The Distribution of Products of Beta, Gamma and Gaussian Random Variables
Melvin D. Springer, William E. Thompson · SIAM Journal on Applied Mathematics · 1970
The probability density functions of products of independent beta, gamma and central Gaussian random variables are shown to be Meijer G-functions. The density function of products of random beta variables is a Meijer G-function which is expressible in closed form when the parameters are integers. Recursion formulas are developed for the evaluation of the Meijer G-functions representing products of random gamma variables and products of random Gaussian variables $N(0,\sigma _i )$. These results include earlier results obtained by Springer and Thompson [1], [2] and Lomnicki [3], [4] as special cases.