Extreme dependence models based on event magnitude

Abstract

By considering pointwise maxima of independent stationary random processes with dependent Cauchy marginals, we define a new process whose univariate limit distributions are Fréchet and the bivariate distributions interpolate between independence and complete dependence. The limiting dependence structure that emerges is suitable to describe dependent margins. However, we show that it is possible to enable different levels of dependence according to the magnitude of extreme events, e.g. the dependence decreases as the extremes’ intensity increases. In particular, with the class of random fields defined here, the dependence of spatial extremes can be modeled. We describe some properties of the dependence structure and we illustrate its utility in assessing the dependence. Combining marginal likelihoods through the composite likelihood approach, we are able to estimate the extremal dependence of extreme values observed in space. We convey the model’s capabilities through an analysis of sea-levels recorded along the coast of the United Kingdom.