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I'm working on a problem for an hour and I wanted to get some hints. Suppose:

$y_1, y_2, y_3, y_4 \sim Dir(\alpha_1, \alpha_2, \alpha_3, \alpha_4)$

what is the distribution of $\frac{y_1}{y_1 + y_2}$ ?

My guess is that distribution should be $Beta(\alpha_1, \alpha_2)$

Could you guys give me some hints on how to show it?

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  • $\begingroup$ What is the beta distribution specified by four parameters? $\endgroup$ – Mankind May 7 '15 at 17:26
  • $\begingroup$ @HowDoIMath, my bad! it's dirichlet. $\endgroup$ – Linda May 7 '15 at 17:35
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Well, actually I'm also looking for this answer. I've found a tool in here: http://research.microsoft.com/en-us/um/cambridge/projects/infernet/codedoc/html/M_MicrosoftResearch_Infer_Distributions_Beta_op_Division.htm

I'm not sure how it can perform the Beta.Division operator, but I think it may help you. Besides, I find out a paper. It also seems helpful.

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