Uniform distributions in a class of convex polyhedrons with applications to drug combination studies

Motivated by experimental designs for drug combination studies, in this paper, we propose a novel approach for generating a uniform distribution on an arbitrary tetragon in two-dimensional Euclidean space R 2 . The key idea is to construct a one-to-one transformation between an arbitrary tetragon and the unit square [ 0 , 1 ] 2 . This transformation then provides a stochastic representation (SR) for the random vector uniformly distributed on the tetragon. An algorithm is proposed for generating a uniform distribution in an arbitrary triangular prism in R 3 . In addition, we develop methods for generating uniform distributions in a class of convex polyhedrons in n -dimensional Euclidean space R n . In particular, SRs for uniform distributions in regions with order restrictions are presented. We apply the proposed method to the experimental design for a drug combination study.