期刊
MATHEMATICS
卷 9, 期 15, 页码 -出版社
MDPI
DOI: 10.3390/math9151782
关键词
residual life; archimedean copula; stochastic order; dependence
类别
资金
- King Saud University, Riyadh, Saudi Arabia [RSP-2021/392]
This paper applies the residual probability function to analyze the survival probability of two used components relative to each other, discussing the behavior in terms of underlying dependence and considering the residual probability order in the dependent case. The study in the class of Archimedean survival copulas shows that the residual probability order implies the usual stochastic order in the reversed direction and the hazard rate order concludes the residual probability order.
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.
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