- Volume 12, Number 5 (2006), 917-930.
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 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.
Bernoulli, Volume 12, Number 5 (2006), 917-930.
First available in Project Euclid: 23 October 2006
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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