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

Summary/Abstract: Various techniques of scale parameter estimation have been proposed in the case of alphastable distributions. In the paper, the authors present an estimation technique that involvesthe k-th record theory. Although this theory is over 40 years old, its implementation in theclassical extreme value theory – being the other cornerstone of the presented approach – isquite new, and tempting. Several theoretical properties of the introduced scale parameterestimators are presented. With the use of Monte Carlo methods, a comparative analysis isperformed between the approach based on k-th records and approaches based on Hill’s andPickands’ estimators. Additionally, the paper uses a real-life data set to illustrate how toeffectively apply the k-th record estimator of the scale parameter. The research indicatesseveral advantages of the k-th record approach over its other counterparts, especially whendealing with incomplete information about the underlying sample.

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