Stochastic rearrangement inequalities
type: Item
instance of: scholarly article
title: Stochastic rearrangement inequalities
zbMATH Open document ID: 0629.60015
DOI: 10.1016/0047-259X(87)90156-4
author: Wai Chan
author: Catherine D'Abadie
author: Frank Proschan
published in: Journal of Multivariate Analysis
publication date: 1987-01-01T00:00:00Z
review text: From authors' introduction: ``Rearrangement inequalities compare the value of a function of vector arguments with the value of the same function after the components of the vectors have been rearranged. The well-known rearrangement inequality of \textit{G. H. Hardy, J. E. Littlewood} and \textit{G. Pólya} [Inequalities. 2nd ed., Cambridge (1952); for a review of the first edition see Zbl 0010.10703)] states that if \(x=(x_ 1,...,x_ n)\) and \(y=(y_ 1,...,y_ n)\) are vectors of nonnegative, increasing components and \(\pi =(\pi (1),...,\pi (n))\) is any permutation, then \[ \sum^{n}_{i=1}x_ iy_ i\geq \sum^{n}_{i=1}x_ iy_{\pi (i)}\geq \sum^{n}_{i=1}x_ iy_{n-i+1}. \] In this paper we develop a general theory for obtaining stochastic versions of results of this nature.'' ``In Sections 5 and 6 we present some illustrative applications of the theory to ranking problems, hypothesis testing problems, and contamination models.''
Mathematics Subject Classification ID: 60C05
Mathematics Subject Classification ID: 60E15
Mathematics Subject Classification ID: 62F07
Mathematics Subject Classification ID: 62G10
zbMATH DE Number: 4024388
zbMATH Keywords: Rearrangement inequalities
zbMATH Keywords: ranking problems
zbMATH Keywords: hypothesis testing problems
zbMATH Keywords: contamination models
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 4024388