.. _continuous-geninvgauss:

Generalized Inverse Gaussian Distribution

The probability density function is given by:

.. math:: :nowrap:

\begin{eqnarray*}
        f(x; p, b) = x^{p-1} \exp(-b(x + 1/x)/2) / (2 K_p(b)),
\end{eqnarray*}

where :math:x > 0 is a real number and the parameters :math:p, b satisfy :math:b > 0. :math:K_v is the modified Bessel function of second kind of order :math:v (scipy.special.kv).

If X is geninvgauss(p, b), then the distribution of 1/X is geninvgauss(-p, b). The inverse Gaussian distribution (scipy.stats.invgauss) is a special case with p=-1/2.

Implementation: scipy.stats.geninvgauss