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File:LogDirichletDensity-alpha 0.3 to alpha 2.0.gif

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LogDirichletDensity-alpha_0.3_to_alpha_2.0.gif (512 × 512 pixels, file size: 3.35 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 0.3 to 2.0.
Source [1]
Author Initial version by Panos Ipeirotis, later modified by Love Sun and Dreams

Code Maple

L'animation a été générée en utilisant Maple 11, avec le code suivant :


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) ;

plotsetup(gif, plotoutput=`LogDirichletDensity-alpha_0.3_to_alpha_2.0.gif`); 

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=0.3..2.0, frames=100);

Licensing

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w:en:Creative Commons
attribution
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Date/TimeThumbnailDimensionsUserComment
current13:52, 20 April 2010Thumbnail for version as of 13:52, 20 April 2010512 × 512 (3.35 MB)Love Sun and Dreams{{Information |Description={{en|1=We illustrate the log of the density function: <math>\log (f(x_1,\dots, x_{K-1}; \alpha_1,\dots, \alpha_K)) = \log\left(\frac{1}{\mathrm{B}(\alpha)} \prod_{i=1}^K x_i^{\alpha_i - 1}\right) = + \sum_{i=1}^K \alpha_i \log

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