# Characterize linear transformation of Dirichlet distributed variables

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.

• Is this a question from a course or textbook? If so, please add the [self-study] tag & read its wiki. – gung - Reinstate Monica May 13 '16 at 6:59
• No, its my own question. – Helmut May 13 '16 at 7:16