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

Andreas Kyriakoussis and Malvina Vamvakari

Communications in Statistics - Theory and Methods, 2017, vol. 46, issue 8, 4088-4102

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.

Date: 2017
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DOI: 10.1080/03610926.2015.1078476

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