Multivariate peaks over thresholds models
Journal article, 2018

Multivariate peaks over thresholds modelling based on generalized Pareto distributions has up to now only been used in few and mostly two-dimensional situations. This paper contributes theoretical understanding, models which can respect physical constraints, inference tools, and simulation methods to support routine use, with an aim at higher dimensions. We derive a general point process model for extreme episodes in data, and show how conditioning the distribution of extreme episodes on threshold exceedance gives four basic representations of the family of generalized Pareto distributions. The first representation is constructed on the real scale of the observations. The second one starts with a model on a standard exponential scale which is then transformed to the real scale. The third and fourth representations are reformulations of a spectral representation proposed in Ferreira and de Haan (Bernoulli 20(4), 1717–1737, 2014). Numerically tractable forms of densities and censored densities are found and give tools for flexible parametric likelihood inference. New simulation algorithms, explicit formulas for probabilities and conditional probabilities, and conditions which make the conditional distribution of weighted component sums generalized Pareto are derived.

multivariate generalized Pareto distrib ution

peaks over threshold likelihoods

Extreme values

simulation of extremes


Holger Rootzen

University of Gothenburg

Mathematical Statistics

Johan Segers

Universite catholique de Louvain

Jennifer L. Wadsworth

Lancaster University


1386-1999 (ISSN) 1572915x (eISSN)

Vol. 21 1 115-145

Areas of Advance

Building Futures (2010-2018)



Basic sciences

Subject Categories

Probability Theory and Statistics



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