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Confidence bounds for compound Poisson process

Author

Listed:
  • Marek Skarupski

    (Eindhoven University of Technology
    Wrocław University of Science and Technology)

  • Qinhao Wu

    (Eindhoven University of Technology)

Abstract

The compound Poisson process (CPP) is a common mathematical model for describing many phenomena in medicine, reliability theory and risk theory. However, in the case of low-frequency phenomena, we are often unable to collect a sufficiently large database to conduct analysis. In this article, we focused on methods for determining confidence intervals for the rate of the CPP when the sample size is small. Based on the properties of process parameter estimators, we proposed a new method for constructing such intervals and compared it with other known approaches. In numerical simulations, we used synthetic data from several continuous and discrete distributions. The case of CPP, in which rewards came from exponential distribution, was discussed separately. The recommendation of how to use each method to have a more precise confidence interval is given. All simulations were performed in R version 4.2.1.

Suggested Citation

  • Marek Skarupski & Qinhao Wu, 2024. "Confidence bounds for compound Poisson process," Statistical Papers, Springer, vol. 65(8), pages 5351-5377, October.
    • Handle: RePEc:spr:stpapr:v:65:y:2024:i:8:d:10.1007_s00362-024-01604-7
    DOI: 10.1007/s00362-024-01604-7
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    References listed on IDEAS

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    1. Gutti Babu & Kesar Singh & Yaning Yang, 2003. "Edgeworth expansions for compound Poisson processes and the bootstrap," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 55(1), pages 83-94, March.
    2. Seri, Raffaello & Choirat, Christine, 2015. "Comparison Of Approximations For Compound Poisson Processes," ASTIN Bulletin, Cambridge University Press, vol. 45(3), pages 601-637, September.
    3. Conghua Cheng, 2022. "Empirical likelihood ratio for two-sample compound Poisson processes under infinite second moment," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 51(11), pages 3787-3798, June.
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