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 enables us to suggest an efficient method for modeling extreme value under power normalization. We present statistical inference about the upper tail distribution for (GPDP). We also compare between the modeling under linear normalization and under power normalization. Finally, in the last chapter of this book the inconsistent and weak consistency of bootstrapping central and intermediate order statistics for an appropriate choice o re-sample size are investigated.

About the Author

Prof. H. M. Barakat, received his Ph.D. in 1986-Math. Stat. Moscow state Univ. In 1989 he was awarded the Egyptian state prize in Math. In 2007, he was awarded distinction national state prize in basic science. In 2010 he was awarded appreciated Zagazig Univ. prize and in 2012, he was awarded the inter. Fiza Al-Kharafi prize in the field of Math.

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