q-Discrete distributions based on q-Meixner and q-Charlier orthogonal polynomials—Asymptotic behaviour

In this manuscript, for 0 < q < 1 we introduce deformed types of q-negative binomial and q-Poisson (Heine) distributions based on discrete q-Meixner and q-Charlier orthogonal polynomials, respectively. These q-discrete distributions arise as steady state distributions from interesting Markov chain models. Furthermore, we study their asymptotic behaviour by showing that all are compatible with a standardized Stieltjes–Wigert distribution induced by the homonymous orthogonal polynomials.