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When is the discrete Weibull distribution infinitely divisible?

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  • Kreer, Markus
  • Kizilersu, Ayse
  • Thomas, Anthony W.

Abstract

For the discrete Weibull probability distribution we prove that it is only infinitely divisible if the shape parameter lies in the range 0<β≤1 . The proof is based on some results of Steutel and van Harn (2004). For this case we construct the corresponding compound Poisson distribution and thus the related Lévy process.

Suggested Citation

  • Kreer, Markus & Kizilersu, Ayse & Thomas, Anthony W., 2024. "When is the discrete Weibull distribution infinitely divisible?," Statistics & Probability Letters, Elsevier, vol. 215(C).
    • Handle: RePEc:eee:stapro:v:215:y:2024:i:c:s0167715224002074
    DOI: 10.1016/j.spl.2024.110238
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    References listed on IDEAS

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    1. Galit Shmueli & Thomas P. Minka & Joseph B. Kadane & Sharad Borle & Peter Boatwright, 2005. "A useful distribution for fitting discrete data: revival of the Conway–Maxwell–Poisson distribution," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 54(1), pages 127-142, January.
    2. James D. Englehardt & Ruochen Li, 2011. "The Discrete Weibull Distribution: An Alternative for Correlated Counts with Confirmation for Microbial Counts in Water," Risk Analysis, John Wiley & Sons, vol. 31(3), pages 370-381, March.
    3. Bondesson, Lennart & Kristiansen, Gundorph K. & Steutel, Fred W., 1996. "Infinite divisibility of random variables and their integer parts," Statistics & Probability Letters, Elsevier, vol. 28(3), pages 271-278, July.
    4. Ospina, A. Valderrama & Gerber, H. U., 1987. "A simple proof of Feller's characterization of the compound Poisson distributions," Insurance: Mathematics and Economics, Elsevier, vol. 6(1), pages 63-64, January.
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