الفهرس 
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Abstract
The first object of this thesis is to study the random upper extremes Xs0(νn ):νn under mild conditions, where all the restricted conditions in Vasudeva and Moridani (2010) will be got rid. Moreover, we aim to obtain the parallel results for the central os. Also, we derive the necessary conditions of the weak convergence of the random extreme and central os in the most considered cases. In addition, we study the asymptotic behavior of the intermediate os of the stationary Gaussian sequences under equi-correlated set up. The second object is to study the limit distributions of extreme, intermediate and central m-gos, as well as m-dgos, of a stationary Gaussian sequence under equi-correlated set up. Moreover, we aim to extend the result of extremes to a wide subclass of gos, as well as dgos. Finally, the last our aim is to extend all the preceding results, by studying the limit distribu- tions of extreme, intermediate and central m-gos, as well as m-dgos, of a stationary Gaussian sequence under equi-correlated set up, when the random sample size is assumed to converge weakly. Moreover, we aim to extend the result of extremes to a wide subclass of gos (as well as dgos) which contains the most important models of ordered random variables (rv’s).
The thesis consists of four chapters, as follows:
Chapter one: This chapter deals with general introduction for distributional the- ory of os with a review for the basic probability limit theorems which will be used ii
in the sequel. Also, we review of the limit theory of os with variable rank, the sta- tionary Gauassian sequence, the extremes with random sample size and a review of gos and dgos.
Chapter two: In this chapter, we study the limit distributions of the extreme, intermediate and central os of a stationary Gaussian sequence under equi-correlated set up. When the random sample size is assumed to converge weakly and to be independent of the basic variables, the sufficient (and in some cases the necessary) conditions for the convergence are derived. Finally, we show that the obtained re- sult for the maximum os, with random sample size, is still applied in the case of the non-constant correlation case.
Chapter three: This chapter, is devoted to study the limit distributions of ex- treme, intermediate and central m-gos, as well as m-dgos, of a stationary Gaussian sequence under equi-correlated set up. Moreover, the result of extremes is extended to a wide subclass of gos, as well as dgos, (which contains the most important models of ordered rv’s), when the parameters γ1,n , γ2,n , ..., γn,n are assumed to be pairwise
different.
Chapter four: This chapter deals with the limit distributions of extreme, interme- diate and central m-gos, as well as m-dgos, of a stationary Gaussian sequence under equi-correlated set up, when the random sample size is assumed to converge weakly. Moreover, the result of extremes is extended to a wide subclass of gos (as well as dgos) which contains the most important models of ordered rv’s.