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Censoring heavy-tail count distributions for parameter estimation with an application to stable distributions

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  • Di Noia, Antonio
  • Marcheselli, Marzia
  • Pisani, Caterina
  • Pratelli, Luca

Abstract

A new approach based on censoring and moment criterion is introduced for parameter estimation of count distributions when the probability generating function is available even though a closed form of the probability mass function and/or finite moments do not exist.

Suggested Citation

  • Di Noia, Antonio & Marcheselli, Marzia & Pisani, Caterina & Pratelli, Luca, 2023. "Censoring heavy-tail count distributions for parameter estimation with an application to stable distributions," Statistics & Probability Letters, Elsevier, vol. 202(C).
    • Handle: RePEc:eee:stapro:v:202:y:2023:i:c:s016771522300127x
    DOI: 10.1016/j.spl.2023.109903
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    References listed on IDEAS

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    1. Zhu, Rong & Joe, Harry, 2009. "Modelling heavy-tailed count data using a generalised Poisson-inverse Gaussian family," Statistics & Probability Letters, Elsevier, vol. 79(15), pages 1695-1703, August.
    2. Christoph, Gerd & Schreiber, Karina, 1998. "Discrete stable random variables," Statistics & Probability Letters, Elsevier, vol. 37(3), pages 243-247, March.
    3. Hong Sun & Maochao Xu & Peng Zhao, 2021. "Modeling Malicious Hacking Data Breach Risks," North American Actuarial Journal, Taylor & Francis Journals, vol. 25(4), pages 484-502, November.
    4. Devroye, Luc, 1993. "A triptych of discrete distributions related to the stable law," Statistics & Probability Letters, Elsevier, vol. 18(5), pages 349-351, December.
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