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...
| Veröffentlicht in: | Bernoulli. - International Statistical Institute and Bernoulli Society for Mathematical Statistics and Probability, 1995. - 12(2006), 5, Seite 917-930 |
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| Format: | Online-Aufsatz |
| Sprache: | English |
| Veröffentlicht: |
2006
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| 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 |
| Zusammenfassung: | 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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| ISSN: | 13507265 |