On a generalization of the binomial distribution and its Poisson-like   limit
  We examine a generalization of the binomial distribution associated with a strictly increasing sequence of numbers and we prove its Poisson-like limit. Such generalizations might be found in quantum optics with imperfect detection. We discuss under which conditions this distribution can have a probabilistic interpretation. 
E. M. F. Curado, J. P. Gazeau, Ligia M. C. S. Rodrigues
math-ph cond-mat.stat-mech math.MP quant-ph