Ferreira, Helena; Ferreira, Marta Tail dependence between order statistics. (English) Zbl 1234.60057 J. Multivariate Anal. 105, No. 1, 176-192 (2012). Summary: We introduce \(s,k\)-extremal coefficients for studying the tail dependence between the \(s\)-th lower and the \(k\)-th upper order statistics of a normalized random vector. If its margins have tail dependence, then so do their order statistics, with the strength of the bivariate tail dependence decreasing as two order statistics get farther apart. Some general properties are derived for these dependence measures which can be expressed via copulas of random vectors. Its relations with other extremal dependence measures used in the literature are discussed, such as multivariate tail dependence coefficients, the coefficient \(\eta \) of tail dependence, coefficients based on tail dependence functions, the extremal coefficient \(\epsilon \), the multivariate extremal index and an extremal coefficient for min-stable distributions. Several examples are presented to illustrate the results, including multivariate exponential and multivariate Gumbel distributions widely used in applications. Cited in 4 Documents MSC: 60G70 Extreme value theory; extremal stochastic processes Keywords:tail dependence; order statistics; measures of tail dependence; multivariate extreme value distribution PDFBibTeX XMLCite \textit{H. Ferreira} and \textit{M. Ferreira}, J. Multivariate Anal. 105, No. 1, 176--192 (2012; Zbl 1234.60057) Full Text: DOI References: [1] Arnold, B. C.; Balakrishnan, N.; Nagaraja, H. N., A First Course in Order Statistics (1992), Wiley: Wiley New York · Zbl 0850.62008 [2] Brummelhuis, R., Serial dependence in ARCH-models as measured by tail dependence coefficients, Extremes, 11, 2, 167-201 (2008) · Zbl 1199.60182 [3] David, H. A., Order Statistics (1981), Wiley: Wiley New York · Zbl 0223.62057 [4] Ferreira, H., Dependence between two multivariate extremes, Statist. Probab. 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