(Sub-)Differentiability of Probability Functions with Elliptical Distributions |
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Authors: | W. van Ackooij I. Aleksovska M. Munoz-Zuniga |
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Affiliation: | 1.EDF R&D, OSIRIS,Palaiseau,France;2.IFP Energies nouvelles,Rueil Malmaison,France |
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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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