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

• Authors: Michał Stachura , Barbara Wodecka

Abstracts

EN

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

EN

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

• Publisher: Główny Urząd Statystyczny
• Journal: Statistics in Transition new series
• Year: 2022
• Volume: 23
• Issue: 4
• Pages: 203-215

Dates

published

2022

Contributors

author

Michał Stachura

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

• https://orcid.org/0000000201153522

author

Barbara Wodecka

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

• https://orcid.org/0000000224271572

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Identifiers

DOI

10.2478/stattrans-2022-0050

Biblioteka Nauki

2156989