具有相同广义帕累托分布的两个序列混合的极值分布

Extreme value distributions of mixing two sequences with the same MDA.

作者信息

Jiang Yue-Xiang

机构信息

College of Economics, Zhejiang University, Hangzhou 310027, China.

出版信息

J Zhejiang Univ Sci. 2004 Mar;5(3):335-42. doi: 10.1007/BF02841019.

DOI:10.1007/BF02841019

PMID:14727310

Abstract

Suppose [(i), i>or=1] and [Y(i), i>or=1] are two independent sequences with distribution functions F(X)(x) and F(Y)(x), respectively. Z(i,n) is the combination of X(i) and Y(i) with a probability p(n) for each i with 1<or=i<or=n. The extreme value distribution G(Z)(x) of this particular triangular array of the i.i.d. random variables Z(1,n), Z(2,n), ..., Z(n,n) is discussed. We found a new form of the extreme value distributions i) Phi(alpha(1))(A)(x)Phi(alpha(2))(x) and ii) Psi(alpha(1))(A)(x)Psi(alpha(2))(x) (alpha(1)<alpha(2)), which are not max-stable. It occurs if F(X) and F(Y) belong to the same MDA(Phi) or MDA(Psi).

摘要

假设[(i), i≥1]和[Y(i), i≥1]是两个相互独立的序列，其分布函数分别为F(X)(x)和F(Y)(x)。对于每个1≤i≤n的i，Z(i,n)是以概率p(n)对X(i)和Y(i)的组合。讨论了独立同分布随机变量Z(1,n), Z(2,n), ..., Z(n,n)这个特定三角阵列的极值分布G(Z)(x)。我们发现了极值分布的一种新形式：i) Phi(alpha(1))(A)(x)Phi(alpha(2))(x)和ii) Psi(alpha(1))(A)(x)Psi(alpha(2))(x)（alpha(1)<alpha(2)），它们不是最大稳定的。当F(X)和F(Y)属于同一个MDA(Phi)或MDA(Psi)时会出现这种情况。