On the interplay between variability and negative dependence for bivariate distributions.
type: Item
instance of: scholarly article
title: On the interplay between variability and negative dependence for bivariate distributions.
zbMATH Open document ID: 1033.60015
DOI: 10.1016/S0167-6377(02)00234-1
author: Alfred Müller
published in: Operations Research Letters
publication date: 2003-11-17T00:00:00Z
review text: The author identifies a mistake in the main result in the paper by \textit{A. Paul} [ibid. 30, 181--188 (2002; Zbl 1027.60012)]. He proves, however, that if \({X}=(X_1,X_2)\) and \({Y}=(Y_1,Y_2)\) have a common conditionally decreasing copula, and if \(X_1\leq_{\text{cx}}Y_1\) and \(X_2\leq_{\text{cx}}Y_2\) (where \(\leq_{\text{cx}}\) denotes the convex stochastic order), then \(Ef(X_1,X_2)\leq Ef(Y_1,Y_2)\) for all submodular and componentwise convex functions \(f\). Some related results are also included.
Mathematics Subject Classification ID: 60E15
zbMATH DE Number: 2005433
reviewed by: Moshe Shaked
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 2005433