In the present paper we define and investigate a novel class of distributions on the simplex, termed normalized infinitely divisible distributions, which includes the Dirichlet distribution. Distributional properties and general moment formulae are derived. Particular attention is devoted to special cases of normalized infinitely divisible distributions which lead to explicit expressions. As a by-product also new distributions over the unit interval and a generalization of the Bessel function distribution are obtained.
For λ ≤ 1 the Concrete is in a class of normalized infinitely divisible distributions (S. Favaro, personal communication) , and the results of REF apply.
On a class of distributions on the simplex
Journal of Statistical Planning and Inference
Mathematics