Open Access
October 2006 Multivariate generalized Pareto distributions
Holger Rootzén, Nader Tajvidi
Author Affiliations +
Bernoulli 12(5): 917-930 (October 2006). DOI: 10.3150/bj/1161614952


Statistical inference for extremes has been a subject of intensive research over the past couple of decades. One approach is based on modelling exceedances of a random variable over a high threshold with the generalized Pareto (GP) distribution. This has proved to be an important way to apply extreme value theory in practice and is widely used. We introduce a multivariate analogue of the GP distribution and show that it is characterized by each of following two properties: first, exceedances asymptotically have a multivariate GP distribution if and only if maxima asymptotically are extreme value distributed; and second, the multivariate GP distribution is the only one which is preserved under change of exceedance levels. We also discuss a bivariate example and lower-dimensional marginal distributions.


Download Citation

Holger Rootzén. Nader Tajvidi. "Multivariate generalized Pareto distributions." Bernoulli 12 (5) 917 - 930, October 2006.


Published: October 2006
First available in Project Euclid: 23 October 2006

zbMATH: 1134.62028
MathSciNet: MR2265668
Digital Object Identifier: 10.3150/bj/1161614952

Keywords: generalized Pareto distribution , multivariate extreme value theory , multivariate Pareto distribution , non-homogeneous poisson process , peaks-over-threshold method

Rights: Copyright © 2006 Bernoulli Society for Mathematical Statistics and Probability

Vol.12 • No. 5 • October 2006
Back to Top