Characterization of a Mixture of Gamma Density

Abstract

We consider a class of probability density functions on (0, ∞) denoted by C, having Laplace transforms with only negative zeros and poles. The class C contains many classes of great importance such as mixtures of m independent exponential random variables, sums of two independent random variables one in mixture and the other in sums of independent exoonential random variables, sums of m independent exponential random variables and mixture of m independent gamma random variables GM _n , _m Characterization theorems for these classes except that of GM _n , _m are given by Sumita, U and Masuda, Y (1987). Here we consider the class GM _n , _m .