An Alternative Point Process Framework for Modeling Multivariate Extreme Values

An alternative limiting point process to that of de Haan (1985) is studied that holds regardless of whether the underlying data generation mechanism is asymptotically dependent or asymptotically independent. We characterize its intensity function in terms of the coefficient of tail dependence and an angular measure which satisfies a normalisation condition. We use this point process to derive a generalisation of standard componentwise maxima results that holds for both asymptotic dependence and asymptotic independence. We illustrate our results using a flexible parametric example and provide methods for simulating from both the limiting point process and the limiting componentwise maxima distribution.