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Tail dependence for heavy-tailed scale mixtures of multivariate distributions. (English) Zbl 1179.62076

Summary: The tail dependence of multivariate distributions is frequently studied via the tool of copulas. We develop a general method, which is based on multivariate regular variation, to evaluate the tail dependence of heavy-tailed scale mixtures of multivariate distributions, whose copulas are not explicitly accessible. Tractable formulae for tail dependence parameters are derived, and a sufficient condition under which the parameters are monotone with respect to the heavy tail index is obtained. The multivariate elliptical distributions are discussed to illustrate the results.

MSC:

62H05 Characterization and structure theory for multivariate probability distributions; copulas
62H10 Multivariate distribution of statistics
62H20 Measures of association (correlation, canonical correlation, etc.)
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