| Issue |
ESAIM: PS
Volume 6, 2002
|
|
|---|---|---|
| Page(s) | 21 - 31 | |
| DOI | https://doi.org/10.1051/ps:2002002 | |
| 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,
Champs-sur-Marne,
77454 Marne-la-Vallee Cedex 2,
France; ramdani@math.univ-mlv.fr.
Received:
26
February
2001
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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