Stochastic comparisons of mixtures of convexly ordered distributions with applications in reliability theory

✍ Scribed by Félix Belzunce; Moshe Shaked

• Publisher: Elsevier Science
• Year: 2001
• Tongue: English
• Weight: 116 KB
• Volume: 53
• Category: Article
• ISSN: 0167-7152
• DOI: 10.1016/s0167-7152(01)00030-x

✦ Synopsis

In this paper we ÿrst obtain several results which compare mixtures of distributions in the (increasing) convex and concave stochastic orders. We employ these results to derive relatively weak conditions on the intensity functions of a pair of nonhomogeneous Poisson processes (in fact, on the distribution functions that are associated with these intensity functions) under which the corresponding epoch times of the two nonhomogeneous Poisson processes are ordered in the increasing convex stochastic order. Applications include bounds on the epoch times of a nonhomogeneous Poisson process whose intensity function is the hazard rate function of a new better than used in expectation (new worse than used in expectation) random variable, and the increasing convex ordering of times to the ÿrst perfect repair in a Bayesian imperfect repair model.