An Offspring of Multivariate Extreme-Value Theory: The Max-Characteristic Function
Probability
2016-10-21 v2
Abstract
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 with 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.
Cite
@article{arxiv.1603.02575,
title = {An Offspring of Multivariate Extreme-Value Theory: The Max-Characteristic Function},
author = {Michael Falk and Gilles Stupfler},
journal= {arXiv preprint arXiv:1603.02575},
year = {2016}
}