Inference about the tail of a distribution. Improvement on the Hill estimator

Details Inference about the tail of a distribution. Improvement on the Hill estimator Inference about the tail of a distribution. Improvement on the Hill estimator

2010-07-25

arxiv.org/abs/1007.4334v1

International Journal of Mathematics and Mathematical Sciences Volume 2010, Article ID 924013

Mathematics

Statistics Theory

22 pages, 4 figures

Scientific paper

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.

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