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On Continuous Limiting Behaviour for the *q(n)*-Binomial Distribution with *q(n)*→1 as n→∞

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Recently, Kyriakoussis and Vamvakari [1] have established a *q*-analogue of the Stirling type for *q*-constant which have lead them to the proof of the pointwise convergence
of the *q*-binomial distribution to a
Stieltjes-Wigert continuous distribution. In the present article, assuming a sequence *q(n)* of *n* with *q(n)*→1 as n→∞, the study of the
affect of this assumption to the *q(n)*-analogue of the
Stirling type and to the asymptotic behaviour of the *q(n)*-Binomial distribution
is presented. Specifically, a *q(n)* analogue of the Stirling type is provided
which leads to the proof of deformed Gaussian limiting behaviour for the *q(n)*-Binomial
distribution. Further, figures using the program MAPLE are presented,
indicating the accuracy of the established distribution convergence even for
moderate values of *n*.

Conflicts of Interest

The authors declare no conflicts of interest.

Cite this paper

*q(n)*-Binomial Distribution with

*q(n)*→1 as n→∞,"

*Applied Mathematics*, Vol. 3 No. 12A, 2012, pp. 2101-2108. doi: 10.4236/am.2012.312A290.

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