Extreme value distributions of mixing two sequences with different MDA's

摘要

Suppose {X_i, i≥1} and {Y_i, i≥1} are two independent sequences with distribution functions F_X(X) and F_Y(x), respectively. Z_(i, n) is the combination of X_i and Y_i with a probability ρ_n for each i with 1≤i≤n. The extreme value distribution G _Z(x) of this particular triangular array of the i.i.d. random variables Z_(1,n), Z_(2,n),t, Z_(n,n) is discussed,. We found a new form of the extreme value distribution A~A(ρx)A(x)(0 <1), which is not max-stable It occurs if F_X(X) and F_Y(x) belong to the same MDA(A). G_Z(x) does not exist as mixture forms of the different types of extreme value distributions.