Choquet integrals integrate functions with respect to fuzzy measures. From a mathematical point of view these integrals generalize the Lebesgue integrals when the measures are additive. From a point of view of aggregation functions, one of the relevant aspects is that they generalize the weighted mean and the OWA. Choquet integrals have been successfully used in decision making problems when there are interactions between criteria. In this setting we can learn or identify the measures from a set of decisions. This fact seems to indicate that we can consider data as generated from distributions based on the Choquet integral. We will present some results on these types of distributions and on their generalizations.