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k-th record estimator of the scale parameter of the α-stable distribution

Author

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  • Stachura Michał

    (Department of Economics and Finance, Faculty of Law and Social Sciences, The Jan Kochanowski University, Kielce, Poland .)

  • Wodecka Barbara

    (Department of Economics and Finance, Faculty of Law and Social Sciences, The Jan Kochanowski University, Kielce, Poland .)

Abstract

Various techniques of scale parameter estimation have been proposed in the case of alpha stable distributions. In the paper, the authors present an estimation technique that involves the k-th record theory. Although this theory is over 40 years old, its implementation in the classical extreme value theory – being the other cornerstone of the presented approach – is quite new, and tempting. Several theoretical properties of the introduced scale parameter estimators are presented. With the use of Monte Carlo methods, a comparative analysis is performed between the approach based on k-th records and approaches based on Hill’s and Pickands’ estimators. Additionally, the paper uses a real-life data set to illustrate how to effectively apply the k-th record estimator of the scale parameter. The research indicates several advantages of the k-th record approach over its other counterparts, especially when dealing with incomplete information about the underlying sample.

Suggested Citation

  • Stachura Michał & Wodecka Barbara, 2022. "k-th record estimator of the scale parameter of the α-stable distribution," Statistics in Transition New Series, Polish Statistical Association, vol. 23(4), pages 203-215, December.
    • Handle: RePEc:vrs:stintr:v:23:y:2022:i:4:p:203-215:n:11
    DOI: 10.2478/stattrans-2022-0050
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    References listed on IDEAS

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    1. Rafał Weron, 2001. "Levy-Stable Distributions Revisited: Tail Index> 2does Not Exclude The Levy-Stable Regime," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 12(02), pages 209-223.
    2. Weron, Rafał, 2004. "Computationally intensive Value at Risk calculations," Papers 2004,32, Humboldt University of Berlin, Center for Applied Statistics and Economics (CASE).
    3. Djamel Meraghni & Abdelhakim Necir, 2007. "Estimating the Scale Parameter of a Lévy-stable Distribution via the Extreme Value Approach," Methodology and Computing in Applied Probability, Springer, vol. 9(4), pages 557-572, December.
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