Generating functions for generalized binomial distributions

TL;DR

This paper introduces a generating function approach to generalized binomial distributions, ensuring nonnegativeness and providing a comprehensive characterization with numerous analytical examples.

Contribution

It offers a novel generating function framework that guarantees nonnegativeness and facilitates analysis of generalized binomial distributions.

Findings

Automatic fulfillment of nonnegativeness constraints

Complete characterization via generating functions

Extensive analytical examples provided

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.