Volume 6, 2002
|Page(s)||21 - 31|
|Published online||15 November 2002|
Penultimate approximation for the distribution of the excesses
Université de Marne-la-Vallée,
Équipe d'Analyse et de Mathématiques Appliquées,
5 boulevard Descartes,
77454 Marne-la-Vallee Cedex 2,
Revised: 5 October 2001
Let F be a distribution function (d.f) in the domain of attraction of an extreme value distribution ; it is well-known that Fu(x), where Fu is the d.f of the excesses over u, converges, when u tends to s+(F), the end-point of F, to , where is the d.f. of the Generalized Pareto Distribution. We provide conditions that ensure that there exists, for , a function Λ which verifies and is such that converges to 0 faster than .
Mathematics Subject Classification: 60G70 / 62G20
Key words: Generalized Pareto Distribution / excesses / penultimate approximation / rate of convergence.
© EDP Sciences, SMAI, 2002
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