DISTRIBUTION OF THE DIFFERENCE OF TWO INDEPENDENT POISSON RANDOM VARIABLES AND ITS APPLICATION TO THE LITERATE POPULATION DATA

Abstract

Study about the distribution of the function of a random variable, in particular the distribution of the sum of two or more random variables, has been done widely. While studies on the distribution of the difference between two random variables still rarely done, moreover for discrete random variables. This work focuses on the derivation of the distribution of two independent Poisson random variables. The methods used to determine the distribution are method of moment generating function and probability mass function. The properties of the distribution are derived through the characteristics of the  k th moment; the first up to fourth moments in particular. Furthermore, the distribution of the difference of two independent Poisson random variables is compared to the Poisson Difference (PD) distribution of Alzaid and Omair (2010) or also known as Skellam distribution. Parameters of the distribution are estimated using method of moment and maximum likelihood estimation. Application to the literate population data is carried out to get a better understanding about the distribution.