On Continuous Limiting Behaviour for the <i>q(n)</i>-Binomial Distribution with <i>q(n)</i>→1 as n→∞
- 1 Department of Informatics and Telematics, Harokopio University of Athens, Athens, Greece
Abstract
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 e ven for moderate values of n .
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