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

Jean Diebolt; Armelle Guillou; Rym Worms

ESAIM: Probability and Statistics (2003)

- 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 (2003): 219-238. <http://eudml.org/doc/245050>.

@article{Diebolt2003,

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},

language = {eng},

pages = {219-238},

publisher = {EDP-Sciences},

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

url = {http://eudml.org/doc/245050},

volume = {7},

year = {2003},

}

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

PY - 2003

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

UR - http://eudml.org/doc/245050

ER -

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