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Received: 2003-03-18

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Journal of Zhejiang University SCIENCE A 2004 Vol.5 No.5 P.509-517

http://doi.org/10.1631/jzus.2004.0509


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


Author(s):  JIANG Yue-xiang

Affiliation(s):  College of Economics, Zhejiang University, Hangzhou 310027, China

Corresponding email(s):   jyxbern@hotmail.com

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


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JIANG Yue-xiang. Extreme value distributions of mixing two sequences with different MDA's[J]. Journal of Zhejiang University Science A, 2004, 5(5): 509-517.

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Abstract: 
Suppose {Xi, i≥1} and {Yi, i≥1} are two independent sequences with distribution functions FX(x) and FY(x), respectively. Zi,n is the combination ofXi and Yi 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 ΛA(ρx)Λ(x) (0<ρ<1), which is not max-stable. It occurs if FX(x) and FY(x) belong to the same MDA(Λ). GZ(x) does not exist as mixture forms of the different types of extreme value distributions.

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Reference

[1] Bingham, N.H., Goldie, C.M., Teugels, J.L., 1983. Regular Variation. Springer-Verlag.

[2] Embrechts, P., Klueppelberg, C., Mikosch, T., 1997. Modelling Extremal Events. Springer-Verlag, Berlin, Heidelberg.

[3] Jiang, Y.X., 2002. Mixed Extreme Value Distributions, Ph.D. Thesis. Berne University, Switzerland.

[4] Jiang, Y.X., 2004. Extreme value distributions of mixing two sequences with the same MDA.Journal of Zhejiang University SCIENCE,5(3):335-342.

[5] Leedbetter, M.R., Lingen, G., Rootzan, H., 1983. Extremes and Related Properties of Random Sequences and Processes, Springen-Verlag.

[6] Resnick, S.I., 1987. Extreme Values, Regular Variation, and Point Processes. Springer-Verlag.

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