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.. _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`
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