Statistical Distributions "generalized" from the principle of maximum entropy

We use a modification of the Maximum Entropy Principle developed by E. Jaynes within the framework of Statistical Mechanics by taking the entropy functional of C. Tsallis with entropic index q I A n and we found generalized versions of some well known statistical densities. We show that this results are in agreement with the classical ones when we take the limit q -> 1 and we recover the usual densities obtained by maximization of the Boltzmann-GibbsShannon entropic functional. The extension of this line of reasoning to other discrete or continuous densities is straightforward and we expect to find some useful applications of these models in the future..