Models for Dependent Extremes Using Stable Mixtures.
Journal article, 2009
This paper unifies and extends results on a class of multivariate Extreme
Value (EV) models studied by Hougaard, Crowder, and Tawn. In these models
both unconditional and conditional distributions are EV, and all lower-dimensional
marginals and maxima belong to the class. This leads to substantial economies of
understanding, analysis and prediction. One interpretation of the models is as size
mixtures of EV distributions, where the mixing is by positive stable distributions. A
second interpretation is as exponential-stable location mixtures (for Gumbel) or as
power-stable scale mixtures (for non-Gumbel EV distributions). A third interpretation is through a Peaks over Thresholds model with a positive stable intensity. The
mixing variables are used as a modeling tool and for better understanding and model checking. We study extreme value analogues of components of variance models, and new time series, spatial, and continuous parameter models for extreme values. The results are applied to data from a pitting corrosion investigation.
multivariate extreme value distribution
positive stable variables.