Multivariate Liouville Distributions, IV

We define a class of distributions, containing the classical Dirichlet and Liouville distributions, in which the random variables take values in a locally compact Abelian group or semigroup. These generalizations retain many properties of the Dirichlet and Liouville distributions, including properties of the marginal and conditional distributions and regression functions. We present a number of examples illustrating the general theory.