Bivariate Generalization of the Inverted Hypergeometric Function Type I Distribution
Keywords:
Appell’s first hypergeometric function, Beta distribution, Gauss hypergeometric function, Humbert’s confluent hypergeometric function, product, transformation. 1Abstract
The bivariate inverted hypergeometric function type I distribution is defined by the probability density function proportional to $ x_1^{\nu_1-1} x_2^{\nu_2-1} \left(1 + x_{1} + x_{2}\right)^{-(\nu_1+\nu_2+\gamma)}$\linebreak $ \leftidx{_2}{F}{_1}
 (\alpha,\beta;\gamma;(1+ x_{1}+x_{2})^{-1} )$, $x_1>0$, $x_2>0$, where  $\nu_1$, $\nu_2$, $\alpha$, $\beta$ and $\gamma$ are suitable constants. In this article, we study several properties of this distribution and derive density functions of $X_1/X_2 $, $X_1/(X_1+X_2)$, $X_1+X_2$ 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.
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Published
2012-07-31
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Mathematical Statistics
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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://www.ejpam.com/index.php/ejpam/article/view/932