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

Guo Liang Tian*, Hong Bin Fang, Ming Tan, Hong Qin, Man Lai TANG

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

9 Citations (Scopus)

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 languageEnglish
Pages (from-to)1854-1865
Number of pages12
JournalJournal of Multivariate Analysis
Volume100
Issue number8
DOIs
Publication statusPublished - Sep 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

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