A shift-optimized Hill-type estimator

TL;DR

This paper addresses the limitations of the Hill estimator for power-law distributions affected by shifts, proposing a new shift-optimized estimator to improve accuracy in empirical data analysis.

Contribution

It introduces a novel shift-optimized Hill-type estimator that extends the applicability of the traditional Hill estimator to shifted power-law distributions.

Findings

The new estimator reduces systematic errors caused by data shifts.

It improves tail exponent estimation accuracy for empirical data.

The method is applicable to a wide range of natural and social phenomena.

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.