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Extreme-value limit of the convolution of exponential and multivariate normal distributions: Link to the Hüsler–Reiß distribution

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  • Krupskii, Pavel
  • Joe, Harry
  • Lee, David
  • Genton, Marc G.

Abstract

The multivariate Hüsler–Reiß copula is obtained as a direct extreme-value limit from the convolution of a multivariate normal random vector and an exponential random variable multiplied by a vector of constants. It is shown how the set of Hüsler–Reiß parameters can be mapped to the parameters of this convolution model. Assuming there are no singular components in the Hüsler–Reiß copula, the convolution model leads to exact and approximate simulation methods. An application of simulation is to check if the Hüsler–Reiß copula with different parsimonious dependence structures provides adequate fit to some data consisting of multivariate extremes.

Suggested Citation

  • Krupskii, Pavel & Joe, Harry & Lee, David & Genton, Marc G., 2018. "Extreme-value limit of the convolution of exponential and multivariate normal distributions: Link to the Hüsler–Reiß distribution," Journal of Multivariate Analysis, Elsevier, vol. 163(C), pages 80-95.
    • Handle: RePEc:eee:jmvana:v:163:y:2018:i:c:p:80-95
    DOI: 10.1016/j.jmva.2017.10.006
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    References listed on IDEAS

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    1. Ho, Zhen Wai Olivier & Dombry, Clément, 2019. "Simple models for multivariate regular variation and the Hüsler–Reiß Pareto distribution," Journal of Multivariate Analysis, Elsevier, vol. 173(C), pages 525-550.

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