Probabilistic properties of discrete mean and variance reversed residual lifetime functions

Abstract

The random variable () () t = where X is a discrete random variable. Besides similar results for discrete and continuous lifetime distributions, relationships with its mean, monotonicity and the associated ageing classes of distributions are obtained for discrete cases. Furthermore, some characterization results about the class of increasing variance reversed residual lifetime distributions based on the mean reversed residual lifetime and the reversed residual coefficient of variation, are presented and the lower and upper bound for them are achieved. Also, we will investigate the connection between discrete increasing variance reversed residual lifetimes and other classes of distributions. I will provide two simple characterizations of the increasing discrete variance reversed residual lifetime class of distributions based on discrete mean and variance reversed residual lifetime. Since Geometric, Weibull, Shift Geometric distributions belong to increasing variance reversed residual lifetime class distributions, therefore the