Multivariate generalized Pareto distributions
Holger Rootzén and Nader Tajvidi
Centre for Mathematical Sciences
Mathematical Statistics
Lund Institute of Technology,
Lund University,
2005
ISSN 14039338

Abstract:

Statistical inference for extremes has been a subject of intensive research
during the past couple of decades. One approach is based on modeling exceedances
of a random variable over a high threshold with the Generalized Pareto (GP)
distribution. This has shown to be an important way to apply extreme value
theory in practice and is widely used. In this paper we introduce a multivariate
analogue of the GP distribution and show that it is characterized by each
of following two properties: (i) exceedances asymptotically has a multivariate
GP distribution if and only if maxima asymptotically are EV distributed,
and (ii) the multivariate GP distribution is the only one which is preserved
under change of exceedance levels. We also give a number of examples and
discuss lowerdimensional marginal distributions.



Key words:

Peaks over threshold method, Generalized Pareto distribution, Multivariate
extreme value theory, Multivariate Pareto distribution, Nonhomogeneous Poisson
process
