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Journal of Zhejiang University SCIENCE A 2004 Vol.5 No.3 P.335-342

http://doi.org/10.1631/jzus.2004.0335


Extreme value distributions of mixing two sequences with the same MDA


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 the same MDA[J]. Journal of Zhejiang University Science A, 2004, 5(3): 335-342.

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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 of Xi 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 distributions i) Φα1A(x)Φα2(x) and ii) Ψα1A(x)Ψα2(x)(α1<α2), which are not max-stable. It occurs if FX and FX belong to the same MDA(Φ) or MDA(Ψ).

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Reference

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

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

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

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

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

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