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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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  • $\begingroup$ Now I also come across the same problem with you. Do you understand the distribution of linear transformation of Dirichlet distributed random vector? $\endgroup$
    – Tang
    Apr 22, 2019 at 9:51
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    $\begingroup$ Of course not, unless $A$ is a permutation matrix. Otherwise, the support changes. $\endgroup$
    – Mateusz Kwaśnicki
    Apr 22, 2019 at 14:33

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