Generalized inverse Gaussian distribution
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In probability theory, the Generalized inverse Gaussian distribution (GIG) is a probability distribution with probability density function
- <math>f(x) = \frac{(a/b)^{p/2}}{2 K_p(\sqrt{ab})} x^{(p-1)} e^{-(ax + b/x)/2}, \, x > 0,</math>
where <math>K_p</math> is a modified Bessel function of the third kind and <math>a>0 </math>, <math>b>0</math>. It is used extensively in geostatistics, statistical linguistics, finance, etc. This distribution was first proposed by Etienne Halphen<ref>V. Seshadri (1997): Halphen's laws. In S. Kotz, C. B. Read and D. L. Banks (eds.): Encyclopedia of Statistical Sciences, Update Volume 1, pp. 302 - 306. Wiley, New York.</ref> It was rediscovered and popularised by Ole Barndorff-Nielsen, who called it the generalized inverse Gaussian distribution, and Herbert Sichel. It is also known as the Sichel Distribution.
A further extension is the "log generalised inverse Gaussian distribution" which, because of its complexity, requires computers to be useful in practice.
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