Michał Stachura https://orcid.org/0000-0002-0115-3522 , Barbara Wodecka https://orcid.org/0000-0002-2427-1572

© Michał Stachura, Barbara Wodecka. Article available under the CC BY-SA 4.0 licence


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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.


stable distribution, scale parameter estimator, k-th record values


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