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Journal of Zhejiang University SCIENCE A 2005 Vol.6 No.7 P.769~774

http://doi.org/10.1631/jzus.2005.A0769


More general results on mixed extreme value distributions


Author(s):  Jiang Yue-xiang

Affiliation(s):  School 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


Jiang Yue-xiang. More general results on mixed extreme value distributions[J]. Journal of Zhejiang University Science A, 2005, 6(7): 769~774.

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DOI - 10.1631/jzus.2005.A0769


Abstract: 
The sequences {Zi,n, 1≤in}, n≥1 are multi-nomial distribution among i.i.d. random variables {X1,i, i≥1}, {X2,i, i≥1}, …, {Xm,i, i≥1}. The extreme value distribution GZ(x) of this particular triangular array of i.i.d. random variables Z1,n, Z2,n, …, Zn,n is discussed. A new type of not max-stable extreme value distributions which are Fréchet mixture, Gumbel mixture and Weibull mixture has been found if Fj,…,Fm belong to the same MDA. Whether mixtures of different types of extreme value distributions exist or not and the more general case are discussed in this paper. We found that GZ(x) does not exist as mixture forms of the different types of extreme value distributions after we investigated all cases.

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Reference

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

[2] Jiang, Y.X., 2004a. Extreme value distributions of mixing two sequences with the same MDA. Journal of Zhejiang University SCIENCE, 5(3):335-334.

[3] Jiang, Y.X., 2004b. Extreme value distributions of mixing two sequences with the different MDA’s. Journal of Zhejiang University SCIENCE, 5(5):509-517.

[4] Jiang, Y.X., 2005. A class of not max-stable extreme value distributions. Journal of Zhejiang University SCIENCE, 6A(4):315-321.

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

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