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Orthant tail dependence of multivariate extreme value distributions. (English) Zbl 1151.62041
Summary: The orthant tail dependence describes the relative deviation of upper- (or lower-) orthant tail probabilities of a random vector from similar orthant tail probabilities of a subset of its components, and can be used in the study of dependence among extreme values. Using the conditional approach, this paper examines the extremal dependence properties of multivariate extreme value distributions and their scale mixtures, and derives the explicit expressions of orthant tail dependence parameters for these distributions. Properties of the tail dependence parameters, including their relations with other extremal dependence measures used in the literature, are discussed. Various examples, involving multivariate exponential, multivariate logistic distributions and copulas of Archimedean type, are presented to illustrate the results.

MSC:
62G32 Statistics of extreme values; tail inference
62H10 Multivariate distribution of statistics
62H20 Measures of association (correlation, canonical correlation, etc.)
62P05 Applications of statistics to actuarial sciences and financial mathematics
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