Simulation of some multivariate distributions related to the Dirichlet distribution with application to Monte Carlo simulations

Simulation of multivariate distributions is important in many applications but remains computationally challenging in practice. In this article, we introduce three classes of multivariate distributions from which simulation can be conducted by means of their stochastic representations related to the Dirichlet random vector. More emphasis is made to simulation from the class of uniform distributions over a polyhedron, which is useful for solving some constrained optimization problems and ha`s many applications in sampling and Monte Carlo simulations. Numerical evidences show that, by utilizing state-of-the-art Dirichlet generation algorithms, the introduced methods become superior to other approaches in terms of computational efficiency.