Aggregation of the Distortion Models Induced by the KL Divergence and Euclidean Distance

Distortion or neighbourhood models are tools within the imprecise probability theory that allow to robustify a probability measure. These are built by considering the closed ball around a probability measure with a given radius and using a distorting function to compare probability measures. These include well-known models such as the linear vacuous, pari-mutuel or total variation models. In this contribution we focus on the distortion models that arise from considering the Euclidean distance or the Kullback-Leibler divergence as distorting functions, and analyse their behaviour under different aggregation rules: conjunction, disjunction or convex mixtures.