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

In this paper the distribution of the sum of independentΓvariables 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 WilksʹΛstatistic is then obtained as a direct application of the results.