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

M. D. Springer and W. E. Thompson
SIAM Journal on Applied Mathematics
Vol. 18, No. 4 (Jun., 1970), pp. 721-737
Stable URL: http://www.jstor.org/stable/2099424
Page Count: 17
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The Distribution of Products of Beta, Gamma and Gaussian Random Variables
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Abstract

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

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