Dependence by reverse regular rule
type: Item
instance of: scholarly article
title: Dependence by reverse regular rule
zbMATH Open document ID: 0621.62054
author: Mei-Ling Ting Lee
published in: The Annals of Probability
publication date: 1985-01-01T00:00:00Z
review text: The paper announced above, Zbl 0621.62053, generalizes the bivariate positive dependence notions of the reviewer [J. Am. Stat. Assoc. 72, 642- 650 (1977; Zbl 0375.62092)] to the multivariate setting. It does this by requiring various iterated integrals of the density of a multivariate random vector to be totally positive of order 2. Some relations with other positive dependence concepts are discussed. Interpretations of the new notions in the context of reliability theory are given. Some examples illustrate the theory. This second paper introduces analogous negative dependence notions. It does this by requiring various iterated integrals of the density of a multivariate random vector to be strongly reverse regular of order 2 in the sense of \textit{S. Karlin} and \textit{Y. Rinott} [J. Multivariate Anal. 10, 499-516 (1980; Zbl 0469.60007)]. Various properties of these negative dependence notions are obtained. Some relationships with other negative dependence concepts are also given.
Mathematics Subject Classification ID: 62H05
Mathematics Subject Classification ID: 60E15
Mathematics Subject Classification ID: 62N05
Mathematics Subject Classification ID: 60K10
zbMATH DE Number: 4007486
zbMATH Keywords: bivariate positive dependence
zbMATH Keywords: iterated integrals of the density
zbMATH Keywords: totally positive of order 2
zbMATH Keywords: reliability
zbMATH Keywords: negative dependence
zbMATH Keywords: strongly reverse regular of order 2
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1214/aop/1176993011
OpenAlex ID: W1970427155
DOI: 10.1214/AOP/1176993011
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description: scientific article; zbMATH DE number 4007486