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On Aging Properties for Bivariate Lifetimes with Archimedean Survival Copulas

Let X = (X, Y ) be a pair of exchangeable lifetimes whose dependence structure is described by an Archimedean copula, and let Xt = [(X − t, Y − t)|X > t, Y > t] denotes the corresponding pair of residual lifetimes after time t, with t ≥ 0. This note deals with stochastic comparisons between X and Xt: some examples where they are stochastically ordered are provided and discussed. This work is mainly based on, and related to, recent papers by Bassan and Spizzichino (2005a and 2005b), Averous and Dortet–Bernadet (2000), Charpentier (2003 and 2006) and Oakes (2005).