Positive Dependence Properties of Conditionally Independent Random Lifetimes

Moshe Shaked and Fabio Spizzichino
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Moshe Shaked: Department of Mathematics, University of Arizona, Tucson, Arizona 85721
Fabio Spizzichino: Departimento di Matematica–Istituto “Guido Castelnuovo,” Università degli Studi di Roma “La Sapienza,” Piazzale Aldo Moro, 2, 00185 Roma, Italy

Mathematics of Operations Research, 1998, vol. 23, issue 4, pages 944-959

Abstract: Conditions under which conditionally independent random variables are positive dependent are described in this paper. For example, it is shown that if the conditionally independent random variables increase in the hazard rate sense in the condition, then they are WBF (weakened by failures). It is also shown that if the conditionally independent random variables increase in the likelihood ratio sense in the condition, then they are MTP 2 (multivariate totally positive of order 2). The results are given for the cases in which the condition is either a random variable or a random vector. Some applications in the areas of imperfect repair, budget allocation, random environments, and discrete-time filtering, illustrate the theory.

Keywords: Reliability theory; total positivity; multivariate total positivity; usual stochastic order; hazard rate order; association; imperfect repair; budget allocation; random environments; discrete-time filtering (search for similar items in EconPapers)
Date: 1998
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Persistent link: http://EconPapers.repec.org/RePEc:inm:ormoor:v:23:y:1998:i:4:p:944-959

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