The maximum domain of attraction of multivariate extreme value distributions is small

被引：2

作者：

Leonetti, Paolo ^{[1
]}

Chokami, Amir Khorrami ^{[2
,3
]}

机构：

[1] Univ Insubria, Dept Econ, Via Monte Generoso 71, I-21100 Varese, Italy

[2] Univ Torino, ESOMAS Dept, Corso Unione Soviet 128 Bis, I-10122 Turin, Italy

[3] Collegio Carlo Alberto, Piazza Arbarello 8, I-10122 Turin, Italy

来源：

ELECTRONIC COMMUNICATIONS IN PROBABILITY | 2022年 / 27卷

关键词：

weak convergence of probability measures; maximum domain of attraction; Banach-Mazur game; Baire category;

D O I：

10.1214/22-ECP501

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

Consider the set of Borel probability measures on R-k and endow it with the topology of weak convergence. We show that the subset of all probability measures which belong to the domain of attraction of some multivariate extreme value distributions is dense and of the first Baire category. In addition, the analogue result holds in the context of free probability theory.

引用

页数：8

共 50 条

[1] DOMAINS OF ATTRACTION OF MULTIVARIATE EXTREME VALUE DISTRIBUTIONS
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[2] On the use of domain of attraction to identify extreme value distributions for maximum flows.
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