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Let $X=(X_1,....,X_K)\sim{}\text{Dir}(\alpha_1,...,\alpha_K)$ be a Dirichlet distribution with parameters $\alpha_1,...,\alpha_K$. Let $A$ be a non-singular linear map and $(Y_1,....,Y_K)=A(X_1,....,X_K)$. Is $(Y_1,....,Y_K)$ Dirichlet distributed?

If so, what are the parameters? If not, as I suspect, how does one characterise the distribution of $(Y_1,....,Y_K)$ and its properties? A reference may be sufficient, as long as it is not the article by Provost and Cheong at http://onlinelibrary.wiley.com/doi/10.2307/3315988/epdf, for which I am little wiser.

Thank you.

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  • $\begingroup$ Is this a question from a course or textbook? If so, please add the [self-study] tag & read its wiki. $\endgroup$ – gung - Reinstate Monica May 13 '16 at 6:59
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    $\begingroup$ No, its my own question. $\endgroup$ – Helmut May 13 '16 at 7:16
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I have concluded that the transformed distribution is not generally a Dirichlet distributed and there appears to be no particularly useful characterisation of their joint distribution.

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