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Poisson generalized Lindley process and its properties

Author

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  • Ji Hwan Cha

    (Ewha Womans University)

  • F. G. Badía

    (University of Zaragoza)

Abstract

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 Cha (Stat Probab Lett 152: 74–81, 2019). 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.

Suggested Citation

  • Ji Hwan Cha & F. G. Badía, 2024. "Poisson generalized Lindley process and its properties," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 87(1), pages 61-74, January.
    • Handle: RePEc:spr:metrik:v:87:y:2024:i:1:d:10.1007_s00184-023-00906-4
    DOI: 10.1007/s00184-023-00906-4
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    References listed on IDEAS

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    1. Jorge Navarro & Yolanda Águila, 2017. "Stochastic comparisons of distorted distributions, coherent systems and mixtures with ordered components," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 80(6), pages 627-648, November.
    2. Cha, Ji Hwan, 2019. "Poisson Lindley process and its main properties," Statistics & Probability Letters, Elsevier, vol. 152(C), pages 74-81.
    3. Jorge Navarro, 2018. "Stochastic comparisons of coherent systems," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 81(4), pages 465-482, May.
    4. Ji Hwan Cha & Maxim Finkelstein, 2018. "Point Processes for Reliability Analysis," Springer Series in Reliability Engineering, Springer, number 978-3-319-73540-5, January.
    5. Francisco Germán Badía & Hyunju Lee, 2020. "On stochastic comparisons and ageing properties of multivariate proportional hazard rate mixtures," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 83(3), pages 355-375, April.
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