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

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  • Andreas Kyriakoussis
  • Malvina Vamvakari

Abstract

In this study, we introduce the Heine process, {Xq(t), t > 0}, 0 0, represents the number of events (occurrences or arrivals) during a time interval (0, t]. The Heine process is introduced as a q-analog of the basic Poisson process. Also, in this study, we prove that the distribution of the waiting time Wν, q, ν ⩾ 1, up to the νth arrival, is a q-Erlang distribution and the interarrival times Tk, q = Wk, q − Wk − 1, q, k = 1, 2, …, ν with W0, q = 0 are independent and equidistributed with a q-Exponential distribution.

Suggested Citation

  • Andreas Kyriakoussis & Malvina Vamvakari, 2017. "Heine process as a q-analog of the Poisson process—waiting and interarrival times," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 46(8), pages 4088-4102, April.
    • Handle: RePEc:taf:lstaxx:v:46:y:2017:i:8:p:4088-4102
    DOI: 10.1080/03610926.2015.1078476
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    Cited by:

    1. Thomas Kamalakis & Malvina Vamvakari, 2021. "q-Random Walks on Zd, d = 1, 2, 3," Methodology and Computing in Applied Probability, Springer, vol. 23(3), pages 947-969, September.

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