Models for Dependent Extremes Using Stable Mixtures

By Anne-Laure Fougères, John P. Nolan, Holger Rootz'en. 2007

61 citations recorded by the source corpus.

Abstract. 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 themselves EV distributions, and all lower‐dimensional marginals and maxima belong to the class. 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 modelling tool and for better understanding and model checking. We study EV 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.

Subfields: Finance, Global and Planetary Change, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/60a082ebc375fadd6edde18b51b608122a425335

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Citations in the corpus

Extreme-value copulas (2009, background): “These distributions can be generated via mixtures of certain extreme-value distributions over stable distributions, a representation that yields large possibilities for modelling that have yet begun to be explored [28, 92].”
MAX-STABLE MODELS FOR MULTIVARIATE EXTREMES (2012, background): “In a search for flexible models in large dimensions, new families are still being constructed, as in Ballani and Schlather (2011), Boldi and Davison (2007), Cooley et al. (2010) and Fougères et al. (2009).”
Asymptotic models and inference for extremes of spatio-temporal data (2010, background): “One such class of max-stable processes is given by Fougères et al. (2009), which are obtained by mixing extreme value distributions over positive stable distributions.”