Asymptotic behaviour of the probability-weighted moments and penultimate approximation
ESAIM: Probability and Statistics, Tome 7 (2003), pp. 219-238.

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.

DOI : 10.1051/ps:2003010
Classification : 60G70, 62G20
Mots-clés : extreme values, domain of attraction, excesses, generalized Pareto distribution, probability-weighted moments, penultimate approximation 
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     title = {Asymptotic behaviour of the probability-weighted moments and penultimate approximation},
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Diebolt, Jean; Guillou, Armelle; Worms, Rym. Asymptotic behaviour of the probability-weighted moments and penultimate approximation. ESAIM: Probability and Statistics, Tome 7 (2003), pp. 219-238. doi : 10.1051/ps:2003010. http://www.numdam.org/articles/10.1051/ps:2003010/

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