Abstract
Heavy-tailed distributions are used in various areas of statistical applications. An important parameter for such distributions is the tail coefficient defined as the regular variation coefficient of the inverse cumulative hazard function. Many estimators, among which perhaps the most well known is the Hill estimator, have been developed for this coefficient. However, the Hill estimator as well as improved versions that are based on it rely on asymptotic expansions that are unlikely to hold for small samples. In this paper, we introduce a new approach to the tail coefficient estimation in the case of Weibull-type distributions that works well for small samples. A simulation study is carried out to characterize the properties of the new estimator and shows that it outperforms existing estimators based on asymptotic assumptions in terms of accuracy and the corresponding uncertainty.
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Acknowledgements
Part of this work was supported by the African Institute for Mathematical Sciences (AIMS), South Africa. The author Kokouvi Gamado is grateful for funding from the Scottish Government’s RESAS. The authors also thank Prof. Glenn Marion at Biomathematics and Statistics Scotland (BioSS) for helping greatly improve the presentation.
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Kpanzou, T.A., Gamado, K.M. & Hounnon, H. A Beran-Inspired Estimator for the Weibull-Type Tail Coefficient. J Stat Theory Pract 13, 20 (2019). https://doi.org/10.1007/s42519-018-0013-8
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DOI: https://doi.org/10.1007/s42519-018-0013-8