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A review of more than one hundred Pareto-tail index estimators

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  • Fedotenkov, Igor

Abstract

This paper reviews more than one hundred Pareto (and equivalent) tail index estimators. It focuses on univariate estimators for nontruncated data. We discuss basic ideas of these estimators and provide their analytical expressions. As samples from heavy-tailed distributions are analysed by researchers from various fields of science, the paper provides nontechnical explanations of the methods, which could be understood by researchers with intermediate skills in statistics. We also discuss strengths and weaknesses of the estimators, if they are known. The paper can be viewed as a catalog or a reference book on Pareto-tail index estimators.

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  • Fedotenkov, Igor, 2018. "A review of more than one hundred Pareto-tail index estimators," MPRA Paper 90072, University Library of Munich, Germany.
    • Handle: RePEc:pra:mprapa:90072
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    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. Kan Chen & Tuoyuan Cheng, 2022. "Measuring Tail Risks," Papers 2209.07092, arXiv.org, revised Nov 2022.
    4. 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.
    5. 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.
    6. 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).
    7. 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.
    8. 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.
    9. 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.
    10. Paweł D. Domański, 2024. "Energy-Aware Multicriteria Control Performance Assessment," Energies, MDPI, vol. 17(5), pages 1-18, March.
    11. 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).
    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; extreme value index;
    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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