ROBUST EXTREME RETURN LEVEL WITH POWER NORMALIZATION FOR EXTREME EVENTS: APPLICATION OF REAL HYDROLOGY DATA

In statistical studies of rare and catastrophic phenomena the distribution of generalized extreme values under linear normalization is always chosen as the appropriate model. It used to estimate the probabilities of events that have not yet been observed. Recently, the extreme value theory (EVT) received a lot of attention both theoretically and practically using just the classical linear model (L-Model) or linear normalization of the maximum to estimate return level. So, in this paper we propose a new multiplicative model based on the distribution of generalized extreme values under non-linear normalization, whose purpose is to raise the strong and weak points between these two models. Our main goal is to use our multiplicative model (P-model) to calculate the return level, as well as the associated confidence interval. The diagnostic fit, test and statistical inference to compare the two models (linear and non-linear) are studied. Finally, a data analysis and discussion are applied at first on real hydrological data for Morocco and South of Australia, then on water levels of lake Erié in Canada. The results show that our multiplicative (non-linear) model is more adaptive because it takes into account the variation of the return period.