File:LogDirichletDensity-alpha 0.3 to alpha 2.0.gif
LogDirichletDensity-alpha_0.3_to_alpha_2.0.gif (512 × 512 pixels, file size: 3.35 MB, MIME type: image/gif, looped, 100 frames)
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Summary
editDescriptionLogDirichletDensity-alpha 0.3 to alpha 2.0.gif |
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
editL'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
editI, the copyright holder of this work, hereby publish it under the following license:
This file is licensed under the Creative Commons Attribution 3.0 Unported license.
- You are free:
- to share – to copy, distribute and transmit the work
- to remix – to adapt the work
- Under the following conditions:
- attribution – You must give appropriate credit, provide a link to the license, and indicate if changes were made. You may do so in any reasonable manner, but not in any way that suggests the licensor endorses you or your use.
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Date/Time | Thumbnail | Dimensions | User | Comment | |
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current | 13:52, 20 April 2010 | 512 × 512 (3.35 MB) | Love Sun and Dreams (talk | contribs) | {{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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