The Distribution of Products of Beta, Gamma and Gaussian Random Variables

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,σ ᵢ ). These results include earlier results obtained by Springer and Thompson [1], [2] and Lomnicki [3], [4] as special cases.