A note on the generalized Rao–Rubin condition and characterization of certain discrete distributions

Abstract

Assuming that the original observation from a discrete distribution is subject to damage according to a binomial probability law, it is shown here that a class of discrete distributions consisting of binomial, Poisson and mixed Poisson distributions, is characterized by the generalized Rao–Rubin condition 0 <π, π′ < 1 are constants. Y denotes the resulting or observed random variable, taking the values r = 0, 1, 2, ….