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Generating uniform random vectors over a simplex with implications to the volume of a certain polytope and to multivariate extremes

Author

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  • Shmuel Onn
  • Ishay Weissman

Abstract

A uniform random vector over a simplex is generated. An explicit expression for the first moment of its largest spacing is derived. The result is used in a proposed diagnostic tool which examines the validity of random number generators. It is then shown that the first moment of the largest uniform spacing is related to the dependence measure of random vectors following any extreme value distribution. The main result is proved by a geometric proof as well as by a probabilistic one. Copyright Springer Science+Business Media, LLC 2011

Suggested Citation

  • Shmuel Onn & Ishay Weissman, 2011. "Generating uniform random vectors over a simplex with implications to the volume of a certain polytope and to multivariate extremes," Annals of Operations Research, Springer, vol. 189(1), pages 331-342, September.
    • Handle: RePEc:spr:annopr:v:189:y:2011:i:1:p:331-342:10.1007/s10479-009-0567-7
    DOI: 10.1007/s10479-009-0567-7
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    Cited by:

    1. Yuanying Guan & Micah Pollak, 2016. "Contagion In Heterogeneous Financial Networks," Advances in Complex Systems (ACS), World Scientific Publishing Co. Pte. Ltd., vol. 19(01n02), pages 1-25, February.
    2. Fried, Sela, 2022. "The restrictiveness of the hazard rate order and the moments of the maximal coordinate of a random vector uniformly distributed on the probability n-simplex," Statistics & Probability Letters, Elsevier, vol. 185(C).
    3. Morton, Alec, 2014. "Aversion to health inequalities in healthcare prioritisation: A multicriteria optimisation perspective," Journal of Health Economics, Elsevier, vol. 36(C), pages 164-173.
    4. Aparicio, Juan & Santín, Daniel, 2022. "A New Malmquist Index Based on a Standard Technology for Measuring Total Factor Productivity Changes," MPRA Paper 114467, University Library of Munich, Germany.

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