Bernoulli

  • Bernoulli
  • Volume 12, Number 5 (2006), 917-930.

Multivariate generalized Pareto distributions

Holger Rootzén and Nader Tajvidi

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Abstract

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.

Article information

Source
Bernoulli, Volume 12, Number 5 (2006), 917-930.

Dates
First available in Project Euclid: 23 October 2006

Permanent link to this document
https://projecteuclid.org/euclid.bj/1161614952

Digital Object Identifier
doi:10.3150/bj/1161614952

Mathematical Reviews number (MathSciNet)
MR2265668

Zentralblatt MATH identifier
1134.62028

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

Citation

Rootzén, Holger; Tajvidi, Nader. Multivariate generalized Pareto distributions. Bernoulli 12 (2006), no. 5, 917--930. doi:10.3150/bj/1161614952. https://projecteuclid.org/euclid.bj/1161614952


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