In this paper we propose a framework for defining and discovering optimal association rules involving a numerical attribute A in the consequent. The consequent has the form of interval conditions (A < x, A x or A ∈ I where I is an interval or a set of intervals of the form [x l , xu)). The optimality is with respect to leverage, one well known association rule interest measure. The generated rules are called Maximal Leverage Rules (MLR) and are generated from Distribution Rules. The principle

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... r finding the MLR is related to the Kolmogorov-Smirnov goodness of fit statistical test. We propose different methods for MLR generation, taking into account leverage optimallity and readability. We theoretically demonstrate the optimality of the main exact methods, and measure the leverage loss of approximate methods. We show empirically that the discovery process is scalable.