On the Levy measure property of gamma distribution

Abstract

The characteristic function of gamma distribution is obtained by using Fourier-Stieltjes transform such that it can be formed into the canonical representation of infinitely divisible characteristic function contained the Levy measure. The characteristic function of gamma distribution is expressed to have the property of continuity, definite positive function and performed the quadratic form. It is used analytical method and the characterization of characteristic function to have the property of Levy measure of infinitely divisible distribution belonging to a class of completely monotones function and measurable on its support.