Sankhya A

, Volume 72, Issue 2, pp 331–343 | Cite as

Convergence properties of Kemp’s q-binomial distribution

  • Stefan Gerhold
  • Martin Zeiner


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. From the results about distributions, we deduce some new convergence results for (q-)Krawtchouk and q-Charlier polynomials. Besides elementary estimates, we apply Mellin transform asymptotics.

Keywords and phrases

q-binomial distribution discrete normal distribution Heine distribution q-Krawtchouk polynomials q-Charlier polynomials Mellin transform limit theorems 

AMS (2000) subject classification

Primary 60F05 secondary 33D15 


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Copyright information

© Indian Statistical Institute 2010

Authors and Affiliations

  1. 1.Vienna University of TechnologyViennaAustria
  2. 2.Graz University of TechnologyGrazAustria
  3. 3.Vienna University of TechnologyViennaAustria
  4. 4.Graz University of TechnologyGrazAustria

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