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11/2012 : On a Family of q-Binomial Distributions

RR Number
11/2012
Author(s)
Martin Zeiner
Abstract
We introduce a family of q-analogues of the binomial distribution, which generalises the Stieltjes-Wigert-, Rogers-Szeg¨o-, and Kemp-distribution. Basic properties of this familiy are provided and several convergence results involving the classical binomial, Poisson, discrete normal distribution, and a family of q-analogues of the Poisson distribution are established. These results generalise convergence properties of Kemp’s-distribution, and some of them are q-analogues of classical convergence properties.
Bibtex
@techreport{Zei12:RR,
  author =       "Martin Zeiner",
  title =        "On a Family of q-Binomial Distributions",
  institution =  "Technische Universit{\"a}t Wien, Institut f{\"u}r Technische Informatik",
  address =      "Treitlstr. 1-3/182-1, 1040 Vienna, Austria",
  type =         "Research Report",
  year =         "2012",
  number =       "11/2012"
}
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