en>ChrisGualtieri: General Fixes using AWB

2013-10-25T00:06:39Z

General Fixes using AWB

← Older revision		Revision as of 02:06, 25 October 2013
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	~~Jayson Berryhill is how I'm called~~ and ~~my wife doesn't like it at all. Since he was eighteen he's been operating as~~ an ~~information officer but he plans on altering it~~. ~~My spouse doesn't like it~~ the ~~way I do but what I really like doing is caving but I don't have~~ the ~~time lately~~. ~~I've usually loved residing in Mississippi~~.<br><br>~~Also visit my weblog~~; ~~[http~~://~~c045~~.~~danah~~.co.kr/~~home~~/~~index~~.~~php?document_srl=1356970&mid~~=~~qna real psychic]~~		== Summary ==
			We illustrate the log of the density function:

			<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>

			for <math>K=3</math>. In other words, we have two parameters <math>x_1, x_2</math> varying on the two axes, and an implicit <math>x_3 = 1-x_1-x_2</math>.

			The picture illustrates the case where <math>\alpha_1=\alpha_2=\alpha_3=\alpha</math> and we vary over time the parameter <math>\alpha</math> from 0.1 to 1.9.

			== Maple Code ==

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

			<code><pre><nowiki>
			restart; with(plots);

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

			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);

			</nowiki></pre></code>
			[[Category:Probability distributions\|Dirichlet]]

			== Licensing ==
			{{cc-by-3.0}}

			Please cite the original work if you create derivatives.

			{{Orphan image}}
			{{Copy to Wikimedia Commons\|bot=Fbot}}

128.192.134.19: /* Definition */

2011-11-28T18:37:50Z

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Jayson Berryhill is how I'm called and my wife doesn't like it at all. Since he was eighteen he's been operating as an information officer but he plans on altering it. My spouse doesn't like it the way I do but what I really like doing is caving but I don't have the time lately. I've usually loved residing in Mississippi.<br><br>Also visit my weblog; [http://c045.danah.co.kr/home/index.php?document_srl=1356970&mid=qna real psychic]

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en>ChrisGualtieri: General Fixes using AWB

128.192.134.19: /* Definition */