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Journal Articles Set-Valued and Variational Analysis Year : 2018

(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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hal-02013571 , version 1 (11-02-2019)

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Wim van Ackooij, I. Aleksovska, M. Munoz-Zuniga. (Sub-)Differentiability of Probability Functions with Elliptical Distributions. Set-Valued and Variational Analysis, 2018, 26 (4), pp.887-910. ⟨10.1007/s11228-017-0454-3⟩. ⟨hal-02013571⟩

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