Study of some measures of dependence between order statistics and systems
type: Item
instance of: scholarly article
title: Study of some measures of dependence between order statistics and systems
zbMATH Open document ID: 1183.62099
author: Jorge Navarro
author: Narayanaswamy Balakrishnan
published in: Journal of Multivariate Analysis
publication date: 2009-11-27T00:00:00Z
review text: Let \(X=(X_1,X_2,\dots,X_n)\) be a random vector and denote by \(X_{1:n},X_{2:n},\dots,X_{n:n}\) the corresponding order statistics. When \(X_1,X_2,\dots,X_n\) represent the life times of \(n\) components in a system, the order statistic \(X_{n-k+1:n}\) represents the life time of a \(k\)-out-of-\(n\) system (i.e., a system which works when at least \(k\) components work). The authors obtain some expressions for the Pearson's correlation coefficient between \(X_{i:n}\) and \(X_{j:n}\). Special attention is paid to the case \(n=2\), that is, to measure the dependence between the first and second failure in a two-component parallel system. Spearman's rho and Kendall's tau coefficients are also obtained when \(X_1,X_2,\dots,X_n\) are independent and identically distributed or when they jointly have an exchangeable distribution.
Mathematics Subject Classification ID: 62H20
Mathematics Subject Classification ID: 62G30
Mathematics Subject Classification ID: 62N05
zbMATH DE Number: 5639704
zbMATH Keywords: coherent systems
zbMATH Keywords: correlation coefficient
zbMATH Keywords: Spearman's rho
zbMATH Keywords: Kendall's tau
zbMATH Keywords: exchangeable distributions
reviewed by: Jarosław Bartoszewicz
MaRDI profile type: Publication
full work available at URL: j.jmva.2009.04.016
OpenAlex ID: W2034878361
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DOI: 10.1016/J.JMVA.2009.04.016
description: scientific article; zbMATH DE number 5639704