Convergence properties of Kemp’s q-binomial distribution

CONVERGENCE PROPERTIES OF KEMP’S q-BINOMIAL DISTRIBUTION

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...

Convergence properties of the q-deformed binomial distribution

We consider the q-deformed binomial distribution introduced by Jing 1994 and Chung et al. 1995 and establish several convergence results involving the Euler and the exponential distribution; some of them are qanalogues of classical results.

Quasi-negative binomial distribution: Properties and applications

In this paper, a quasi-negative binomial distribution (QNBD) derived from the class of generalized Lagrangian probability distributions is studied. The negative binomial distribution is a special case of QNBD. Some properties of QNBD, including the upper tail behavior and limiting distributions, are investigated. It is shown that the moments do not exist in some situations and the limiting dist...

ON PROPERTIES OF BINOMIAL Q-CHARTS FOR ATTJUBUTES by Cbarles

The Negative q-Binomial

Interpretations for the q-binomial coefficient evaluated at −q are discussed. A (q, t)-version is established, including an instance of a cyclic sieving phenomenon involving unitary spaces. 1. The q-binomial The q-binomial coefficient is defined for integers k and n, with 0 ≤ k ≤ n, and an indeterminate q by