TITLE:
On Continuous Limiting Behaviour for the q(n)-Binomial Distribution with q(n)→1 as n→∞
AUTHORS:
Malvina Vamvakari
KEYWORDS:
Stirling Formula; q(n) -Factorial Number of Order n; Saddle Point Method; q(n)-Binomial Distribution; Pointwise Convergence; Gauss Distribution
JOURNAL NAME:
Applied Mathematics,
Vol.3 No.12A,
December
31,
2012
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 even for
moderate values of n.