Ensembles with non-equiprobable states—which have been studied in a previous work (Auger 1984)—are applied to various empirical and theoretical distributions. The equilibrium distributions are calculated by the Lagrange method. Firstly, we determine the state probabilities necessary to obtain empirical distributions, such as Pareto's iaw. Secondly, we calculate equilibrium distributions for an ethotogical example concerning activity frequencies of animals. We also study an ecological example in population dynamics concerning the age-class distribution of animals belonging to a given population. This method can be used either to explain empirical equilibrium distributions or to calculate theoretical equilibrium distributions from chosen graphs of transition states.