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Cha, Ji Hwan; Badía, F. G.

Poisson generalized Lindley process and its properties. (English) Zbl 1528.60087

Metrika 87, No. 1, 61-74 (2024).
Summary: In spite of the practical usefulness of the nonhomogeneous Poisson process, it still has some restrictions. To overcome these restrictions, the Poisson Lindley process has been recently developed and introduced in [J. H. Cha, Stat. Probab. Lett. 152, 74–81 (2019; Zbl 1451.60050)]. In this paper, we further generalize the Poisson Lindley process, so that the developed counting process model should have the restarting property and it should include the generalized Polya process as a special case. Some basic stochastic properties of the developed counting process model are derived. Dependence properties and stochastic comparisons are also discussed under a more general framework.

MSC:

60K10 Applications of renewal theory (reliability, demand theory, etc.)
60G55 Point processes (e.g., Poisson, Cox, Hawkes processes)
62P30 Applications of statistics in engineering and industry; control charts

Keywords:

Poisson generalized Lindley process; stochastic properties; restarting property; generalized polya process; positive dependence

Citations:

Zbl 1451.60050
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Full Text: DOI

References:

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