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arXiv · 0905.3096

A shift-optimized Hill-type estimator

Éva Rácz·János Kertész·Zoltán Eisler
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Abstract

A wide range of natural and social phenomena result in observables whose distributions can be well approximated by a power-law decay. The well-known Hill estimator of the tail exponent provides results which are in many respects superior to other estimators in case the asymptotics of the distribution is indeed a pure power-law, however,systematic errors occur if the distribution is altered by simply shifting it. We demonstrate some related problems which typically emerge when dealing with empirical data and suggest a procedure designed to extend the applicability of the Hill estimator.

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Éva Rácz, János Kertész, Zoltán Eisler. 2009-05-19. A shift-optimized Hill-type estimator. https://arxiv.org/abs/0905.3096

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