Definition:Generalized Inverse Gaussian Distribution

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Definition

The generalized inverse Gaussian distribution (GIG) is a three-parameter family of continuous probability distributions with probability density function:

$\displaystyle \forall x > 0: f \left({x}\right) = \frac { \left({a/b}\right)^{p/2} } {2 K_p \left({\sqrt{a b} }\right)} x^{\left({p - 1}\right)} e^{-\left({a x + b / x}\right) / 2}$

where:

$K_p$ is a modified Bessel function of the second kind
$a > 0, b > 0, p$ are real.