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Let $𝐗=(X,Y)$ be a pair of exchangeable lifetimes whose dependence structure is described by an Archimedean survival copula, and let ${𝐗}_t=\left[(X-t,Y-t)\right|X>t,Y>t]$ denotes the corresponding pair of residual lifetimes after time $t$, with $t\ge 0$. This note deals with stochastic comparisons between $𝐗$ and ${𝐗}_t$: 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...

A weak version of the joint hazard rate order, useful to stochastically compare not independent random variables, has been recently defined and studied in [4]. In the present paper, further results on this order are proved and discussed. In particular, some statements dealing with the relationships between the jointweak hazard rate order and other stochastic orders are generalized to the case of non symmetric copulas, and its relations with some multivariate aging notions (studied in [2]) are presented....