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Poisson Lindley process and its main properties

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  • Cha, Ji Hwan

Abstract

Until now, the nonhomogeneous Poisson process has been intensively applied in various practical applications due to its merits. However, at the same time, it has also critical limitations in applications. To overcome these limitations, a new counting process model (called Poisson Lindley Process) is developed. It will be shown that this new counting process model does not have such limitations. Some basic stochastic properties are derived. In addition, a new concept for positive dependent increments is defined and the dependence structure is analyzed. Some of the properties obtained in this paper will be stated in general forms. One of the important contributions of this paper is to provide a new counting process model which allows explicit expression of the likelihood function.

Suggested Citation

  • Cha, Ji Hwan, 2019. "Poisson Lindley process and its main properties," Statistics & Probability Letters, Elsevier, vol. 152(C), pages 74-81.
    • Handle: RePEc:eee:stapro:v:152:y:2019:i:c:p:74-81
    DOI: 10.1016/j.spl.2019.04.008
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    References listed on IDEAS

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    Cited by:

    1. Ritik Soni & Ashok Kumar Pathak, 2024. "Generalized Iterated Poisson Process and Applications," Journal of Theoretical Probability, Springer, vol. 37(4), pages 3216-3245, November.
    2. Syuhada, Khreshna & Tjahjono, Venansius & Hakim, Arief, 2024. "Compound Poisson–Lindley process with Sarmanov dependence structure and its application for premium-based spectral risk forecasting," Applied Mathematics and Computation, Elsevier, vol. 467(C).

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