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The generalised inverse Gaussian distribution

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Distribution name

Generalised inverse Gaussian distribution (GIG)

Common notation

Parameters

 = parameter ()

 = parameter ()

 = parameter ()

Domain

Probability density function

where  is the modified Bessel function of the third kind with index .

Mean

Variance

Characteristic function

Other comments

When   and  the non-central moments are:

 

Some commentators use GIG to refer to the generalised integer gamma distribution (which is not the same as the generalised inverse Gaussian distribution).

 

Nematrian web functions

 

This distribution is not currently supported within the Nematrian web function library. For details of other supported probability distributions see here.

 


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