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

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• 作者：Michael Falk^a ; ^{michael.falk@uni-wuerzburg.de} ; Gilles Stupfler^b ; ^{Gilles.Stupfler@nottingham.ac.uk}
• 关键词：primary ; 60E10 ; secondary ; 60F99 ; 60G70
• 刊名：Journal of Multivariate Analysis
• 出版年：2017
• 出版时间：February 2017
• 年：2017
• 卷：154
• 期：Complete
• 页码：85-95
• 全文大小：432 K
• 卷排序：154

文摘

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 RdRd, 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.