Extreme Value Analysis: an Introduction

Charras-Garrido, Myriam; Lezaud, Pascal

Journal de la société française de statistique, Tome 154 (2013) no. 2, pp. 66-97.

Nous donnons un aperçu des résultats probabilistes et statistiques utilisés dans la théorie des valeurs extrêmes, dont l’objectif est de prédire l’occurrence d’événements rares. Dans la première partie de l’article, nous expliquons que la distribution asymptotique des valeurs extrêmes appartient, dans un certain sens, à la famille des distributions des valeurs extrêmes généralisées qui dépendent d’un paramètre réel, appelé l’indice de valeur extrême. Dans la seconde partie, nous discutons des méthodes d’évaluation statistiques des queues basées sur l’estimation de l’indice des valeurs extrêmes.

We provide an overview of the probability and statistical tools underlying the extreme value theory, which aims to predict occurrence of rare events. Firstly, we explain that the asymptotic distribution of extreme values belongs, in some sense, to the family of the generalised extreme value distributions which depend on a real parameter, called the extreme value index. Secondly, we discuss statistical tail estimation methods based on estimators of the extreme value index.

Keywords: extreme value theory, max stable distributions, extreme value index, distribution tail estimation
Mot clés : théorie des valeurs extrêmes, lois max-stables, indice des valeurs extrêmes, estimation en queue de distribution

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