Abstract: 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 ofXi 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 distribution ΛA(ρx)Λ(x) (0<ρ<1), which is not max-stable. It occurs if F_X(x) and F_Y(x) belong to the same MDA(Λ). G_Z(x) does not exist as mixture forms of the different types of extreme value distributions.

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

Please provide your name, email address and a comment

Your Name: Affili: E-Mail Address:

Comment (Please comment in English):


Verification Code(click to change a pic):