The Generalized Integer Gamma Distribution--A Basis for Distributions in Multivariate Statistics

In this paper the distribution of the sum of independent[Gamma]variables with different scale parameters is obtained by direct integration, without involving a series expansion. One of its particular cases is the distribution of the product of some particular independent Beta variables. Both distributions are obtained in a concise manageable form readily applicable to research work in the area of multivariate statistics distributions. The exact distribution of the generalized Wilks'[Lambda]statistic is then obtained as a direct application of the results.