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)
Please use this url to cite or link to this publication:
https://lup.lub.lu.se/record/384230
- author
- Rootzén, Holger
LU
and Tajvidi, Nader
LU
- organization
- publishing date
- 2006
- 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
- 2022-03-30 07:09:37
@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}},
keywords = {{peaks-over-threshold method; non-homogeneous Poisson process; multivariate Pareto distribution; generalized Pareto distribution; multivariate extreme value theory}},
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}},
}