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Asymptotic analysis of generalized Greenwood statistics for very heavy tails

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  • Albrecher, Hansjörg
  • García Flores, Brandon

Abstract

We consider some variants of the classical Greenwood statistic and analyze their asymptotic properties for regularly varying random variables with arbitrary index of variation. We also investigate the convergence rate of these asymptotics and study how many terms are asymptotically relevant for the resulting expressions. This naturally generalizes and unifies some earlier results in the literature.

Suggested Citation

  • Albrecher, Hansjörg & García Flores, Brandon, 2022. "Asymptotic analysis of generalized Greenwood statistics for very heavy tails," Statistics & Probability Letters, Elsevier, vol. 185(C).
    • Handle: RePEc:eee:stapro:v:185:y:2022:i:c:s0167715222000396
    DOI: 10.1016/j.spl.2022.109429
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    References listed on IDEAS

    as
    1. Joan Del Castillo & Jalila Daoudi & Richard Lockhart, 2014. "Methods to Distinguish Between Polynomial and Exponential Tails," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 41(2), pages 382-393, June.
    2. Hansjörg Albrecher & Christian Y. Robert & Jef L. Teugels, 2014. "Joint asymptotic distributions of smallest and largest insurance claims," Post-Print hal-01294387, HAL.
    3. Christian Yann Robert & Hansjörg Albrecher & Jef Teugels, 2014. "Joint Asymptotic Distributions of Smallest and Largest Insurance Claims," Post-Print hal-02006777, HAL.
    4. Hansjörg Albrecher & Christian Y. Robert & Jef L. Teugels, 2014. "Joint Asymptotic Distributions of Smallest and Largest Insurance Claims," Risks, MDPI, vol. 2(3), pages 1-26, July.
    Full references (including those not matched with items on IDEAS)

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