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

Michał Stachura and Wodecka Barbara ()
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Wodecka Barbara: Department of Economics and Finance, Faculty of Law and Social Sciences, The Jan Kochanowski University, Kielce, Poland .

Statistics in Transition New Series, 2022, vol. 23, issue 4, 203-215

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.

Keywords: stable distribution; scale parameter estimator; k-th record values (search for similar items in EconPapers)
Date: 2022
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Persistent link: https://EconPapers.repec.org/RePEc:vrs:stintr:v:23:y:2022:i:4:p:203-215:n:11

DOI: 10.2478/stattrans-2022-0050

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