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

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  • Tian, Guo-Liang
  • Fang, Hong-Bin
  • Tan, Ming
  • Qin, Hong
  • Tang, Man-Lai

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 . 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 . In addition, we develop methods for generating uniform distributions in a class of convex polyhedrons in n-dimensional Euclidean space . 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.

Suggested Citation

  • Tian, Guo-Liang & Fang, Hong-Bin & Tan, Ming & Qin, Hong & Tang, Man-Lai, 2009. "Uniform distributions in a class of convex polyhedrons with applications to drug combination studies," Journal of Multivariate Analysis, Elsevier, vol. 100(8), pages 1854-1865, September.
    • Handle: RePEc:eee:jmvana:v:100:y:2009:i:8:p:1854-1865
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    References listed on IDEAS

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    1. Rubinstein, R. Y., 1982. "Generating random vectors uniformly distributed inside and on the surface of different regions," European Journal of Operational Research, Elsevier, vol. 10(2), pages 205-209, June.
    2. Francis C. Hsuan, 1979. "Generating Uniform Polygonal Random Pairs," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 28(2), pages 170-172, June.
    3. Gupta, Rameshwar D. & Richards, Donald St.P., 1987. "Multivariate Liouville distributions," Journal of Multivariate Analysis, Elsevier, vol. 23(2), pages 233-256, December.
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    Cited by:

    1. Huang, Hengzhen & Chen, Xueping, 2021. "Compromise design for combination experiment of two drugs," Computational Statistics & Data Analysis, Elsevier, vol. 157(C).
    2. Wolf-Dieter Richter & Kay Schicker, 2017. "Simulation of polyhedral convex contoured distributions," Journal of Statistical Distributions and Applications, Springer, vol. 4(1), pages 1-19, December.
    3. Cyril Bachelard & Apostolos Chalkis & Vissarion Fisikopoulos & Elias Tsigaridas, 2024. "Randomized Control in Performance Analysis and Empirical Asset Pricing," Papers 2403.00009, arXiv.org.

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