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A Review of More than One Hundred Pareto-Tail Index Estimators

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  • Igor Fedotenkov

    (European Commission)

Abstract

Heavy-tailed distributions are often encountered in economics, finance, biology, telecommunications, geology, etc. The heaviness of a tail is measured by a tail index. Numerous methods for tail index estimation have been proposed. This paper reviews more than one hundred Pareto (and equivalent) tail index estimators. It focuses on univariate estimators for non-truncated data. We discuss the basic features of these estimators and provide their analytical expressions. As samples from heavy-tailed distributions are often analysed by researchers from various sciences, the paper provides nontechnical explanations of the methods, so as to be understood by researchers with intermediate skills in statistics. We also discuss the strengths and weaknesses of the estimators, if known. The main focus of the paper is semi-parametric estimators; however, a number of parametric estimators under-represented in previous reviews are also discussed. The paper can be viewed as a catalog or a reference work on Pareto-tail index estimators. A Monte-Carlo comparison of more than 90 estimators is presented.

Suggested Citation

  • 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.
    • Handle: RePEc:bot:rivsta:v:80:y:2020:i:3:p:245-299
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    2. David Anthoff & Richard S. J. Tol, 2022. "Testing the Dismal Theorem," Journal of the Association of Environmental and Resource Economists, University of Chicago Press, vol. 9(5), pages 885-920.
    3. Gareth W. Peters & Matteo Malavasi & Georgy Sofronov & Pavel V. Shevchenko & Stefan Truck & Jiwook Jang, 2022. "Cyber Loss Model Risk Translates to Premium Mispricing and Risk Sensitivity," Papers 2202.10588, arXiv.org, revised Mar 2023.
    4. Kan Chen & Tuoyuan Cheng, 2022. "Measuring Tail Risks," Papers 2209.07092, arXiv.org, revised Nov 2022.
    5. Paweł D. Domański, 2024. "Energy-Aware Multicriteria Control Performance Assessment," Energies, MDPI, vol. 17(5), pages 1-18, March.
    6. Priscilla Avegliano & Jaime Simão Sichman, 2023. "Equation-Based Versus Agent-Based Models: Why Not Embrace Both for an Efficient Parameter Calibration?," Journal of Artificial Societies and Social Simulation, Journal of Artificial Societies and Social Simulation, vol. 26(4), pages 1-3.
    7. Ivanilda Cabral & Frederico Caeiro & M. Ivette Gomes, 2022. "On the comparison of several classical estimators of the extreme value index," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 51(1), pages 179-196, January.
    8. Nelson, Kenric P., 2022. "Independent Approximates enable closed-form estimation of heavy-tailed distributions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 601(C).
    9. Tjeerd de Vries & Alexis Akira Toda, 2022. "Capital and Labor Income Pareto Exponents Across Time and Space," Review of Income and Wealth, International Association for Research in Income and Wealth, vol. 68(4), pages 1058-1078, December.
    10. González-Sánchez, Mariano & Nave Pineda, Juan M., 2023. "Where is the distribution tail threshold? A tale on tail and copulas in financial risk measurement," International Review of Financial Analysis, Elsevier, vol. 86(C).
    11. Gareth W. Peters & Matteo Malavasi & Georgy Sofronov & Pavel V. Shevchenko & Stefan Trück & Jiwook Jang, 2023. "Cyber loss model risk translates to premium mispricing and risk sensitivity," The Geneva Papers on Risk and Insurance - Issues and Practice, Palgrave Macmillan;The Geneva Association, vol. 48(2), pages 372-433, April.
    12. Magdy El-Adll & H. M. Barakat & Amany Aly & Ning Cai, 2022. "Asymptotic Prediction for Future Observations of a Random Sample of Unknown Continuous Distribution," Complexity, Hindawi, vol. 2022, pages 1-15, April.
    13. Frank Cowell & Emmanuel Flachaire, 2021. "Inequality Measurement: Methods and Data," Post-Print hal-03589066, HAL.

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    More about this item

    Keywords

    Heavy tails; Pareto distribution; Tail index; Review;
    All these keywords.

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C18 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Methodolical Issues: General
    • C58 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Financial Econometrics

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