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ZJUS-A
Journal of Zhejiang University-SCIENCE A (Applied Physics & Engineering)  2004, Vol. 5 Issue (3): 335-342    DOI: 10.1631/jzus.2004.0335
Mathematics     
Extreme value distributions of mixing two sequences with the same MDA
JIANG Yue-xiang
College of Economics, Zhejiang University, Hangzhou 310027, China
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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).

Key words： Extreme value distribution      Maximum domain of attraction (MDA)      Mixed distribution functions     
Received: 18 May 2003     
CLC:  O211.4  
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Cite this article:

JIANG Yue-xiang. Extreme value distributions of mixing two sequences with the same MDA. Journal of Zhejiang University-SCIENCE A (Applied Physics & Engineering), 2004, 5(3): 335-342.

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http://www.zjujournals.com/xueshu/zjus-a/10.1631/jzus.2004.0335     OR     http://www.zjujournals.com/xueshu/zjus-a/Y2004/V5/I3/335

[1] Jiang Yue-xiang. More general results on mixed extreme value distributions*[J]. Journal of Zhejiang University-SCIENCE A (Applied Physics & Engineering), 2005, 6( 7): 27-.
[2] JIANG Yue-xiang. A class of not max-stable extreme value distributions[J]. Journal of Zhejiang University-SCIENCE A (Applied Physics & Engineering), 2005, 6( 4): 11-.
[3] JIANG Yue-xiang. Extreme value distributions of mixing two sequences with different MDA\'s[J]. Journal of Zhejiang University-SCIENCE A (Applied Physics & Engineering), 2004, 5(5): 509-517.