Extensions for Rare Events

Michael Falk (), Jürg Hüsler () and Rolf-Dieter Reiss ()
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Michael Falk: University of Würzburg, Institute of Mathematics
Jürg Hüsler: University of Berne, Department of Mathematical Statistics and Actuarial Science
Rolf-Dieter Reiss: University of Siegen, Department of Mathematics

Chapter Chapter 11 in Laws of Small Numbers: Extremes and Rare Events, 2011, pp 419-454 from Springer

Abstract: Abstract In the following sections we discuss some extensions which were mentioned in the previous chapters. Of main interest is the extension to general rare events in relation to a random sequence applying the same method as used for dealing with exceedances. In addition we treat now also the point process of all exceedances if clustering occurs. These results are applied to the processes of peaks over a threshold and of rare events. Finally, in the same way general rare events are considered without relation to a random sequence. Here triangular arrays of rare events will be analyzed by the same approach. This extension unifies easily the different local dependence conditions. Its application to multivariate extremes is then straightforward. As a particular case, triangular arrays of rare events in relation with exceedances of Gaussian sequences are considered since they are basic for maxima of a continuous Gaussian process. This analysis reveals also a new definition of Pickands constants.

Keywords: Point Process; Rare Event; Random Measure; Extremal Index; Compound Poisson Process (search for similar items in EconPapers)
Date: 2011
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-0348-0009-9_11

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DOI: 10.1007/978-3-0348-0009-9_11

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