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

ABSTRACT

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.

KEYWORDS:

• Dirichlet distribution
• Inverted Dirichlet distribution
• Liouville distribution
• Monte Carlo simulation
• Uniform distribution over a polyhedron

MATHEMATICS SUBJECT CLASSIFICATION:

• Primary 60E05
• Secondary 65C05
• 65C10

Acknowledgments

The authors would like to thank the editor and three anonymous referees for their valuable comments and suggestions that help improve this manuscript.

Funding

This work was supported by the research grant MOST 102-2118-M-004-001.