Extreme value distributions of mixing two sequences with different MDA＇s

摘要

Suppose {Xi, i≥l } and {Yi, i≥l } are two independent sequences with distribution functions Fx(x) and Fr(x), respectively. Zi,n is the combination of Xi and Y1 with a probability pn for each i with 1≤i≤<_n. The extreme value distribution Gz(x) of this particular triangular array of the i.i.d, random variables Z1,n, Z2.n ,..., Zn.n is discussed. We found a new form of the extreme value distribution A^A(px)A(x)(0＜p＜1), which is not max-stable. It occurs if Fx(x) and Fr(x) belong to the same MDA(A). Gz(x) does not exist as mixture forms of the different types of extreme value distributions.