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.


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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