On a class of distributions over the unit simplex

In the present paper we define and investigate a novel class of distributions over the unit 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.