Abstract: Suppose {X_i, i≥1} and {Yi, 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 pn 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,...,Z_n,n is discussed. We found a new form of the extreme value distributions i) Φ_α1^A(x)Φ_α2(x) and ii) Ψ_α1^A(x)Ψ_α2(x)(α1<α2), which are not max-stable. It occurs if F_X and F_X belong to the same MDA(Φ) or MDA(Ψ).

Key words: Extreme value distribution, Maximum domain of attraction (MDA), Mixed distribution functions

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