Structural Properties of the Generalized Dirichlet Distributions

We study the general structure of the generalized Dirichlet distributions, deriving general formulas for the marginal and conditional probability density functions of those distributions. We develop the multivariate reverse rule properties of these distributions, apply those properties to derive probability inequalities, and derive stochastic representations and orderings for the distributions. Further, we study approaches for estimating the parameters of these distributions and recommend that parameter estimation be carried out by the maximum likelihood method.