Convergence Properties of Kemp's q-Binomial Distribution

2008/04/03 by Stefan Gerhold, Gerhold, Stefan, Martin Zeiner +1
Mathematics · #33D15 #60F05 #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #Combinatorics (math.CO) #FOS: Mathematics #Mathematical functions and polynomials #Probability (math.PR) #math.CO #math.PR #msc:33D15 #msc:60F05

paper · pdf · doi:10.48550/arxiv.0804.0534

arxiv created 2008/04/03 · openalex publication_date 2008/04/03 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider Kemp's q-analogue of the binomial distribution. Several convergence results involving the classical binomial, the Heine, the discrete normal, and the Poisson distribution are established. Some of them are q-analogues of classical convergence properties. Besides elementary estimates, we apply Mellin transform asymptotics.

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