Convergence Properties of Kemp's q-Binomial Distribution

TL;DR

This paper investigates the convergence behavior of Kemp's q-binomial distribution, establishing various q-analogues of classical limit theorems using elementary estimates and Mellin transform asymptotics.

Contribution

It provides new convergence results for Kemp's q-binomial distribution, connecting it with classical distributions through q-analogues and advanced asymptotic analysis.

Findings

Convergence to classical binomial distribution

Convergence to the Heine distribution

Convergence to the Poisson distribution

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.