# Bivariate Generalization of the Inverted Hypergeometric Function Type I Distribution

## Authors

• Paula A. Bran-Cardona
• Edwin Zarrazola
• Daya Krishna Nagar Departamento de MatemÃ¡ticas, Universidad de Antioquia Calle 67, No. 53-108, MedellÃ­n, COLOMBIA

## Keywords:

Appellâ€™s first hypergeometric function, Beta distribution, Gauss hypergeometric function, Humbertâ€™s confluent hypergeometric function, product, transformation. 1

## Abstract

The bivariateÂ  inverted hypergeometric function type I distribution
Â is defined by the probability density functionÂ proportional to $x_1^{\nu_1-1} x_2^{\nu_2-1}Â \left(1 + x_{1} +Â x_{2}\right)^{-(\nu_1+\nu_2+\gamma)}$\linebreak $Â \leftidx{_2}{F}{_1} Â (\alpha,\beta;\gamma;(1+ x_{1}+x_{2})^{-1} )$, $x_1>0$, $x_2>0$, whereÂ Â $\nu_1$, $\nu_2$, $\alpha$, $\beta$ and $\gamma$ are suitable constants.Â  In thisÂ article, we study several properties of this distribution and deriveÂ density functions of $X_1/X_2$,Â $X_1/(X_1+X_2)$,Â  $X_1+X_2$Â  andÂ  $Â X_1 X_2$. We also considerÂ several otherÂ  products involving bivariateÂ  inverted hypergeometricÂ Â function type I, beta type I, beta type II, beta typeÂ III, Kummer-beta and hypergeometric function type I variables.

2012-07-31

## Section

Mathematical Statistics

## How to Cite

Bivariate Generalization of the Inverted Hypergeometric Function Type I Distribution. (2012). European Journal of Pure and Applied Mathematics, 5(3), 317-332. https://ejpam.com/index.php/ejpam/article/view/932