Gauss hypergeometric distribution

The probability density function for the Gauss hypergeometric distribution is:

.. math::

f(x, a, b, c, z) = C x^{a-1} (1-x)^{b-1} (1+zx)^{-c}

where :math:0 \le x \le 1, a > 0, b > 0, z > -1, and :math:C = \frac{1}{B(a,b)F[2,1](c,a,a+b,-z)}. :math:F[2,1] is the Gauss hypergeometric function.