Characterizations of Extreme Value Extended Marshall-Olkin Models with Exponential Marginals (original) (raw)

International Journal of Statistics and Probability

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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