The Property of Continuity And Positively Definite Characteristic Function of Compound Poisson Distribution As The Sum of Geometric Distribution

Abstract

The compound Poisson distribution as the sum of independent and identically random variables from geometric distribution is characterized by using characteristic function. The characteristic function of this compound distribution is obtained by Laplace-Stieltjes transform. It is provided a characterization of this compound distribution employing the properties of characteristic function as continuous and positively definite function.