Abstract
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 R2. 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 R3. In addition, we develop methods for generating uniform distributions in a class of convex polyhedrons in n-dimensional Euclidean space Rn. 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.
Original language | English |
---|---|
Pages (from-to) | 1854-1865 |
Number of pages | 12 |
Journal | Journal of Multivariate Analysis |
Volume | 100 |
Issue number | 8 |
DOIs | |
Publication status | Published - Sept 2009 |
Scopus Subject Areas
- Statistics and Probability
- Numerical Analysis
- Statistics, Probability and Uncertainty
User-Defined Keywords
- Convex polyhedron
- Drug combination study
- Stochastic representation
- Tetragon
- Uniform design
- Uniform distribution