An offspring of multivariate extreme value theory: The max-characteristic function

被引：6

作者：

Falk, Michael ^{[1
]}

Stupfler, Gilles ^{[2
]}

机构：

[1] Univ Wurzburg, D-97074 Wurzburg, Germany

[2] Univ Nottingham, Sch Math Sci, Univ Pk, Nottingham NG7 2RD, England

来源：

JOURNAL OF MULTIVARIATE ANALYSIS | 2017年 / 154卷

关键词：

Multivariate extreme-value theory; Max-characteristic function; Wasserstein metric; Convergence;

D O I：

10.1016/j.jmva.2016.10.007

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：

This paper introduces max-characteristic functions (max-CFs), which are an offspring of multivariate extreme-value theory. A max-CF characterizes the distribution of a random vector in R-d, whose components are nonnegative and have finite expectation. Pointwise convergence of max-CFs is shown to be equivalent to convergence with respect to the Wasserstein metric. The space of max-CFs is not closed in the sense of pointwise convergence. An inversion formula for max-CFs is established. (C) 2016 Elsevier Inc. All rights reserved.

引用

页码：85 / 95

页数：11

共 12 条

[1]

[Anonymous], 2010, Laws of small numbers: extremes and rare events

[2] Max-stable processes and the functional D-norm revisited [J].