| Let {Xi, 1≤i≤n} bc an independent identically distributed random variables with common distribution F(x), and Xl,n≤X2,n≤…Xn,n be the associated order statistics of X1, X2…, Xn. It is well known that if there exist constants an＞O, bn∈R, such thatGγ(x) is called extreme value distribution with extreme value indexγ, and F(x) is said to be in the domains of attractions of Gγ(x), denoted as F∈D(Gγ). Estimating the parameterγ, has become an important part in extreme value theory as F(x) is unknown. In this paper, a new kind of moment-type estimator is proposed,denotcd aswhereandThe arrangement of this thesis is: In the first part of this paper, asymptotic properties such as weak and strong consistency and asymptotic distribution ofγn have been considered under some weakly conditions. The expansions ofγn and its distribution are discussed in the second part under second regular variation conditions. Lastly some comparison ofγn and Moment type extreme value index estimator provided by Dekkers and de Haan are given by Monte Carlo Simulation.Keywords: Moment estimator; regular varying function; Weak and strong consistency; asymptotic normality; order statistics...
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