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

Abstract

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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.

How to cite

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Diebolt, 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 -

References

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