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Total Positivity of Markov Chains and the Failure Rate Character of Some First Passage Times

Part of: Markov processes Survival analysis and censored data Distribution theory

Published online by Cambridge University Press:  01 July 2016

Shiowjen Lee  and
J. Lynch
Shiowjen Lee*
Affiliation:
University of West Florida
J. Lynch*
Affiliation:
University of South Carolina
*
∗ Postal address; Department of Mathematics and Statistics, The University of West Florida, FL32514-5750, USA. Research partially supported by an NSF/EPSCOR grant.
∗∗ Postal address: Department of Statistics, University of South Carolina, Columbia, SC 29208, USA. Research partially supported by an NSF/EPSCOR grant and NSF grant no. DMS-9503104.
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Abstract

It is shown that totally positive order 2 (TP2) properties of the infinitesimal generator of a continuous-time Markov chain with totally ordered state space carry over to the chain's transition distribution function. For chains with such properties, failure rate characteristics of the first passage times are established. For Markov chains with partially ordered state space, it is shown that the first passage times have an IFR distribution under a multivariate total positivity condition on the transition function.

Keywords

FAILURE RATELOG-CONCAVITYTOTAL POSITIVITYMULTIVARIATE TOTAL POSITIVITY

MSC classification

Primary: 62E10: Characterization and structure theory
Secondary: 60J20: Applications of Markov chains and discrete-time Markov processes on general state spaces (social mobility, learning theory, industrial processes, etc.) 62N05: Reliability and life testing
Type
General Applied Probability
Information
Advances in Applied Probability , Volume 29 , Issue 3 , September 1997 , pp. 713 - 732
Copyright
Copyright © Applied Probability Trust 1997 

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