Abstract: The sequences {Z_i,n, 1≤i≤n}, n≥1 have 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 in this paper. We found a new type of not max-stable extreme value distributions, i) ; ii) ; iii) , r≥2, 0<α₁≤α₂≤…≤α_r and λ_i∈(0,1] for i, 1≤i≤r-1 which occur if F_j, …, F_m belong to the same MDA.

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

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