Abstract
The main topic of this work is the statistical analysis of extreme values with applications to hydrology, more specifically, to rainfalls. Statistical inference of rainfall is very important as we consider the risk of damage to agriculture, ecology, infrastructure systems and also risk of drought. The main aim of this study is 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 method is applied when we use generalized Pareto (GP) distribution, after testing of course stationarity of time serie in hand. Concerning estimation of parameters, we use: maximum likelihood estimation, probability weighted moments, and profile of maximum likelihood for both models (GEV and GP). With these models, we derive estimates of T-years return levels for different periods T and vice-versa.
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