Erlang And Mixed General Normal Distribution And Weak Convergence Of Exceedances Point Process

This paper is consisted of three parts, which includes the convergence rate of extreme value distribution from Erlang distribution, the related properties of mixed generalized normal distri-bution and the asymptotic distribution of the point process of exceedances.Based on the Extreme Types Theorem and properties of second-order regular variation. the limiting distribution of the extremes with parent following Erlang distribution and the associated rates of convergence are derived in the second chapter.In the third part of this paper. with the properties of generalized normal distribution and finite mixed distribution, a new kind of finite mixed generalized normal distribution is proposed. Based on the related properties of the generalized normal distribution, we study some properties of the mixed generalized normal distribution. which includes the nth moment and the nth central moment, the asymptotic distribution of the extreme order statistics, and characteristic function and correlation for some special cases.Let Nn and Nn be the exceedances point process formed by random variables from complete and incomplete samples, and define Nn=Nn+Nn. In the forth chapter of this thesis, we consider the week convergence of the exceedances point processes Nn,Nn and Nn, and the joint asymptotic distribution of the associated order statistics in the case of dependent Normal sequences.