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

A W  Kemp

doi:10.1016/j.jspi.2005.02.009

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

A W Kemp

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Abstract

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 language	English
Pages (from-to)	107-120
Number of pages	14
Journal	Journal of Statistical Planning and Inference
Volume	135
Issue number	1
DOIs	https://doi.org/10.1016/j.jspi.2005.02.009
Publication status	Published - 1 Nov 2005

Keywords

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
POISSON-DISTRIBUTION
HEINE

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10.1016/j.jspi.2005.02.009

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title = "Steady-state Markov chain models for certain q-confluent hypergeometric distributions",

abstract = "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.",

keywords = "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, POISSON-DISTRIBUTION, HEINE",

author = "Kemp, {A W}",

note = "Special issue on lattice path combinatorics and discrete distributions , Lattice path combinatorics and discrete distributions",

year = "2005",

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doi = "10.1016/j.jspi.2005.02.009",

language = "English",

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TY - JOUR

T1 - Steady-state Markov chain models for certain q-confluent hypergeometric distributions

AU - Kemp, A W

N1 - Special issue on lattice path combinatorics and discrete distributions , Lattice path combinatorics and discrete distributions

PY - 2005/11/1

Y1 - 2005/11/1

N2 - 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.

AB - 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.

KW - Heine distribution

KW - q-hyper-Poisson I distribution

KW - Morse distribution

KW - exton distribution

KW - third q-Poisson analogue

KW - confluent Bailey-Daum distribution

KW - confluent q-Chu-Vandermonde distribution

KW - O/U distribution

KW - over-and-underdispersion

KW - M/M/1 queues with balking

KW - birth-abort-death processes

KW - success-run processes

KW - current-age models

KW - success-run processes with stagnation

KW - POISSON-DISTRIBUTION

KW - HEINE

U2 - 10.1016/j.jspi.2005.02.009

DO - 10.1016/j.jspi.2005.02.009

M3 - Article

SN - 0378-3758

VL - 135

SP - 107

EP - 120

JO - Journal of Statistical Planning and Inference

JF - Journal of Statistical Planning and Inference

IS - 1

ER -

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

Abstract

Keywords

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