Extremal properties of the extended skew-normal distribution
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The skew-normal and related families are flexible and asymmetric parametric models suitable for modelling a diverse range of systems. We focus on the highly flexible extended skew-normal distribution, and consider when interest is in the extreme values that it can produce. We derive the well-known Mills' inequalities and ratio for the univariate extended skew-normal distribution and establish the asymptotic extreme value distribution for the maxima of samples drawn from this distribution. We show that the multivariate maximum of a high-dimensional extended skew-normal random sample has asymptotically independent components and derive the speed of convergence of the joint tail. To describe the possible dependence among the components of the multivariate maximum, we show that under appropriate conditions an approximate multivariate extreme-value distribution that leads to a rich dependence structure can be derived.
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