Inequalities for probability contents of convex sets via geometric average
type: Item
instance of: scholarly article
title: Inequalities for probability contents of convex sets via geometric average
zbMATH Open document ID: 0641.60024
DOI: 10.1016/0047-259X(88)90043-7
author: Y. L. Tong
author: Moshe Shaked
published in: Journal of Multivariate Analysis
publication date: 1988-01-01T00:00:00Z
review text: It is shown that: If \((X_ 1,X_ 2)\) is a permutation-invariant central convex unimodal random vector and if A is a symmetric (about 0), permutation-invariant convex set then \(P\{(aX_ 1,X_ 2/a)\in A\}\) is non-decreasing as a varies from \(0+\) to 1, and is nonincreasing as a varies from 1 to \(\infty\) (that is, \(P\{(a_ 1X_ 1,a_ 2X_ 2)\in A\}\) is a Schur-concave function of (log \(a_ 1,\log a_ 2))\). Some extensions of this result for the n-dimensional case are discussed. Applications are given for elliptically contoured distributions and scale parameter families.
Mathematics Subject Classification ID: 60E15
Mathematics Subject Classification ID: 60D05
Mathematics Subject Classification ID: 52A10
Mathematics Subject Classification ID: 26D15
Mathematics Subject Classification ID: 62H99
zbMATH DE Number: 4044841
zbMATH Keywords: peakedness
zbMATH Keywords: permutation-invariant convex set
zbMATH Keywords: elliptically contoured distributions
zbMATH Keywords: scale parameter families
reviewed by: Jean-Claude Massé
MaRDI profile type: Publication
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full work available at URL: 0047-259x(88)90043-7
OpenAlex ID: W2082598659
description: scientific article; zbMATH DE number 4044841