On the non-central Dirichlet distribution

Our goal is to provide a valid point of reference for the theoretical study and the practical use of the Non-central Dirichlet distribution. An Achilles' heel of such model is the limited mathematical manageability of its joint density function, which is the main obstacle to the conduct of a further exploration of it. This paper is thus intended to enrich the little range of the already existing findings referring to this distribution by offering new insights into its analysis. An operating procedure to employ the Non-central Dirichlet as a model to be fitted to data consisting of vectors of proportions subject to the unit-sum constraint is illustrated. Simulation studies are performed to confirm the validity of the derived moments formula and to investigate the finite-sample performance of the asymptotic properties of the Maximum-Likelihood estimators and the Likelihood-Ratio tests used to accomplish the abovementioned applied matters.