Gauss Hypergeometric DistributionΒΆ
\(x\in\left[0,1\right]\) , \(\alpha>0,\,\beta>0\)
\[C^{-1}=B\left(\alpha,\beta\right)\,_{2}F_{1}\left(\gamma,\alpha;\alpha+\beta;-z\right)\]
\[ \begin{eqnarray*} f\left(x;\alpha,\beta,\gamma,z\right) & = & Cx^{\alpha-1}\frac{\left(1-x\right)^{\beta-1}}{\left(1+zx\right)^{\gamma}}\\ \mu_{n}^{\prime} & = & \frac{B\left(n+\alpha,\beta\right)}{B\left(\alpha,\beta\right)}\frac{\,_{2}F_{1}\left(\gamma,\alpha+n;\alpha+\beta+n;-z\right)}{\,_{2}F_{1}\left(\gamma,\alpha;\alpha+\beta;-z\right)}\end{eqnarray*}\]
Implementation: scipy.stats.gausshyper