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Title: On univariate and bivariate aging for dependent lifetimes with Archimedean survival copulas (English)
Author: Pellerey, Franco
Language: English
Journal: Kybernetika
ISSN: 0023-5954
Volume: 44
Issue: 6
Year: 2008
Pages: 795-806
Summary lang: English
Category: math
Summary: Let $\mbox{\boldmath$X$} = (X,Y)$ be a pair of exchangeable lifetimes whose dependence structure is described by an Archimedean survival copula, and let $\mbox{\boldmath$X$}_t= [(X-t,Y-t) \vert X>t, Y>t]$ denotes the corresponding pair of residual lifetimes after time $t$, with $t \ge 0$. This note deals with stochastic comparisons between $\mbox{\boldmath$X$}$ and $\mbox{\boldmath$X$}_t$: we provide sufficient conditions for their comparison in usual stochastic and lower orthant orders. Some of the results and examples presented here are quite unexpected, since they show that there is not a direct correspondence between univariate and bivariate aging. This work is mainly based on, and related to, recent papers by Bassan and Spizzichino ([4] and [5]), Averous and Dortet-Bernadet [2], Charpentier ([6] and [7]) and Oakes [16]. (English)
Keyword: stochastic orders
Keyword: positive dependence orders
Keyword: residual lifetimes
Keyword: NBU
Keyword: IFR
Keyword: bivariate aging
Keyword: survival copulas
MSC: 60E15
MSC: 60K10
MSC: 62H05
MSC: 62N05
idZBL: Zbl 1181.62166
idMR: MR2488907
Date available: 2009-09-24T20:40:18Z
Last updated: 2013-09-21
Stable URL:
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