The Definite Positive Property of Characteristic Function from Compound Geometric Distribution as The Sum of Gamma Distribution

Abstract

In this expository article we survey characterization of compound geometric distribution as the sum of gamma distribution. The characterization of this compound distribution is obtained by using the property of characteristic function as the Laplace-Stieltjes transform. The property of definite positive characteristice function of compound geometric distribution as the sum of gamma distribution is explained by analytical methods as the quadratic form of characteristic function.