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Multivariate generalized Pareto distributions

Rootzén, Holger LU and Tajvidi, Nader LU (2006) In Bernoulli 12(5). p.917-930
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... (More)
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. (Less)
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author
and
organization
publishing date
type
Contribution to journal
publication status
published
subject
keywords
peaks-over-threshold method, non-homogeneous Poisson process, multivariate Pareto distribution, generalized Pareto distribution, multivariate extreme value theory
in
Bernoulli
volume
12
issue
5
pages
917 - 930
publisher
Chapman and Hall
external identifiers
  • wos:000241620800008
  • scopus:36549020018
ISSN
1350-7265
language
English
LU publication?
yes
id
989734ad-0d5a-492d-b30f-05e35f942001 (old id 384230)
alternative location
http://projecteuclid.org/euclid.bj/1161614952
date added to LUP
2016-04-01 16:20:54
date last changed
2020-10-11 04:23:42
@article{989734ad-0d5a-492d-b30f-05e35f942001,
  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.},
  author       = {Rootzén, Holger and Tajvidi, Nader},
  issn         = {1350-7265},
  language     = {eng},
  number       = {5},
  pages        = {917--930},
  publisher    = {Chapman and Hall},
  series       = {Bernoulli},
  title        = {Multivariate generalized Pareto distributions},
  url          = {http://projecteuclid.org/euclid.bj/1161614952},
  volume       = {12},
  year         = {2006},
}