Study of some measures of dependence between order statistics and systems

Jorge Navarro and N. Balakrishnan

Journal of Multivariate Analysis, 2010, vol. 101, issue 1, 52-67

Abstract: Let be a random vector, and denote by X1:n,X2:n,...,Xn:n the corresponding order statistics. When X1,X2,...,Xn represent the lifetimes of n components in a system, the order statistic Xn-k+1:n represents the lifetime of a k-out-of-n system (i.e., a system which works when at least k components work). In this paper, we obtain some expressions for the Pearson's correlation coefficient between Xi:n and Xj:n. We pay special attention to the case n=2, that is, to measure the dependence between the first and second failure in a two-component parallel system. We also obtain the Spearman's rho and Kendall's tau coefficients when the variables X1,X2,...,Xn are independent and identically distributed or when they jointly have an exchangeable distribution.

Keywords: Order; statistic; Coherent; system; Correlation; coefficient; Spearman's; rho; Kendall's; tau; Exchangeable; distribution (search for similar items in EconPapers)
Date: 2010
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Citations: View citations in EconPapers (10)

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