Bivariate Generalization of the Inverted Hypergeometric Function Type I Distribution (European Journal of Pure and Applied Mathematics, 2012)
The bivariate inverted hypergeometric function type I distribution is defined by the probability density function proportional to $ x_1^{ u_1-1} x_2^{ u_2-1} \left(1 + x_{1} + x_{2}\right)^{-( u_1+ u_2+γ)}$\linebreak $ \leftidx{_2}{F}{_1} (α,β;γ;(1+ x_{1}+x_{2})^{-1} )$, $x_1>0$, $x_2>0$, where $ u_1$, $ u_2$, $α$, $β$ and $γ$ are suitable constants. In this article, we study several properties of this distribution and derive density functions of $X_1/X_2 $, $X_1/(X_1+X_2)$, $X_1+X_2$ and $ X_1 X_2 $. We also consider several other products involving bivariate inverted hypergeometric function type I, beta type I, beta type II, beta type III, Kummer-beta and hypergeometric function type I variables.