# On univariate and bivariate aging for dependent lifetimes with Archimedean survival copulas

Kybernetika (2008)

- Volume: 44, Issue: 6, page 795-806
- ISSN: 0023-5954

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topPellerey, Franco. "On univariate and bivariate aging for dependent lifetimes with Archimedean survival copulas." Kybernetika 44.6 (2008): 795-806. <http://eudml.org/doc/33965>.

@article{Pellerey2008,

abstract = {Let $\mbox\{$X$\} = (X,Y)$ be a pair of exchangeable lifetimes whose dependence structure is described by an Archimedean survival copula, and let $\mbox\{$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 $\mbox\{$X$\}$ and $\mbox\{$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].},

author = {Pellerey, Franco},

journal = {Kybernetika},

keywords = {stochastic orders; positive dependence orders; residual lifetimes; NBU; IFR; bivariate aging; survival copulas; stochastic orders; positive dependence orders; residual lifetimes; NBU; IFR; bivariate aging; survival copulas},

language = {eng},

number = {6},

pages = {795-806},

publisher = {Institute of Information Theory and Automation AS CR},

title = {On univariate and bivariate aging for dependent lifetimes with Archimedean survival copulas},

url = {http://eudml.org/doc/33965},

volume = {44},

year = {2008},

}

TY - JOUR

AU - Pellerey, Franco

TI - On univariate and bivariate aging for dependent lifetimes with Archimedean survival copulas

JO - Kybernetika

PY - 2008

PB - Institute of Information Theory and Automation AS CR

VL - 44

IS - 6

SP - 795

EP - 806

AB - Let $\mbox{$X$} = (X,Y)$ be a pair of exchangeable lifetimes whose dependence structure is described by an Archimedean survival copula, and let $\mbox{$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 $\mbox{$X$}$ and $\mbox{$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].

LA - eng

KW - stochastic orders; positive dependence orders; residual lifetimes; NBU; IFR; bivariate aging; survival copulas; stochastic orders; positive dependence orders; residual lifetimes; NBU; IFR; bivariate aging; survival copulas

UR - http://eudml.org/doc/33965

ER -

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