Abstract

We construct and characterize bivariate extreme value distributions with exponential marginals generated by the stochastic representation (X1,X2) = (min(T1,T3), min(T2,T3)) where the random variable T3 is independent of random variables T1 and T2 which are assumed to be  dependent. A building procedure is suggested when the joint distribution of  (T1,T2) is absolutely continuous and Ti's are not necessarily exponentially distributed, i=1,2,3. The  Pickands representation of the vector (X1,X2) is computed. We illustrate the general relations by examples.

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