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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