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Robust Estimations for the Tail Index of Weibull-Type Distribution

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  • Chengping Gong

    (School of Mathematics and Statistics, Southwest University, Chongqing 400715, China
    These authors contributed equally to this work.)

  • Chengxiu Ling

    (School of Mathematics and Statistics, Southwest University, Chongqing 400715, China
    Department of Actuarial Science, University of Lausanne, Chamberonne, 1015 Lausanne, Switzerland
    These authors contributed equally to this work.)

Abstract

Based on suitable left-truncated or censored data, two flexible classes of M -estimations of Weibull tail coefficient are proposed with two additional parameters bounding the impact of extreme contamination. Asymptotic normality with n -rate of convergence is obtained. Its robustness is discussed via its asymptotic relative efficiency and influence function. It is further demonstrated by a small scale of simulations and an empirical study on CRIX.

Suggested Citation

  • Chengping Gong & Chengxiu Ling, 2018. "Robust Estimations for the Tail Index of Weibull-Type Distribution," Risks, MDPI, vol. 6(4), pages 1-15, October.
    • Handle: RePEc:gam:jrisks:v:6:y:2018:i:4:p:119-:d:174942
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    References listed on IDEAS

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    5. Vandewalle, B. & Beirlant, J. & Christmann, A. & Hubert, M., 2007. "A robust estimator for the tail index of Pareto-type distributions," Computational Statistics & Data Analysis, Elsevier, vol. 51(12), pages 6252-6268, August.
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    Cited by:

    1. Fung, Tsz Chai, 2022. "Maximum weighted likelihood estimator for robust heavy-tail modelling of finite mixture models," Insurance: Mathematics and Economics, Elsevier, vol. 107(C), pages 180-198.

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