Sums, Products, and Ratios of Non-central Beta Variables
关键词: Turn (biochemistry) 、 Mathematics 、 Type (model theory) 、 Density estimation 、 Beta distribution 、 Beta (velocity) 、 Pure mathematics 、 Mathematical analysis 、 Hypergeometric function 、 Variables 、 Random variable
摘要: Abstract Recent papers by Professor T. Pham-Gia derived distributions of sums, products, and ratios independent beta random variables. In this article, we extend Pham-Gia's results when X 1 2 are variables distributed according to the non-central distribution Type I, II, doubly distribution. For each these three distributions, derive exact expressions for densities S = X 1 + X 2, D = X 1 − X P = X R = X 2/X 1. The turn out involve hypergeometric functions one two
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