An Interesting Extension of the Dirichlet Model

Abstract

A k variable integral is introduced, which will produce the total integral eqivalent to the total integral in a $$(k-1)$$ -variate type-1 Dirichlet integral. Hence this author calls the new integral as type-1 pseudo Dirchilet integral. A statistical density is introduced based on this pseudo Dirichlet integral, which will be called the type-1 pseudo Dirichlet density. Marginal densities, moments and other properties are studied. Then several transformations are considered which will give different forms of the type-1 pseudo Dirichlet density. Then the corresponding real matrix-variate situation is studied and the real matrix-variate type-1 pseudo Dirichlet density is introduced. Several transformations in the matrix-variate case are also discussed which will give different representations of the proposed density and finally leading to a real type-1 Dirichlet density.