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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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