Sufficient conditions for negative association of random variables
type: Item
instance of: scholarly article
title: Sufficient conditions for negative association of random variables
zbMATH Open document ID: 0935.62060
DOI: 10.1016/S0167-7152(99)00056-5
author: Taizhong Hu
author: Jinjin Hu
published in: Statistics \& Probability Letters
publication date: 2000-05-08T00:00:00Z
review text: Negative association has been recognized as an interesting property, especially for reliability applications. The paper investigates sufficient conditions for a random vector \[ \mathbf X=(X_1,X_2,\dots,X_n) \] to be negatively associated, conditional on an increasing function, say \(\psi\). Till now, two forms of the function \(\psi\) were known to possess this property. The sum and the permutation of the randorn vector \({\mathbf X}\). The authors derive sufficient conditions that generalize the existing results for negative association. It is shown that conditional distributions based on order statistics can provide the sufficient conditions needed. The connection with the notion of negative dependence is also shown. An illustration, for a reliability scheme with a lot of components with negative association, is also given.
reviewed by: Dimitris Karlis
Mathematics Subject Classification ID: 62H05
Mathematics Subject Classification ID: 60E15
Mathematics Subject Classification ID: 62G30
Mathematics Subject Classification ID: 62H20
zbMATH DE Number: 1367951
zbMATH Keywords: permutation distribution
zbMATH Keywords: log concavity
zbMATH Keywords: negative association
zbMATH Keywords: order statistics
zbMATH Keywords: negative dependence
zbMATH Keywords: reliability
MaRDI profile type: Publication
cites work: Q3924997
cites work: Probability inequalities via negative dependence for random variables conditioned on order statistics
cites work: Increasing Properties of Polya Frequency Function
cites work: Negative association of random variables, with applications
cites work: Polya Type Distributions of Convolutions
cites work: Classes of orderings of measures and related correlation inequalities. II. Multivariate reverse rule distributions
cites work: A note on the almost sure convergence of sums of negatively dependent random variables
cites work: On stochastic comparison of random vectors
cites work: Moment inequalities and weak convergence for negatively associated sequences
description: scientific article; zbMATH DE number 1367951