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Summary

Description
English: A plot of the Generalized inverse Gaussian distribution. a, b, and p are described on the Wikipedia page for that distribution as of June 2013.
Date 24 February 2012 (original upload date)
Source Mebden (talk) (Uploads)
Author Mebden (talk) (Uploads)

MATLAB Source code

x = 0.01:0.01:3; close all, figure, hold on, box off
% Gamma example (note: simpler if b doesn't quite equal zero)
alpha =1; beta =1; a =2*beta; b = 1e-10; p = alpha;
f = (a/b)^(p/2) / (2*besselk(p,sqrt(a*b))) * x.^(p-1) .* exp(-(a*x+b./x)/2);
plot (x,f,'b')
% Inverse Gaussian example
mu = 1; lambda = 1; a=lambda/mu^2; b=lambda; p = -.5;
f = (a/b)^(p/2) / (2*besselk(p,sqrt(a*b))) * x.^(p-1) .* exp(-(a*x+b./x)/2);
plot (x,f,'k')
% Other examples
a=2; b=1; p = 2;
f = (a/b)^(p/2) / (2*besselk(p,sqrt(a*b))) * x.^(p-1) .* exp(-(a*x+b./x)/2);
plot (x,f,'r')
a=2; b=1; p = -1;
f = (a/b)^(p/2) / (2*besselk(p,sqrt(a*b))) * x.^(p-1) .* exp(-(a*x+b./x)/2);
plot (x,f,'g')
legend ('a = 2, b = 0, p = 1', 'a = 1, b = 1, p = -1/2', 'a = 2, b = 1, p = 2', 'a = 2, b = 1, p = -2')

Licensing

Public domain This work has been released into the public domain by its author, Mebden at English Wikipedia. This applies worldwide.
In some countries this may not be legally possible; if so:
Mebden grants anyone the right to use this work for any purpose, without any conditions, unless such conditions are required by law.

Original upload log

Transferred from en.wikipedia to Commons by Sfan00_IMG using CommonsHelper.

The original description page was here. All following user names refer to en.wikipedia.
  • 2012-02-24 12:36 Mebden 561×420× (5939 bytes) I created this file today using the following Matlab code: x = 0.01:0.01:3; close all, figure, hold on, box off alpha =1; beta =1; a =2*beta; b = 1e-10; p = alpha; % gamma f = (a/b)^(p/2) / (2*besselk(p,sqrt(a*b))) * x.^(p-1) .* exp(-(a*x+b./x)/2); plot

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24 February 2012

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Date/TimeThumbnailDimensionsUserComment
current15:45, 24 July 2013Thumbnail for version as of 15:45, 24 July 2013561 × 420 (6 KB)File Upload Bot (Magnus Manske)Transfered from en.wikipedia by User:Sfan00_IMG using CommonsHelper
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