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

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  • Jean Nuyts

Abstract

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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  • Jean Nuyts, 2010. "Inference about the Tail of a Distribution: Improvementon the Hill Estimator," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2010, pages 1-16, June.
    • Handle: RePEc:hin:jijmms:924013
    DOI: 10.1155/2010/924013
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    Cited by:

    1. Igor Fedotenkov, 2020. "A Review of More than One Hundred Pareto-Tail Index Estimators," Statistica, Department of Statistics, University of Bologna, vol. 80(3), pages 245-299.
    2. Dicks, Matthew & Paskaramoorthy, Andrew & Gebbie, Tim, 2024. "A simple learning agent interacting with an agent-based market model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 633(C).

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