Ensemble equivalence for non-Boltzmaniann distributions

6 pages.-- Final full-text version of the paper available at: http://dx.doi.org/10.1016/j.physa.2006.01.040.We discuss the possibility of using generalized canonical distributions, i.e., using other factors than exp(-βE), in order to compute the equilibrium properties of physical systems. It will be shown that some other choices can, in certain cases, lead to a simpler calculation of those properties. The corresponding equivalence between the canonical and the generalized canonical distributions is derived using well-known principles of statistical mechanics and we exemplify the method by deriving in a simple way the equilibrium properties of the long-range Ising model.This work is supported by the Ministerio de Ciencia y Tecnología (Spain) and FEDER, projects FIS2004-5073-C04-03 and FIS2004-953