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

A W Kemp

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17 Citations (Scopus)


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. (c) 2005 Elsevier B.V. All rights reserved.

Original languageEnglish
Pages (from-to)107-120
Number of pages14
JournalJournal of Statistical Planning and Inference
Issue number1
Publication statusPublished - 1 Nov 2005


  • Heine distribution
  • q-hyper-Poisson I distribution
  • Morse distribution
  • exton distribution
  • third q-Poisson analogue
  • confluent Bailey-Daum distribution
  • confluent q-Chu-Vandermonde distribution
  • O/U distribution
  • over-and-underdispersion
  • M/M/1 queues with balking
  • birth-abort-death processes
  • success-run processes
  • current-age models
  • success-run processes with stagnation


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