Moment-based approximations for the law of functionals of Dirichlet processes

The paper deals with the approximation of the law of a random functional of a Dirichlet process using a finite number of its moments. In particular, three classes of approximation procedures – expansions in series of orthonormal polynomials, the maximum entropy method and mixtures of known distributions – are discussed. A comparison of the different approximation procedures is performed by a few examples. Moreover, some new results on the support and the existence of the moment generating function of the Dirichlet functional variance are given.