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 =$f(x) = \frac{(a/b)^{p/2}}{2 K_p(\sqrt{ab})} x^{(p-1)} e^{-(ax + b/x)/2}$| cdf =| mean =$\frac{\sqrt{b}\ K_{p+1}(\sqrt{a b}) }{ \sqrt{a}\ K_{p}(\sqrt{a b})}$| median =| mode =$\frac{(p-1)+\sqrt{(p-1)^2+ab}}{a}$| variance =$\left(\frac{b}{a}\right)\left[\frac{K_{p+2} (\sqrt{ab})}{K_p(\sqrt{ab})}-\left(\frac{K_{p+1}(\sqrt{ab})} {K_p(\sqrt{ab})}\right)^2\right]$| skewness =| kurtosis =| entropy =| mgf =$\left(\frac{a}{a-2t}\right)^{\frac{p}{2}} \frac{K_p(\sqrt{b(a-2t})}{K_p(\sqrt{ab})}$| char =$\left(\frac{a}{a-2it}\right)^{\frac{p}{2}} \frac{K_p(\sqrt{b(a-2it})}{K_p(\sqrt{ab})}$| }} 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]]: :$f(x) = \frac{(a/b)^{p/2}}{2 K_p(\sqrt{ab})} x^{(p-1)} e^{-(ax + b/x)/2},\qquad x>0,$ where ''Kp'' is a [[modified Bessel function]] of the second kind, ''a'' > 0, ''b'' > 0 and ''p'' a real parameter. The above code is ©2010 M. Musatov http://meami.org. All rights are reserved. Nothing is left out.  |  Pages: 1 Prev: Halting problemNext: When download speed falls to 0, how is ETA estimated?