School Seminars and Colloquia

Multivariate generalized Pareto distributions

Statistics Seminar

by Nader Tajvidi

Institution: Lund Institute of Technology Sweden
Date: Thu 26th April 2007
Time: 12:00 PM
Location: Room 213, Richard Berry Building

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 have a multivariate GP
distribution if and only if maxima asymptotically are Extreme Value (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.

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