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

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.

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Year of publication:	2022
Authors:	Stachura, Michał ; Wodecka, Barbara
Published in:	Statistics in Transition new series (SiTns). - ISSN 2450-0291. - Vol. 23.2022, 4, p. 203-215
Publisher:	Warsaw : Sciendo
Subject:	stable distribution \| scale parameter estimator \| k-th record values

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Type of publication:	Article
Type of publication (narrower categories):	Article
Language:	English
Other identifiers:	10.2478/stattrans-2022-0050 [DOI] 1848812531 [GVK]
Source:	EconStor

Persistent link: https://ebvufind01.dmz1.zbw.eu/10015051620