Uniform and radial Dirichlet copulas

Abstract We give copula densities for all symmetric Dirichlet distributions. In fact, since the number of variables in a Dirichlet distribution can be viewed in two different ways, there are two copulas for every Dirichlet distribution of which one is singular. We pay particular attention to the copulas of the Dirichlet distribution whose density is the normalised product of its own one variable marginal densities. The singular copula of that Dirichlet distribution is uniform and spherical in the Lp space with p equal to the number of free variables while the non singular copula is radial in the Lp space.