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How to make a Hill Plot

Author

Listed:
  • Holger Drees

    (University of Cologne)

  • Laurens F.M. de Haan

    (Erasmus University Rotterdam)

  • Sidney Resnick

    (Cornell University)

Abstract

An abundance of high quality data sets requiring heavy tailed models necessitates reliablemethods 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 isencumbered by several difficulties. We show that an alternative method of plotting Hillestimator values is more revealing than the standard method unless the underlyingdata comes from a Pareto distribution.

Suggested Citation

  • Holger Drees & Laurens F.M. de Haan & Sidney Resnick, 1998. "How to make a Hill Plot," Tinbergen Institute Discussion Papers 98-090/4, Tinbergen Institute.
    • Handle: RePEc:tin:wpaper:19980090
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    References listed on IDEAS

    as
    1. Kaufmann, E. & Reiss, R. -D., 1998. "Approximation of the Hill estimator process," Statistics & Probability Letters, Elsevier, vol. 39(4), pages 347-354, August.
    2. Dekkers, A. L. M. & Dehaan, L., 1993. "Optimal Choice of Sample Fraction in Extreme-Value Estimation," Journal of Multivariate Analysis, Elsevier, vol. 47(2), pages 173-195, November.
    3. Jansen, Dennis W & de Vries, Casper G, 1991. "On the Frequency of Large Stock Returns: Putting Booms and Busts into Perspective," The Review of Economics and Statistics, MIT Press, vol. 73(1), pages 18-24, February.
    4. Drees, Holger & Kaufmann, Edgar, 1998. "Selecting the optimal sample fraction in univariate extreme value estimation," Stochastic Processes and their Applications, Elsevier, vol. 75(2), pages 149-172, July.
    5. Laurens F.M. de Haan & Liang Peng & T.T. Pereira, 1997. "A Bootstrap-based Method to Achieve Optimality in Estimating the Extreme-value Index," Tinbergen Institute Discussion Papers 97-099/4, Tinbergen Institute.
    6. Holger Drees, 1998. "On Smooth Statistical Tail Functionals," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 25(1), pages 187-210, March.
    7. McNeil, Alexander J., 1997. "Estimating the Tails of Loss Severity Distributions Using Extreme Value Theory," ASTIN Bulletin, Cambridge University Press, vol. 27(1), pages 117-137, May.
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    Cited by:

    1. Younes Bensalah, 2000. "Steps in Applying Extreme Value Theory to Finance: A Review," Staff Working Papers 00-20, Bank of Canada.
    2. Andreas Jobst, 2007. "Consistent Quantitative Operational Risk Measurement and Regulation: Challenges of Model Specification, Data Collection and Loss Reporting," IMF Working Papers 2007/254, International Monetary Fund.

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