Probabilistic enhancement of classical robustness margins: a class of nonsymmetric distributions

In this note, we address the problem of risk assessment when the robustness margin is exceeded, without a priori knowledge of the distribution of the uncertainty. The only assumption is that the distribution belongs to a given class. In contrast to previous work, this class contains both symmetric and nonsymmetric distributions. We prove that the assessment of risk can be done using only a subset of the admissible distributions. Also, if the set of uncertainties that verify the specifications is convex, it is proven that risk assessment can be done using only a finite subset of the class. Finally, a way of estimating risk is provided for the nonconvex case.