On a new multivariate IFR ageing notion based on the standard construction

Abstract

Many criteria of ageing for random variables or vectors have been proposed in the literature over many years. For instance, a random variable is increasing in failure rate (IFR) if, and only if, it can be ordered with an exponentially distributed random variable in the univariate convex transform order proposed by van Zwet [35]. Recently, Belzunce et al. [9] introduced a multivariate generalization of the convex transform order. In this work, we proposed a new multivariate IFR notion for multivariate distributions based on comparisons in this new order with a properly defined exponentially distributed random vector. Properties, applications and illustrations of this new notion are given as well.