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Neighbourhood models induced by the Euclidean distance and the Kullback-Leibler divergence

Neighbourhood or distortion models are particular imprecise probability models that appear by creating a neighbourhood around a probability measure given a distorting function and a distortion parameter. This paper investigates the distortion models obtained when considering the Euclidean distance or the Kullback-Leibler divergence as distorting function. We analyse the main properties of the credal sets induced by these two distorting functions as well as the main properties of the associated coherent lower previsions. To conclude the paper, we compare these two models with other well-known distortion models: the pari-mutuel, linear vacuous, constant odds ratio and total variation models.