Affiliations: Department of Informatics and Telematics, Harokopion University, El. Venizelou 2, 17-671 Athens, Greece, [email protected] | Department of Informatics and Telematics, Harokopion University, Athens, Greece, [email protected]
Note: [] Address for correspondence: Dept. Informatics and Telematics, Harokopion University, El. Venizelou 70, Athens Greece
Abstract: 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 from Markov 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.
Keywords: q-Gauss hypergeometric series distributions, q-factorial moments, q-Hahn and big q-Jacobi orthogonal polynomials, Birth-abort-death processes, q-hypergeometric distribution, inverse q-hypergeometric distribution, negative and inverse negative q-hypergeometric distributions, q-Hahn and big q-Jacobi processes
