Symmetric generalized binomial distributions

Abstract

In two recent articles we have examined a generalization of the binomial distribution associated with a sequence of positive numbers, involving asymmetric expressions of probabilities that break the symmetry {\it win-loss}. We present in this article another generalization (always associated with a sequence of positive numbers) that preserves the symmetry {\it win-loss}. This approach is also based on generating functions and presents constraints of non-negativeness, similar to those encountered in our previous articles.

23 pages, 2 figures

References in corpus (3)

• Generating functions for generalized binomial distributions
• On a generalization of the binomial distribution and its Poisson-like limit
• A note about combinatorial sequences and Incomplete Gamma function

Cited by in corpus (6)

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• Lowering Helstrom Bound with non-standard coherent states
• Central limit theorem for a class of globally correlated random variables
• Emergence of $q$-statistical functions in a generalized binomial distribution with strong correlations
• A note about combinatorial sequences and Incomplete Gamma function
• Entropies of deformed binomial distributions