Bivariate generalization of the inverted hypergeometric function type I distribution

Abstract

The bivariate inverted hypergeometric function type I distribution is defined by the probability density function proportional to $x^{v_1-1}_1x^{v_2-1}_2$($1+x_1+x_2$$)^{-(v_1+_2+gamma)}$ $_2F_1 ( alpha, beta; gamma;$ ($1+x_1 + x_2)^{-1}$), $x_1$ > 0, $x_2$ > 0, where $v_{1,} v_{2,} alpha, beta$and $gamma$ are suitable constants. In this article, we study several properties of this distribution and derive density functions of $X_1/X_{2,}X_1/(X_1 +X_2$) and $X_1 +X_2$. We also consider several 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. 2010 Mathematics Subject Classifications: 62E15, 60E05