Convergence properties of Kemp’s q-binomial distribution

被引：3
作者：
Gerhold S. [1 ,3 ]
Zeiner M. [2 ,4 ]
机构：
[1] Vienna University of Technology, Vienna
[2] Graz University of Technology, Graz
[3] Vienna University of Technology, Wiedner Hauptstrasse 8-10, Vienna
[4] Graz University of Technology, Steyrergasse 30, Graz
来源：
Sankhya A | 2010年 / 72卷 / 2期
基金：
奥地利科学基金会;
关键词：
-binomial distribution; discrete normal distribution; Heine distribution; -Krawtchouk polynomials; -Charlier polynomials; Mellin transform; limit theorems; Primary 60F05; secondary 33D15;
D O I：
10.1007/s13171-010-0019-0
中图分类号：
学科分类号：
摘要：
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. © 2010, Indian Statistical Institute.
引用
收藏
页码：331 / 343
页数：12
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