Press:  14 July 2016

John A. D. Aston  and
Donald E. K. Martin
John A. D. Aston*
Affiliation:
Academia Sinica, Taiwan
Donald E. K. Martin*
Affiliation:
Howard University and U.S. Census Bureau
*
∗Postal address: Institute of Statistical Science, Academia Sinica, 128 Academia Road, Sec. 2, Taipei, 115, Taiwan, Republic of China. Email address: [email protected]
∗∗Postal address: Department of Mathematics, Howard University, Washington, DC 20059, USA. Email address: [email protected]
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Abstract

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Competing patterns are compound patterns that compete to be the first to occur pattern-specific numbers of times. They represent a generalisation of the sooner waiting time problem and of start-up demonstration tests with both acceptance and rejection criteria. Through the use of finite Markov chain imbedding, the waiting time distribution of competing patterns in multistate trials that are Markovian of a general order is derived. Also obtained are probabilities that each particular competing pattern will be the first to occur its respective prescribed number of times, both in finite time and in the limit.

Keywords

Multistate trialsfinite Markov chain imbeddingsooner waiting time distributionstart-up demonstration testcompeting compound patterns

MSC classification

Primary: 60E05: Distributions
Secondary: 60J05: Discrete-time Markov processes on general state spaces
Type
Research Papers
Information
Journal of Applied Probability , Volume 42 , Issue 4 , December 2005 , pp. 977 - 988
Copyright
© Applied Probability Trust 2005 

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