TY - JOUR

T1 - 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

AU - Fried, Sela

N1 - Funding Information:
Research was supported by the Israel Science Foundation (ISF) through Grant No. 1456/18 and European Research Council Grant number: 949707.
Publisher Copyright:
© 2022 Elsevier B.V.

PY - 2022/6/1

Y1 - 2022/6/1

N2 - 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.

AB - 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.

KW - Dilcher's formula

KW - Hazard rate order

KW - Probability simplex

KW - Randomness testing

KW - Whitworth's formula

UR - http://www.scopus.com/inward/record.url?scp=85124810146&partnerID=8YFLogxK

U2 - 10.1016/j.spl.2022.109414

DO - 10.1016/j.spl.2022.109414

M3 - Article

AN - SCOPUS:85124810146

VL - 185

JO - Statistics and Probability Letters

JF - Statistics and Probability Letters

SN - 0167-7152

M1 - 109414

ER -