International Journal of Mathematics and Mathematical Sciences
Volume 2010 (2010), Article ID 924013, 16 pages
Research Article

Inference about the Tail of a Distribution: Improvementon the Hill Estimator

Department of Theoretical and Mathematical Physics, Université de Mons, 20 Place du Parc, 7000 Mons, Belgium

Received 7 July 2009; Revised 14 March 2010; Accepted 15 April 2010

Academic Editor: Kenneth Berenhaut

Copyright © 2010 Jean Nuyts. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


The Hill estimator is often used to infer the power behavior in tails of experimental distribution functions. This estimator is known to produce bad results in certain situations which have lead to the so-called Hill horror plots. In this brief note, we propose an improved estimator which is simple and coherent and often provides an efficient remedy in the bad situations, especially when the distribution is decreasing slowly, when the data is restricted by external cuts to lie within a finite domain, or even when the distribution is increasing.