A transformation of probability mass functions for a class of discrete random variables
Abstract
Let us consider a discrete random variable X that takes only non-negative integer values. Let Rx and px(x) denote the range of X and the probability mass function of X, respectively. The aim of this paper is to provide a transformation method used to transform px(x) into a probability mass function of a discrete random variable X whose range is Rx = {k in N: k >= minRx}. We obtain a representation of the characteristic function of X in terms of the characteristic function of X. Moreover, the distribution-preserving property of the transformation is shown in some specific cases.