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STOCHASTIC COMPARISONS OF NONHOMOGENEOUS PROCESSES

Published online by Cambridge University Press:  10 April 2001

Félix Belzunce ,
Rosa E. Lillo ,
José-Maria Ruiz  and
Moshe Shaked
Félix Belzunce
Affiliation:
Departmento Estadística e I.O., Universidad de Murcia, 30100 Espinardo (Murcia), Spain, E-mail: [email protected]
Rosa E. Lillo
Affiliation:
Departmento Estadística y Econometría, Universidad Carlos III de Madrid, 28903 Getafe, Madrid, Spain, E-mail: [email protected]
José-Maria Ruiz
Affiliation:
Departmento Estadística e I.O., Universidad de Murcia, 30100 Espinardo (Murcia), Spain, E-mail: [email protected]
Moshe Shaked
Affiliation:
Department of Mathematics, University of Arizona, Tucson, AZ 85721, E-mail: [email protected]
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Abstract

The purpose of this article is to describe various conditions on the parameters of pairs of nonhomogeneous Poisson or pure birth processes under which the corresponding epoch times or interepoch intervals are stochastically ordered in various senses. We derive results involving the usual stochastic order, the multivariate hazard rate order, the multivariate likelihood ratio order, as well as the dispersive and the mean residual life orders. A sample of applications involving generalized Yule processes, load-sharing models, and minimal repairs in reliability theory illustrate the usefulness of the new results.

Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 15 , Issue 2 , April 2001 , pp. 199 - 224
Copyright
© 2001 Cambridge University Press

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