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arXiv · 1203.3936

Generating functions for generalized binomial distributions

H. Bergeron·E. M. F. Curado·J. P. Gazeau·Ligia M. C. S. Rodrigues
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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.

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H. Bergeron, E. M. F. Curado, J. P. Gazeau, Ligia M. C. S. Rodrigues. 2012-03-18. Generating functions for generalized binomial distributions. https://doi.org/10.1063/1.4757601

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