# Asymptotic behaviour of the probability-weighted moments and penultimate approximation

Jean Diebolt; Armelle Guillou; Rym Worms

ESAIM: Probability and Statistics (2010)

- Volume: 7, page 219-238
- ISSN: 1292-8100

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topDiebolt, Jean, Guillou, Armelle, and Worms, Rym. "Asymptotic behaviour of the probability-weighted moments and penultimate approximation." ESAIM: Probability and Statistics 7 (2010): 219-238. <http://eudml.org/doc/104305>.

@article{Diebolt2010,

abstract = {
The P.O.T. (Peaks-Over-Threshold) approach
consists of using the Generalized Pareto Distribution (GPD)
to approximate the distribution of excesses over a threshold.
We use the probability-weighted moments
to estimate the parameters of the approximating distribution.
We study the asymptotic behaviour of
these estimators (in particular their asymptotic bias) and also the
functional bias of the GPD as an estimate of the
distribution function of the excesses. We adapt penultimate
approximation results to the case where parameters are estimated.
},

author = {Diebolt, Jean, Guillou, Armelle, Worms, Rym},

journal = {ESAIM: Probability and Statistics},

keywords = {Extreme values; domain of attraction;
excesses; Generalized Pareto Distribution; probability-weighted
moments; penultimate approximation.; extreme values; excesses; generalized Pareto distribution; probability-weighted moments; penultimate approximation},

language = {eng},

month = {3},

pages = {219-238},

publisher = {EDP Sciences},

title = {Asymptotic behaviour of the probability-weighted moments and penultimate approximation},

url = {http://eudml.org/doc/104305},

volume = {7},

year = {2010},

}

TY - JOUR

AU - Diebolt, Jean

AU - Guillou, Armelle

AU - Worms, Rym

TI - Asymptotic behaviour of the probability-weighted moments and penultimate approximation

JO - ESAIM: Probability and Statistics

DA - 2010/3//

PB - EDP Sciences

VL - 7

SP - 219

EP - 238

AB -
The P.O.T. (Peaks-Over-Threshold) approach
consists of using the Generalized Pareto Distribution (GPD)
to approximate the distribution of excesses over a threshold.
We use the probability-weighted moments
to estimate the parameters of the approximating distribution.
We study the asymptotic behaviour of
these estimators (in particular their asymptotic bias) and also the
functional bias of the GPD as an estimate of the
distribution function of the excesses. We adapt penultimate
approximation results to the case where parameters are estimated.

LA - eng

KW - Extreme values; domain of attraction;
excesses; Generalized Pareto Distribution; probability-weighted
moments; penultimate approximation.; extreme values; excesses; generalized Pareto distribution; probability-weighted moments; penultimate approximation

UR - http://eudml.org/doc/104305

ER -

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