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From: Turing's Worst Nightmare on 13 May 2010 22:19
== Encoded Probable Distrubtion and Software Generation Techniques ==

In computers the following is found to be true:

{{Probability distribution|
name =Generalized inverse Gaussian|
type =density|
pdf_image =|
cdf_image =|
parameters =''a'' > 0, ''b'' > 0, ''p'' real|
support =''x'' > 0|
pdf =<math>f(x) = \frac{(a/b)^{p/2}}{2 K_p(\sqrt{ab})}
x^{(p-1)} e^{-(ax + b/x)/2}</math>|
cdf =|
mean =<math>\frac{\sqrt{b}\ K_{p+1}(\sqrt{a b}) }{ \sqrt{a}\
K_{p}(\sqrt{a b})}</math>|
median =|
mode =<math>\frac{(p-1)+\sqrt{(p-1)^2+ab}}{a}</math>|
variance =<math>\left(\frac{b}{a}\right)\left[\frac{K_{p+2}
(\sqrt{ab})}{K_p(\sqrt{ab})}-\left(\frac{K_{p+1}(\sqrt{ab})}
{K_p(\sqrt{ab})}\right)^2\right]</math>|
skewness =|
kurtosis =|
entropy =|
mgf =<math>\left(\frac{a}{a-2t}\right)^{\frac{p}{2}}
\frac{K_p(\sqrt{b(a-2t})}{K_p(\sqrt{ab})}</math>|
char =<math>\left(\frac{a}{a-2it}\right)^{\frac{p}{2}}
\frac{K_p(\sqrt{b(a-2it})}{K_p(\sqrt{ab})}</math>|
}}
In [[probability theory]] and [[statistics]], the '''generalized
inverse Gaussian distribution''' ('''GIG''') is a three-parameter
family of continuous [[probability distribution]]s 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},\qquad x>0,</math> where ''K<sub>p</sub>'' is a [[modified
Bessel function]] of the second kind, ''a''&nbsp;>&nbsp;0,
''b''&nbsp;>&nbsp;0 and ''p'' a real parameter.

The above code is ©2010 M. Musatov http://meami.org. All rights are
reserved. Nothing is left out.


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