Modeling of conditional extreme values distributions under right censored data with application

Abstract

In this thesis we are interested to the statistical analysis of extreme values (EVA) and Modeling of Conditional Extreme Values Distributions under Right Censored Data with Applications. Our goal, in the first place, is to propose an estimator of the mean of a heavy-tailed distribution under right random censored data in presence of covariates by combining the generalized Kaplan-Meier estimator before a threshold and a parametric model; Generalized Pareto Distribution (GPD) which approximates the excesses over threshold in order to overcome the bad behavior of Kaplan Meier estimator (K-M) in the heavy-tail of distribution, then we determined the asymptotic normality of our estimator in case of deterministic covariates. Secondly, as application of extreme value theory to hydrology 1 , more specifically, to rainfalls. We have done a study to find out the most adequate fitting distributions of rainfalls taken in Khemis-Miliana region (Algeria) during the period 1975-2006. The method of Block Maxima (BM) is adopted when we use Generalized Extreme Value (GEV) distribution to fit the data, and the Peak Over Threshold (POT) method is applied when we use Generalized Pareto (GP) distribution, after testing stationarity of time serie in hand.