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Suppose that the vector $\tilde{a} = (a_1,a_2,...,a_J)$ has a multivariate normal distribution and let $$A = \Sigma_{j=1}^J a_j\,.$$

Then what is the distribution of $a_j/A$ or $\tilde{a}/A$ called?

I do know that Dirichlet distribution can be used to deal with a vector of which the sum of the elements is one, but I'm asking the special case where the vector has a multivariate Normal distribution.

Glen_b
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user67275
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  • http://en.wikipedia.org/wiki/Ratio_distribution. For a more specific discussion, please see http://stats.stackexchange.com/a/3644/919, which answers your question (because $(a_j, A)$ have a bivariate normal distribution). – whuber Feb 02 '14 at 05:08

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