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(Sub-)Differentiability of Probability Functions with Elliptical Distributions

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Abstract

In this paper we investigate probability functions acting on nonlinear systems wherein the random vector can follow an elliptically symmetric distribution. We provide first and second order differentiability results as well as readily implementable formulæ. We also demonstrate that these formulæ can be readily employed within standard non-linear programming software through a set of illustrative numerical experiments.

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Acknowledgements

The authors gratefully acknowledge the PGMO project “Optimisation sous contraintes de fiabilité de systèmes complexes - Application à l’ancrage des supports d’éolienne flottante” through which part of this work was funded. The authors would also like to thank two anonymous referees whose evaluation was greatly appreciated.

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Authors and Affiliations

  1. EDF R&D, OSIRIS, 7 Boulevard Gaspard Monge, F-91120, Palaiseau, France

    W. van Ackooij

  2. IFP Energies nouvelles, 1-4 Avenue du Bois Préau, 92852, Rueil Malmaison, France

    I. Aleksovska & M. Munoz-Zuniga

Authors
  1. W. van Ackooij
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  2. I. Aleksovska
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  3. M. Munoz-Zuniga
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Correspondence to W. van Ackooij.

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Grant PGMO -“Application à l’ancrage des supports d’éolienne flottante”

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van Ackooij, W., Aleksovska, I. & Munoz-Zuniga, M. (Sub-)Differentiability of Probability Functions with Elliptical Distributions. Set-Valued Var. Anal 26, 887–910 (2018). https://doi.org/10.1007/s11228-017-0454-3

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  • DOI: https://doi.org/10.1007/s11228-017-0454-3

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