  We discuss the possibility of using generalized canonical distributions, i.e.
using other factors than $\exp(-\beta E)$, in order to compute the equilibrium
properties of physical systems. It will be show 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.
