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Estimation of the generalized Pareto distribution

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  • del Castillo, Joan
  • Daoudi, Jalila

Abstract

This paper provides precise arguments to explain the anomalous behavior of the likelihood surface when sampling from the generalized Pareto distribution for small or moderate samples. The behavior of the profile-likelihood function is characterized in terms of the empirical coefficient of variation. A sufficient condition is given for the global maximum of the likelihood function of the Pareto distribution to be at a finite point.

Suggested Citation

  • del Castillo, Joan & Daoudi, Jalila, 2009. "Estimation of the generalized Pareto distribution," Statistics & Probability Letters, Elsevier, vol. 79(5), pages 684-688, March.
    • Handle: RePEc:eee:stapro:v:79:y:2009:i:5:p:684-688
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    References listed on IDEAS

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    1. Joan Castillo, 1994. "The singly truncated normal distribution: A non-steep exponential family," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 46(1), pages 57-66, March.
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    Cited by:

    1. Castillo, Joan del & Serra, Isabel, 2015. "Likelihood inference for generalized Pareto distribution," Computational Statistics & Data Analysis, Elsevier, vol. 83(C), pages 116-128.
    2. Arthur Charpentier & Emmanuel Flachaire, 2022. "Pareto models for top incomes and wealth," The Journal of Economic Inequality, Springer;Society for the Study of Economic Inequality, vol. 20(1), pages 1-25, March.
    3. Arthur Charpentier & Emmanuel Flachaire, 2019. "Pareto Models for Top Incomes," Working Papers hal-02145024, HAL.
    4. Diamoutene, Abdoulaye & Kamsu-Foguem, Bernard & Noureddine, Farid & Barro, Diakarya, 2018. "Prediction of U.S. General Aviation fatalities from extreme value approach," Transportation Research Part A: Policy and Practice, Elsevier, vol. 109(C), pages 65-75.
    5. Cramer, Erhard & Schmiedt, Anja Bettina, 2011. "Progressively Type-II censored competing risks data from Lomax distributions," Computational Statistics & Data Analysis, Elsevier, vol. 55(3), pages 1285-1303, March.
    6. Marek Arendarczyk & Tomasz J. Kozubowski & Anna K. Panorska, 2022. "The Greenwood statistic, stochastic dominance, clustering and heavy tails," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 49(1), pages 331-352, March.
    7. J. Martin van Zyl, 2012. "Estimation of the shape parameter of a generalized Pareto distribution based on a transformation to Pareto distributed variables," Papers 1210.7642, arXiv.org, revised Dec 2012.
    8. Joan Del Castillo & Jalila Daoudi & Richard Lockhart, 2014. "Methods to Distinguish Between Polynomial and Exponential Tails," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 41(2), pages 382-393, June.
    9. Belkhir, Mohamed & Saad, Mohsen & Samet, Anis, 2020. "Stock extreme illiquidity and the cost of capital," Journal of Banking & Finance, Elsevier, vol. 112(C).

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