Abstract: The sequences {Z_i,n, 1≤i≤n}, n≥1 are multi-nomial distribution among i.i.d. random variables {X_1,i, i≥1}, {X_2,i, i≥1}, …, {X_m,i, i≥1}. The extreme value distribution G_Z(x) of this particular triangular array of i.i.d. random variables Z_1,n, Z_2,n, …, Z_n,n is discussed. A new type of not max-stable extreme value distributions which are Fréchet mixture, Gumbel mixture and Weibull mixture has been found if F_j,…,F_m belong to the same MDA. Whether mixtures of different types of extreme value distributions exist or not and the more general case are discussed in this paper. We found that G_Z(x) does not exist as mixture forms of the different types of extreme value distributions after we investigated all cases.

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

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