| Author : | Tian, Guo-Liang; Fang, Hong-Bin; Tan, Ming; Qin Hong; Tang, Man-Lai |
|---|---|
| Category : | Journal Article |
| Department : | |
| Year / Month : | 2009 |
| ISSN: | 0047-259X |
| Source : | Journal of Multivariate Analysis, 100, 1854 - 1865. |
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 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.
Keywords
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