Generating functions for generalized binomial distributions

Abstract

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.

PDFLaTex, 27 pages, 5 figures

References in corpus (3)

• A scale-invariant probabilistic model based on Leibniz-like pyramids
• On a generalization of the binomial distribution and its Poisson-like limit
• Proof of a conjecture by Gazeau et al. using the Gould Hopper polynomials

Cited by in corpus (6)

• Coherent states in Quantum Optics: An oriented overview
• Symmetric generalized binomial distributions
• Lowering Helstrom Bound with non-standard coherent states
• Emergence of $q$-statistical functions in a generalized binomial distribution with strong correlations
• Proof of a conjecture by Gazeau et al. using the Gould Hopper polynomials
• Entropies of deformed binomial distributions