Heine process as a q-analog of the Poisson process—waiting and interarrival times

DOI10.1080/03610926.2015.1078476zbMath1369.60037OpenAlexW2346975625MaRDI QIDQ4976277

Malvina G. Vamvakari, Andreas George Kyriakoussis

Publication date: 27 July 2017

Published in: Communications in Statistics - Theory and Methods (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/03610926.2015.1078476

zbMATH Keywords

\(q\)-exponential distribution\(q\)-binomial distributionHeine distributionHeine process\(q\)-Erlang distribution

Mathematics Subject Classification ID

Stochastic processes (60G99) Point processes (e.g., Poisson, Cox, Hawkes processes) (60G55)

Related Items (6)

On multivariate discrete q-Distributions-A multivariate q-Cauchy’s formula ⋮ A \(q\)-random walk approximated by a \(q\)-Brownian motion ⋮ Correction notice to “Heine process as a q-analog of the Poisson process-waiting and interarrival times” ⋮ On the \(q\)-moment determinacy of probability distributions ⋮ \(q\)-random walks on \(\mathbb Z^d\), \(d = 1, 2, 3\) ⋮ Moment determinacy versus \(q\)-moment determinacy of probability distributions

Cites Work

• Discrete \(q\)-distributions on Bernoulli trials with a geometrically varying success probability
• The moment problem associated with the \(q\)-Laguerre polynomials
• A \(q\)-analogue of the Stirling formula and a continuous limiting behaviour of the \(q\)-binomial distribution -- numerical calculations
• Heine-euler extensions of the poisson distribution
• Certain state-dependent processes for dichotomised parasite populations
• Steady-state Markov chain models for the Heine and Euler distributions

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