Abstract
Suppose {X i, i≥1} and {Y i, i≥1} are two independent sequences with distribution functionsF X(x) andF Y(x), respectively.Z i,n is the combination ofX i andY i with a probabilityp n for eachi with 1≤i≤n. The extreme value distributionG Z(x) of this particular triangular array of the i.i.d. random variablesZ 1,n, Z1,n,..., Zn,n is discussed. We found a new form of the extreme value distribution ΓA(ϱx)Γ(0<ϱ<1), which is not max-stable. It occurs ifFx(x) andFy(x) belong to the sameMDA(Λ).G Z(x) does not exist as mixture forms of the different types of extreme value distributions.
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Jiang, Yx. Extreme value distributions of mixing two sequences with different MDA's. J. Zheijang Univ.-Sci. 5, 509–517 (2004). https://doi.org/10.1631/jzus.2004.0509
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DOI: https://doi.org/10.1631/jzus.2004.0509