The Annals of Statistics

How to make a Hill plot

Holger Drees, Sidney Resnick, and Laurens de Haan

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An abundance of high quality data sets requiring heavy tailed models necessitates reliable methods of estimating the shape parameter governing the degree of tail heaviness. The Hill estimator is a popular method for doing this but its practical use is encumbered by several difficulties. We show that an alternative method of plotting Hill estimator values is more revealing than the standard method unless the underlying data comes from a Pareto distribution.

Article information

Ann. Statist., Volume 28, Number 1 (2000), 254-274.

First available in Project Euclid: 14 March 2002

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 60G75
Secondary: 62G05: Estimation 62G20: Asymptotic properties

Estimation extreme value index heavy tails Hill estimator order statistics Pareto tails regular variation


Drees, Holger; de Haan, Laurens; Resnick, Sidney. How to make a Hill plot. Ann. Statist. 28 (2000), no. 1, 254--274. doi:10.1214/aos/1016120372.

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