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ZJUS-A
Journal of Zhejiang University-SCIENCE A (Applied Physics & Engineering)  2004, Vol. 5 Issue (5): 509-517    DOI: 10.1631/jzus.2004.0509
Applied & Financial Mathematics     
Extreme value distributions of mixing two sequences with different MDA\'s
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 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.

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

JIANG Yue-xiang. Extreme value distributions of mixing two sequences with different MDA\'s. Journal of Zhejiang University-SCIENCE A (Applied Physics & Engineering), 2004, 5(5): 509-517.

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http://www.zjujournals.com/xueshu/zjus-a/10.1631/jzus.2004.0509     OR     http://www.zjujournals.com/xueshu/zjus-a/Y2004/V5/I5/509

[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 the same MDA[J]. Journal of Zhejiang University-SCIENCE A (Applied Physics & Engineering), 2004, 5(3): 335-342.