الفهرس 
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Abstract
One of the most important model of ordered statistical data models is the order statistics. This model can be applied in testing the strength of material, reliability analysis, life time studies, air pollution, risk management, insurance and many other activities such as economics and Engineering. It is known that the study of the asymptotic behavior of order statistics model is the cornerstone in building accurate statistical models to describe and study those important activities.
The main aim of this thesis is studying the Generalized Extreme Value distribution under Linear Normalization (GEVL), and Power normalization with their applications in case of independent and identically random variables (i.i.d.r.v’s), by using different method of estimation for air pollution data. Furthermore compare between the modeling under linear normalization and power normalization by using Kolmogorov-Simirnov test (K-S). Also, More General extreme value distribution based on the idea of Box-Cox transformation is introduced. Application of bivariate extreme value distribution to analyze the maximum concentration of air pollution data from Barking Dagenham station in London city is done. This thesis consists of four chapters besides a list of references and arabic summary. The outlines of this thesis are:
Chapter 1: It includes general review and consists of five sections. The first and the second sections present the extreme value theory under linear and power normalization. The third section shows the generalized Pareto distributions under
linear and power normalization. The fourth section includes some of estimation
methods such as maximum likelihood, Genetic Algorithm and moment method.
The last section contains fitting tools such as Likelihood ratio test and
Kolmogorov-Simirnov test.
Chapter 2: In this chapter the parameters of generalized extreme value under
linear and power normalization were estimated by using some methods such as:
Maximum likelihood (ML), Genetic algorithms (GAs), Moment method (M).
Moreover comparison between them by Kolmogorov-Simirnov test (K-S) is
done.
Chapter 3: In this chapter, a new model was introduced by using Box-Cox
transformation is used for generalized pareto distribution under power
normalization (GPDP) and generalized extreme value distribution under power
normalization (GEVP). Likelihood ratio test is used for comparing between them.
Also, the suggested model is successfully applied to daily maximum air pollution
from Barking Dagenham station which is one of the London Air Quality
Monitoring Network (LAQN), since 1/1/2010 to 31/12/2015.
Chapter 4 : This chapter deals with the applications of bivariate extreme value
models. Three models for analyzing the data monitoring air pollutant NO, NO2
and SO2 are used. The first model is Gumble Type II, the second model is HuslerReiss
model and the third model is Marshall-Olkin. The parameter of marginal
under generalized extreme value of linear normalization (GEVL) distribution was
estimated. The dependent parameter was calculated by using maximum
likelihood method also the Bivariate generalized Pareto was applied and the
relationship between dependent parameter and the number of extreme data peak
over threshold was studied.