Study of some measures of dependence between order statistics and systems
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.
Year of publication: |
2010
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Authors: | Navarro, Jorge ; Balakrishnan, N. |
Published in: |
Journal of Multivariate Analysis. - Elsevier, ISSN 0047-259X. - Vol. 101.2010, 1, p. 52-67
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Publisher: |
Elsevier |
Keywords: | Order statistic Coherent system Correlation coefficient Spearman's rho Kendall's tau Exchangeable distribution |
Saved in:
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