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

Shmuel Onn; Ishay Weissman

doi:https://doi.org/10.1007/s10479-009-0567-7

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

Shmuel Onn, Ishay Weissman

Data and Decision Sciences

Technion - Israel Institute of Technology

Research output: Contribution to journal › Article › peer-review

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.

Original language	English
Pages (from-to)	331-342
Number of pages	12
Journal	Annals of Operations Research
Volume	189
Issue number	1
DOIs	https://doi.org/10.1007/s10479-009-0567-7
State	Published - Sep 2011

Keywords

Convex polytope
Multivariate extreme value distribution
Pickands dependence function
Simplex
Triangulation
Uniform spacings

All Science Journal Classification (ASJC) codes

General Decision Sciences
Management Science and Operations Research

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https://doi.org/10.1007/s10479-009-0567-7

Cite this

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

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.",

keywords = "Convex polytope, Multivariate extreme value distribution, Pickands dependence function, Simplex, Triangulation, Uniform spacings",

author = "Shmuel Onn and Ishay Weissman",

note = "Funding Information: Acknowledgements The research of Shmuel Onn was supported in part by a grant from ISF—the Israel Science Foundation and by a VPR grant at the Technion. Both authors acknowledge the support of the Fund for Promotion of Research at the Technion.",

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AU - Onn, Shmuel

AU - Weissman, Ishay

N1 - Funding Information: Acknowledgements The research of Shmuel Onn was supported in part by a grant from ISF—the Israel Science Foundation and by a VPR grant at the Technion. Both authors acknowledge the support of the Fund for Promotion of Research at the Technion.

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N2 - 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.

AB - 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.

KW - Convex polytope

KW - Multivariate extreme value distribution

KW - Pickands dependence function

KW - Simplex

KW - Triangulation

KW - Uniform spacings

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DO - https://doi.org/10.1007/s10479-009-0567-7

M3 - مقالة

SN - 0254-5330

VL - 189

SP - 331

EP - 342

JO - Annals of Operations Research

JF - Annals of Operations Research

IS - 1

ER -

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

Abstract

Keywords

All Science Journal Classification (ASJC) codes

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