Hiroshima Math. J. 53 (1), 1-25, (March 2023) DOI: 10.32917/h2020102
Rahmouna Mecene, Mohamed Ali Ghorbel
KEYWORDS: Dirichlet type 3 distribution, Dirichlet distribution, gamma distribution, selection, Gibbs measure, Gauss hypergeometric function, 60G57, 62E17, 60K99, 62E15, 62E20
In this paper, we investigate the Dirichlet type 3 distribution. First, some main properties are elaborated and illustrated. Next, we set forward a representation which allows to compute many functionals in a closed form, making the Dirichlet type 3 distribution an exactly soluble model. Furthermore, we consider the Gibbs version of the Dirichlet type 3 distribution including selection. By using the representation mentioned above, we obtain the moment function of the geometrical average of the random variables according to the new distribution; special types of Bell polynomials are shown to be involved. Finally, we provide a concrete example to illustrate the performance of the Dirichlet type 3 distribution.