Publication: Stochastic comparisons of nonhomogeneous processes
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2000-02
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Abstract
The purpose of this paper is to describe various conditions on the parameters of pairs of nonhomogeneous Poisson or birth processes under which the corresponding epoch or inter-epoch times are stochastically ordered in various senses. We derive results involving the usual stochastic order, the multivariate hazard rate order, the multivariate likelihood ratio order, and the multivariate mean residual life order. A sample of applications involving generalized Yule processes, load-sharing models, and minimal repairs in reliability theory, illustrate the usefulness of the new results.
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Nonhomogeneous Poisson process, Nonhomogeneous birth process, Nonstationary birth process, Nonstationary birth process, Hazar rate order, Likelihood ratio order, Mean residual life order, Yule process, Load-sharing, Minimal repair, Dispersive order