## Tail dependence for multivariate copulas and its monotonicity.(English)Zbl 1152.62342

Summary: The tail dependence indexes of a multivariate distribution describe the amount of dependence in the upper right tail or lower left tail of the distribution and can be used to analyse the dependence among extremal random events. This paper examines the tail dependence of multivariate $$t$$-distributions whose copulas are not explicitly accessible. The tractable formulas of tail dependence indexes of a multivariate $$t$$-distribution are derived in terms of the joint moments of its underlying multivariate normal distribution, and the monotonicity properties of these indexes with respect to the distribution parameters are established. Simulation results are presented to illustrate the results.

### MSC:

 62H05 Characterization and structure theory for multivariate probability distributions; copulas 62H20 Measures of association (correlation, canonical correlation, etc.) 62P05 Applications of statistics to actuarial sciences and financial mathematics
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### References:

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