The definition, properties, and calculational advantages of the binomial transform representation of a class of finitely enumerated discrete probability distributions that generalize the standard binomial distribution are investigated. Discrete distributions of this type appear in various models of hadron multiparticle production among other physical applications. The compact representations of the generating functions for factorial moments of these discrete distributions obtained using the binomial transform are used to relate the behavior of the complex zeros of the generating functions to different models for the distribution of charged and neutral particles in multihadron production.