Multivariate Generalized Pareto Distributions

Multivariate Generalized Pareto Distributions

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 extrem...

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Veröffentlicht in:Bernoulli. - International Statistical Institute and Bernoulli Society for Mathematical Statistics and Probability, 1995. - 12(2006), 5, Seite 917-930
1. Verfasser: Rootzén, Holger (VerfasserIn)
Weitere Verfasser: Tajvidi, Nader
Format: Online-Aufsatz
Sprache:English
Veröffentlicht: 2006
Zugriff auf das übergeordnete Werk:Bernoulli
Schlagworte:Generalized Pareto distribution Multivariate extreme value theory Multivariate Pareto distribution Non-homogeneous Poisson process Peaks-over-threshold method Mathematics Philosophy Physical sciences Behavioral sciences
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520 |a 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. 
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