Residual Probability Function for Dependent Lifetimes

Mhamed Mesfioui and Mohamed Kayid
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Mhamed Mesfioui: Département de Mathématiques et D’informatique, Université du Québec à Trois-Rivières, 3351 Boulevard des Forges, Trois-Rivières, QC G9A 5H7, Canada
Mohamed Kayid: Department of Statistics and Operations Research, College of Science, King Saud University, P.O. Box 2455, Riyadh 11451, Saudi Arabia

Mathematics, 2021, vol. 9, issue 15, 1-13

Abstract: In this paper, the residual probability function is applied to analyze the survival probability of two used components relative to each other in the case when their lifetimes are dependent. The expression of the function by copulas has been derived along with some examples of particular copulas. The behaviour of the residual probability function in terms of the underlying dependence is also discussed. The residual probability order is also considered in the dependent case. In the class of Archimedean survival copulas, we prove that the residual probability order implies the usual stochastic order in the reversed direction, and the hazard rate order concludes the residual probability order.

Keywords: residual life; archimedean copula; stochastic order; dependence (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
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