This is a bit of a vague question but: Is there a distribution on the $n$-simplex that is like the Dirichlet distribution but reparameterizable as the pushforward of the uniform distribution on the $n$-simplex under a simple closed-form diffeomorphism?
Are there any good (elegant) examples of nontrivial diffeomorphisms from the simplex to itself that could do that?
@user76284 , please ask that on the main site. There we have better facilities for asking & answering questions (e.g. formatting options will work) and the information will be available for people with the same question. That isn't a chat item.
