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In the last two decades E. Pancheva and her collaborators were investigating various limit theorems for extremes using a wider class of normalizing mapping than the linear ones to get a wider class of limit laws. This wider class of extreme limits can be used in solving approximation problems. For extreme order statistics, in a recent paper by Sreehari (2009), the domains of attraction for general nonlinear normalizations are fully characterized, including the question of how to choose suitable norming functions from the knowledge of the sample distribution. The main aim of this thesis is...

The main aim of this work is to apply Generalized Extreme Value distribution under Linear normalization (GEVL) and Generalized Pareto Distribution under Linear normalization (GPDL) to modeling air pollutant in El Sharkia governorate in Egypt. Also, to solve the problem of the choice peak over threshold in the case of GPDL and the validity of bootstrap method in the case of GEVL modeling. We suggest the sub-sample bootstrap method to convert any data to block data to use it for GEVL modeling. Moreover, we introduced the Generalized Pareto Distribution under Power normalization (GPDP), which...

For a long period of time, the probability theory was meant to interpret the laws of averages but even within this theory occurrences now associated with extreme values had been viewed as accidents or surprises without regular laws. This view has changed only quite recently, and in this work we deal with some of the present stage problems of extreme value theory from the mathematical and practical points of view. The main aim of this work is to study the limiting behavior of the random maximum of np-dimensional distributed random variables, which are non-identical. The results of this study...