Positive dependence orderings
type: Item
instance of: scholarly article
title: Positive dependence orderings
zbMATH Open document ID: 0617.62006
author: George Kimeldorf
author: Allan R. Sampson
published in: Annals of the Institute of Statistical Mathematics
publication date: 1987-01-01T00:00:00Z
review text: The authors introduce a positive dependence ordering called \(TP_ 2PDO\) and establish a list of nine properties of this ordering. While the \(TP_ 2\)-ordering of \textit{S. Karlin} and \textit{Y. Rinott} [see J. Multivariate Anal. 10, 467-498 (1980; Zbl 0469.60006)] is defined (in the case of densities) by \(f(x_ 1,y_ 1)g(x_ 2,y_ 2)\geq f(x_ 1,y_ 2)g(x_ 2,y_ 1)\) for \(x_ 1\leq x_ 2\), \(y_ 1\leq y_ 2\) the new ordering implies the more complicated relation \[ f(x_ 1,y_ 1)f(x_ 2,y_ 2)g(x_ 1,y_ 2)g(x_ 2,y_ 1)\leq g(x_ 1,y_ 1)g(x_ 2,y_ 2)f(x_ 1,y_ 2)f(x_ 2,y_ 1). \] The converse relation remains open.
Mathematics Subject Classification ID: 62E10
Mathematics Subject Classification ID: 62H05
zbMATH DE Number: 4001173
zbMATH Keywords: total positivity of order 2
zbMATH Keywords: positive dependence ordering
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 4001173