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Received: 2004-07-19

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Journal of Zhejiang University SCIENCE A 2005 Vol.6 No.4 P.315~321

http://doi.org/10.1631/jzus.2005.A0315


A class of not max-stable 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. A class of not max-stable extreme value distributions[J]. Journal of Zhejiang University Science A, 2005, 6(4): 315~321.

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publisher="Zhejiang University Press & Springer",
doi="10.1631/jzus.2005.A0315"
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T1 - A class of not max-stable extreme value distributions
A1 - JIANG Yue-xiang
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DOI - 10.1631/jzus.2005.A0315


Abstract: 
The sequences {Zi,n, 1≤in}, n≥1 have 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 in this paper. We found a new type of not max-stable extreme value distributions, i) ; ii) ; iii) , r≥2, 0<α1α2≤…≤αr and λi∈(0,1] for i, 1≤ir-1 which occur if Fj, …, Fm belong to the same MDA.

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

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