Inferring Bayesian ageing notions of bivariate distributions from univariate ageing

Abstract

In the present work, we attempt to identify classes of bivariate distributions of random vector (X, Y) in which ageing concepts like increasing hazard rates, decreasing mean residual life, etc. can be inferred from univariate ageing properties of a random variable Z whose distribution specifies the dependence structure between the components of (X, Y). It is shown that a family of bivariate exponential distributions and those obtained by monotone transformations from them, and the time-transformed exponential models satisfy this property. The bivariate distributions considered here are exchangeable and the notions of ageing are interpreted in a Bayesian sense.