Abstract
Recent papers by Professor T. Pham-Gia derived distributions of sums, products, and ratios of independent beta random variables. In this article, we extend Professor Pham-Gia's results when X 1 and X 2 are independent random variables distributed according to the non-central beta distribution of Type I, the non-central beta distribution of Type II, and the doubly non-central beta distribution. For each of these three distributions, we derive exact expressions for the densities of S = X 1 + X 2, D = X 1 − X 2, P = X 1 X 2, and R = X 2/X 1. The expressions turn out to involve the hypergeometric functions of one and two variables.
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