Best-possible bounds on sets of bivariate distribution functions
type: Item
instance of: scholarly article
title: Best-possible bounds on sets of bivariate distribution functions
zbMATH Open document ID: 1057.62038
author: Roger B. Nelsen
author: José Juan Quesada-Molina
author: José Antonio Rodríguez-Lallena
author: Manuel Úbeda-Flores
published in: Journal of Multivariate Analysis
publication date: 2004-10-01T00:00:00Z
review text: The aim of this paper is to present a method for finding bounds on arbitrary sets of joint distribution functions \(H\) of continuous random variables \(X\) and \(Y\), \(H\) having the marginal distribution functions \(F\) and \(G\), respectively. The paper uses copulas \(C\) (uniquely determined by the relation \(H(x, y)= C(F(x),G(y)))\) and quasi-copulas to narrow the classical Fréchet-Hoeffding inequality (and bounds) in order to obtain pointwise best possible bounds on non-empty sets of distribution functions. As an application, the proposed procedure is illustrated by finding bounds when the values of \(H\) are known at quartiles of \(X\) and \(Y\).
reviewed by: Neculai Curteanu
Mathematics Subject Classification ID: 62H05
Mathematics Subject Classification ID: 60E15
Mathematics Subject Classification ID: 62E10
Mathematics Subject Classification ID: 62H20
zbMATH DE Number: 2105299
zbMATH Keywords: best-possible bounds
zbMATH Keywords: copulas
zbMATH Keywords: quasi-copulas
zbMATH Keywords: Fréchet-Hoeffding inequality sharpening
zbMATH Keywords: distribution functions
zbMATH Keywords: Kendall's tau
zbMATH Keywords: quartiles
MaRDI profile type: Publication
full work available at URL: j.jmva.2003.09.002
OpenAlex ID: W2066459312
cites work: On the characterization of a class of binary operations on distribution functions
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cites work: A characterization of quasi-copulas
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cites work: BOUNDS ON BIVARIATE DISTRIBUTION FUNCTIONS WITH GIVEN MARGINS AND MEASURES OF ASSOCIATION
cites work: Q3281461
DOI: 10.1016/J.JMVA.2003.09.002
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description: scientific article; zbMATH DE number 2105299