Steady-state Markov chain models for certain q-confluent hypergeometric distributions

This paper draws attention to those members of the q-confluent hypergeometric family of discrete distributions that either (i) have special properties or (ii) arise as steady-state distributions from interesting Markov chains. They include (i) the Exton and O/U distributions and (ii) the q-hyper-Poisson I, Morse, confluent Bailey-Daum, and confluent q-Chu-Vandermonde distributions.