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File:LogDirichletDensity-alpha 0.1 to alpha 1.9.gif

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LogDirichletDensity-alpha_0.1_to_alpha_1.9.gif (364 × 364 pixels, file size: 2.03 MB, MIME type: image/gif, looped, 100 frames)

Summary

Description
English: We illustrate the log of the density function:

for . In other words, we have two parameters varying on the two axes, and an implicit .

The picture illustrates the case where and we vary over time the parameter from 0.1 to 1.9.

Maple Code

The animated plot was generated using Maple 11, with the following code:

restart; with(plots);

B := (a1, a2, a3) -> (GAMMA(1.0*a1) * GAMMA(1.0*a2) * GAMMA(1.0*a3)) / GAMMA(1.0*a1+1.0*a2+1.0*a3);

f := (x1, x2, a1, a2, a3) ->  (x1^(a1-1)) * (x2^(a2-1)) * ( (1-x1-x2)^(a3-1)) /B(a1,a2,a3) ;

animate ( plot3d,  [eval(log(f(x1, x2, a1, a2, a3)), {a1=a, a2=a, a3=a}), 
x1=0.00..1, x2=0.00..1, axes=BOXED, grid=[25,25],gridstyle=triangular,orientation=[-135, 60],
shading=zhue, contours=20, style=surfacecontour, view=-3..2 ], a=0.1..1.9, frames=100);

Dirichlet


Please cite the original work if you create derivatives.
Date 27 October 2007 (original upload date)
Source Transferred from en.wikipedia to Commons.
Author The original uploader was Ipeirotis at English Wikipedia.

Licensing

w:en:Creative Commons
attribution
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You are free:
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Under the following conditions:
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Original upload log

The original description page was here. All following user names refer to en.wikipedia.
Date/Time Dimensions User Comment
2007-10-27 21:06 364×364× (2128038 bytes) Ipeirotis The log of the density function Dir(a): <math>\log (f(x_1,\dots, x_{K-1}; \alpha_1,\dots, \alpha_K)) = \log(\frac{1}{\mathrm{B}(\alpha)} \prod_{i=1}^K x_i^{\alpha_i - 1}) </math> We have two parameters <math>x_1, x_2</math> varying on the two axes, and

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27 October 2007

File history

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Date/TimeThumbnailDimensionsUserComment
current04:02, 26 January 2019Thumbnail for version as of 04:02, 26 January 2019364 × 364 (2.03 MB)BD2412Transferred from en.wikipedia via #commonshelper
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