Abstracts
Résumé
L’analyse fréquentielle des événements extrêmes est un des outils privilégiés pour l’estimation des débits de crue et de leurs périodes de retour. En analyse fréquentielle, les observations doivent être indépendantes et identiquement distribuées (iid). Ces hypothèses ne sont pas souvent respectées et les paramètres de la loi à ajuster sont fonction du temps ou de covariables. Le modèle GEV non stationnaire permet de tenir compte de cette dépendance. L’objectif du présent travail est de comparer la méthode du maximum de vraisemblance pour l’estimation des quantiles à la méthode du maximum de vraisemblance généralisée (GML) et à une généralisation de la méthode des L‑moments dans le cas non stationnaire. Trois modèles sont considérés : le modèle stationnaire (GEV0), le cas où le paramètre de position est une fonction linéaire de la covariable (GEV1) et le cas d’une dépendance quadratique (GEV2). Un cas d’étude des précipitations à une station de la Californie montre le potentiel des modèles non stationnaires.
Mots-clés:
- Valeurs extrêmes,
- maximum de vraisemblance généralisé,
- L-moments,
- Indice d’oscillations du sud
Abstract
In frequency analysis, data must generally be independent and identically distributed (i.i.d), which implies that they must meet the statistical criteria of independence, stationarity and homogeneity. In reality, the probability distribution of extreme events can change with time, indicating the existence of non-stationarity. The objective of the present study was to develop efficient estimation methods for the use of the GEV distribution for quantile estimation in the presence of non-stationarity. Parameter estimation in the non-stationary GEV model is generally done with the Maximum Likelihood Estimation method. In this work, we suggest two other estimation methods: the Generalized Maximum Likelihood Estimation (GML) and the generalization of the L-moment method for the non-stationary case. A simulation study was carried out to compare the performances of these three estimation methods in the case of the stationary GEV model (GEV0), the non-stationary case with a linear dependence (GEV1), and the non-stationary case with a quadratic dependence on covariates (GEV2). The non-stationary GEV model was also applied to a case study from the State of California to illustrate its potential.
Keywords:
- Extreme value,
- Generalized maximum likelihood,
- L-moments,
- Southern oscillation index
Appendices
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