I am working with some compositional data and looking for the appropriate prior distribution over the simplex. It appears that the dirichlet distribution does not allow heavy enough tails for the data and am looking at other choices.

I have come across several alternative 1 parameter distributions that I can implement in Stan, namely the normalized inverse Gaussian, and the normalized 1/2-stable distribution. However, I am looking for a two parameter distribution that nests the Dirichlet as a special case.

The normalized generalized Gamma, normalized stable distribution, Pitman-Yor type process distribution fit the bill, but do not appear to have analytic solutions to the density function.

Is there a way to implement these in Stan? Is there an alternative distribution that might be suitable?