2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/230807A 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.5 pages, 7 figuresData Analysis, Statistics and Probabilitytext