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Multivariate measures of positive dependence

In this paper a set of desirable properties for measures of positive dependence of ordered n-tuples of continuous random variables (n >= 2) is proposed and a class of multivariate positive dependence measures is introduced. We consider the comonotonicity dependence structure as the strong dependency structure and so the class consists of measures that take values in the range [0, 1] and are defined in such a way that they equal 1 in case the random vector is comonotonic and equal 0 in case it is independent.