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

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  • Falk, Michael
  • Stupfler, Gilles

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 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.

Suggested Citation

  • Falk, Michael & Stupfler, Gilles, 2017. "An offspring of multivariate extreme value theory: The max-characteristic function," Journal of Multivariate Analysis, Elsevier, vol. 154(C), pages 85-95.
    • Handle: RePEc:eee:jmvana:v:154:y:2017:i:c:p:85-95
    DOI: 10.1016/j.jmva.2016.10.007
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    References listed on IDEAS

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    1. Stefan Aulbach & Verena Bayer & Michael Falk, 2012. "A multivariate piecing-together approach with an application to operational loss data," Papers 1205.1617, arXiv.org.
    2. Falk, Michael, 2015. "On idempotent D-norms," Journal of Multivariate Analysis, Elsevier, vol. 139(C), pages 283-294.
    3. Aulbach, Stefan & Falk, Michael & Hofmann, Martin, 2012. "The multivariate Piecing-Together approach revisited," Journal of Multivariate Analysis, Elsevier, vol. 110(C), pages 161-170.
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    Citations

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    Cited by:

    1. Meintanis, S.G. & Milošević, B. & Jiménez–Gamero, M.D., 2024. "Goodness–of–fit tests based on the min–characteristic function," Computational Statistics & Data Analysis, Elsevier, vol. 197(C).
    2. Hashorva, Enkelejd, 2018. "Representations of max-stable processes via exponential tilting," Stochastic Processes and their Applications, Elsevier, vol. 128(9), pages 2952-2978.
    3. Falk Michael & Stupfler Gilles, 2019. "On a class of norms generated by nonnegative integrable distributions," Dependence Modeling, De Gruyter, vol. 7(1), pages 259-278, January.
    4. Michael Falk & Gilles Stupfler, 2021. "The Min-characteristic Function: Characterizing Distributions by Their Min-linear Projections," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 83(1), pages 254-282, February.

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