Abstract The sequences {Zi,n, 1?üi?ün}, n?Y1 have multi-nomial distribution among i.i.d. random variables {X1,i, i?Y1}, {X2,i, i?Y1}, ?-, {Xm,i, i?Y1}. The extreme value distribution GZ(x) of this particular triangular array of i.i.d. random variables Z1,n, Z2,n, ..., Zn,n is discussed in this paper. We found a new type of not max-stable extreme value distributions, i) ; ii) ; iii) , r?Y2, 0<|á1?ü|á2?ü?-?ü|ár and |?i?ê(0,1] for i, 1?üi?ür-1 which occur if Fj, ?-, Fm belong to the same MDA.
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