Author : Kareem, Amaal
On Characterization of Some Extreme Value Distributions Through the Conditional Expectations of Generalized Order Statistics
journal of kerbala university,
2012, Volume 8, Issue 4, Pages 186-189
Let X_1,X_2,……,X_n be continuous independent and identically distributed (i.i.d) random variable with d.f. F(x) and p.d.f. f(x).Characterization theorems for a general class of distributions are presented in terms of the function E[〖g(X〗_(j:n:m:m+1) ├|X_(j-p:n:m:m+1)=x,┤ X_(j+q:n:m:m+1)=y]=A(x,y) where k=m+1.In this article We give characterization conditions for the frechet distribution such that F(x)=1-e^(〖-x〗^(-α) ), x>0 ,α>0
and generalized extreme value distribution such that F(x)=e^(〖-(1-εx)〗^(1⁄ε) ) ifε≠0
by conditional expectation of generalized order statistics .