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On Terminating and Non-Terminating q-Gauss Hypergeometric Series Distributions and the Associated q-Orthogonal Polynomials

Kyriakoussis A., Vamvakari M.

Fundamenta Informaticae

2012

Vol. 117, nr 1-4

229-248

In this paper, we establish the families of terminating and non-terminating q-Gauss hypergeometric series discrete distributions and we associate them with defined classes of generalized q- Hahn and big q-Jacobi orthogonal polynomials, respectively. Also, we give the q-factorial moments and the usual moments for these two families of q-Gauss hypergeometric series distributions. Moreover, we present their probabilistic interpretation as q-steady-state distributions fromMarkov chains and we designate the generalized q-Hahn processes and generalized big q-Jacobi processes emerged by these q-Markov chains. As special cases the q-hypergeometric, the negative q-hypergeometric distributions and their inverses are presented.