Generating functions for generalized binomial distributions
  In a recent article a generalization of the binomial distribution associated with a sequence of positive numbers was examined. The analysis of the nonnegativeness of the formal expressions was a key-point to allow to give them a statistical interpretation in terms of probabilities. In this article we present an approach based on generating functions that solves the previous difficulties: the constraints of nonnegativeness are automatically fulfilled, a complete characterization in terms of generating functions is given and a large number of analytical examples becomes available. 
H. Bergeron, E. M. F. Curado, J. P. Gazeau, Ligia M. C. S. Rodrigues
math-ph cond-mat.stat-mech math.MP quant-ph