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

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 Rd, whose components are nonnegative and have finite expectation. Pointwise convergence of max-CFs is shown to be e...

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Bibliographic Details
Main Authors: Falk, Michael, Stupfler, Gilles
Format: Article
Published: Elsevier 2017
Subjects:
Online Access:https://eprints.nottingham.ac.uk/43808/
Description
Summary: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 Rd, 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.