Bivariate extreme-value copulas with discrete Pickands dependence measure

It is shown how bivariate extreme-value copulas with discrete Pickands measure can be represented as the geometric mean of bivariate extreme-value copulas whose Pickands measure has at most two atoms. Arbitrary bivariate extreme-value copulas can thus be represented as the limit of this construction, when the number of involved basis copulas tends to infinity. Besides the theoretical value of such a representation, properties of the represented copula can be deduced from properties of the involved basis copulas. Moreover, a probabilistic representation is available which can be used to sample a general bivariate extreme-value copula, for which a generic algorithm is provided.     «

It is shown how bivariate extreme-value copulas with discrete Pickands measure can be represented as the geometric mean of bivariate extreme-value copulas whose Pickands measure has at most two atoms. Arbitrary bivariate extreme-value copulas can thus be represented as the limit of this construction, when the number of involved basis copulas tends to infinity. Besides the theoretical value of such a representation, properties of the represented copula can be deduced from properties of the involv...     »