IDEAS home Printed from https://ideas.repec.org/a/eee/jmvana/v100y2009i8p1854-1865.html
   My bibliography  Save this article

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

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0047-259X(09)00045-1
    Download Restriction: Full text for ScienceDirect subscribers only
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Stefanescu Stefan V., 2000. "Generating uniform random points inside a cone," Monte Carlo Methods and Applications, De Gruyter, vol. 6(2), pages 115-130, December.
    2. Jones, M.C. & Marchand, Éric, 2019. "Multivariate discrete distributions via sums and shares," Journal of Multivariate Analysis, Elsevier, vol. 171(C), pages 83-93.
    3. Jay Simon, 2020. "Weight Approximation for Spatial Outcomes," Sustainability, MDPI, vol. 12(14), pages 1-18, July.
    4. Alessandra Carleo & Francesco Cesarone & Andrea Gheno & Jacopo Maria Ricci, 2017. "Approximating exact expected utility via portfolio efficient frontiers," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 40(1), pages 115-143, November.
    5. Denuit, Michel & Robert, Christian Y., 2020. "Conditional tail expectation decomposition and conditional mean risk sharing for dependent and conditionally independent risks," LIDAM Discussion Papers ISBA 2020018, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    6. Enrico Giorgi & Thorsten Hens & János Mayer, 2007. "Computational aspects of prospect theory with asset pricing applications," Computational Economics, Springer;Society for Computational Economics, vol. 29(3), pages 267-281, May.
    7. Niels Waller & Jeff Jones, 2011. "Investigating the Performance of Alternate Regression Weights by Studying All Possible Criteria in Regression Models with a Fixed Set of Predictors," Psychometrika, Springer;The Psychometric Society, vol. 76(3), pages 410-439, July.
    8. Bhattacharya, Bhaskar, 2006. "Maximum entropy characterizations of the multivariate Liouville distributions," Journal of Multivariate Analysis, Elsevier, vol. 97(6), pages 1272-1283, July.
    9. Ongaro, A. & Migliorati, S., 2013. "A generalization of the Dirichlet distribution," Journal of Multivariate Analysis, Elsevier, vol. 114(C), pages 412-426.
    10. Volkmar Henschel, 2002. "Statistical inference in simplicially contoured sample distributions," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 56(3), pages 215-228, December.
    11. de Almeida Filho, Adiel T. & Clemente, Thárcylla R.N. & Morais, Danielle Costa & de Almeida, Adiel Teixeira, 2018. "Preference modeling experiments with surrogate weighting procedures for the PROMETHEE method," European Journal of Operational Research, Elsevier, vol. 264(2), pages 453-461.
    12. Edward Hoyle & Levent Ali Menguturk, 2020. "Generalised Liouville Processes and their Properties," Papers 2003.11312, arXiv.org, revised May 2020.
    13. Fortin, Alain-Philippe & Simonato, Jean-Guy & Dionne, Georges, 2023. "Forecasting expected shortfall: Should we use a multivariate model for stock market factors?," International Journal of Forecasting, Elsevier, vol. 39(1), pages 314-331.
    14. Abbas, Ali E. & Hupman, Andrea C., 2023. "Scale dependence in weight and rate multicriteria decision methods," European Journal of Operational Research, Elsevier, vol. 309(1), pages 225-235.
    15. Malini Iyengar & Dipak Dey, 2002. "A semiparametric model for compositional data analysis in presence of covariates on the simplex," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 11(2), pages 303-315, December.
    16. Vetschera, Rudolf, 2017. "Deriving rankings from incomplete preference information: A comparison of different approaches," European Journal of Operational Research, Elsevier, vol. 258(1), pages 244-253.
    17. Gupta, Rameshwar D. & Richards, Donald St. P., 2002. "Moment Properties of the Multivariate Dirichlet Distributions," Journal of Multivariate Analysis, Elsevier, vol. 82(1), pages 240-262, July.
    18. Tian, Guo-Liang & Tang, Man-Lai & Yuen, Kam Chuen & Ng, Kai Wang, 2010. "Further properties and new applications of the nested Dirichlet distribution," Computational Statistics & Data Analysis, Elsevier, vol. 54(2), pages 394-405, February.
    19. Mohammed, Nawaf & Furman, Edward & Su, Jianxi, 2021. "Can a regulatory risk measure induce profit-maximizing risk capital allocations? The case of conditional tail expectation," Insurance: Mathematics and Economics, Elsevier, vol. 101(PB), pages 425-436.
    20. Fang, B. Q., 2003. "The skew elliptical distributions and their quadratic forms," Journal of Multivariate Analysis, Elsevier, vol. 87(2), pages 298-314, November.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:jmvana:v:100:y:2009:i:8:p:1854-1865. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/wps/find/journaldescription.cws_home/622892/description#description .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.