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Further Applications of D-Norms to Probability & Statistics

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Multivariate Extreme Value Theory and D-Norms

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Abstract

This section introduces max-characteristic functions (max-CFs), which are an offspring of D-norms. A max-CF characterizes the distribution of an rv in \(\mathbb R^d\), whose components are non-negative and have finite expectation. Pointwise convergence of a max-CF is shown to be equivalent to convergence with respect to the Wasserstein metric. An inversion formula for max-CF is established as well.

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  1. Fakultät für Mathematik und Informatik, Universität Würzburg, Würzburg, Germany

    Michael Falk

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  1. Michael Falk
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Falk, M. (2019). Further Applications of D-Norms to Probability & Statistics. In: Multivariate Extreme Value Theory and D-Norms. Springer Series in Operations Research and Financial Engineering. Springer, Cham. https://doi.org/10.1007/978-3-030-03819-9_5

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