Generalized Inverse Gaussian Distribution

The probability density function is given by:

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

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