These functions provide information about the generalized inverse
Gaussian distribution with mean equal to m, dispersion equal to
s, and family parameter equal to f: density,
cumulative distribution, quantiles, log hazard, and random generation.
The generalized inverse Gaussian distribution has density
$$
f(y) =
\frac{y^{\nu-1}}{2 \mu^\nu K(1/(\sigma \mu),abs(\nu))}
\exp(-(1/y+y/\mu^2)/(2*\sigma))$$
where \(\mu\) is the mean of the distribution,
\(\sigma\) the dispersion, \(\nu\) is the family
parameter, and \(K()\) is the fractional Bessel function of
the third kind.
\(\nu=-1/2\) yields an inverse Gaussian distribution,
\(\sigma=\infty\), \(\nu>0\) a gamma
distribution, and \(\nu=0\) a hyperbola distribution.