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Threshold Models

Extremes and Environmental Risk

  1. Holger Drees

Published Online: 15 JAN 2013

DOI: 10.1002/9780470057339.vat009.pub2

Encyclopedia of Environmetrics

Encyclopedia of Environmetrics

How to Cite

Drees, H. 2013. Threshold Models . Encyclopedia of Environmetrics. 6.

Author Information

  1. University of Hamburg, Germany

Publication History

  1. Published Online: 15 JAN 2013


Models for exceedances over high thresholds are motivated by limit theorems from extreme value theory. For univariate observations this approach leads to generalized Pareto models. In contrast, natural models for the dependence of vectors of exceedances are infinite dimensional.


  • asymptotic independence;
  • excess distributions;
  • extreme value theory;
  • generalized Pareto distribution;
  • spectral measure;
  • tail dependence