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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

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  • Fried, Sela

Abstract

Continuing the work of Fried (2021) who defined the restrictiveness of stochastic orders and calculated it for the usual stochastic order and for the likelihood ratio order, we calculate the restrictiveness of the hazard rate order. Inspired by the works of Onn and Weissman (2011) and Weissman (2011), we propose an application of the restrictiveness of stochastic orders in randomness testing. We then apply the inductive dimension reduction technique, that proved useful in obtaining the restrictiveness results, and provide an alternative proof for Whitworth’s formula, which we then use to derive the moments of the maximal coordinate of a random vector that is uniformly distributed on the probability n-simplex.

Suggested Citation

  • 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).
    • Handle: RePEc:eee:stapro:v:185:y:2022:i:c:s0167715222000311
    DOI: 10.1016/j.spl.2022.109414
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    References listed on IDEAS

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    1. Fried, Sela, 2021. "On the restrictiveness of the usual stochastic order and the likelihood ratio order," Statistics & Probability Letters, Elsevier, vol. 170(C).
    2. 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.
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