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On univariate and bivariate aging for dependent lifetimes with Archimedean survival copulas. (English) Zbl 1181.62166
Let $$\mathbf{X}=(X,Y)$$ be a vector of exchangeable random life times, and let $\mathbf{X}_t=[(X-t,Y-t)\,|\,X>t,Y>t]$ be the vector of the corresponding residual life times at time $$t$$, with $$t>0$$. Suppose that the dependence structure of $$(X,Y)$$ is described by an Archimedean survival copula. The author provides sufficient conditions for the comparison of $$\mathbf{X}$$ and $$\mathbf{X}_t$$ in the usual and in the lower orthant stochastic orders.

##### MSC:
 62N05 Reliability and life testing 60E15 Inequalities; stochastic orderings 62H05 Characterization and structure theory for multivariate probability distributions; copulas
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