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Pareto Tail Index Estimation Revisited

Author

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  • Mark Finkelstein
  • Howard G. Tucker
  • Jerry Alan Veeh

Abstract

An estimator of the tail index of a Pareto distribution is given that is based on the use of the probability integral transform. This new estimator provides performance that is comparable to the best robust estimators, while retaining conceptual and computational simplicity. A tuning parameter in the new estimator can be adjusted to control the tradeoff between robustness and efficiency. The method used to compute the estimator also can be used to find a confidence interval for the tail index that is guaranteed to have the nominal confidence level for any given sample size. Guidelines for the use of the new estimator are provided.

Suggested Citation

  • Mark Finkelstein & Howard G. Tucker & Jerry Alan Veeh, 2006. "Pareto Tail Index Estimation Revisited," North American Actuarial Journal, Taylor & Francis Journals, vol. 10(1), pages 1-10.
    • Handle: RePEc:taf:uaajxx:v:10:y:2006:i:1:p:1-10
    DOI: 10.1080/10920277.2006.10596236
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    Citations

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    Cited by:

    1. 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.
    2. Safari, Muhammad Aslam Mohd & Masseran, Nurulkamal & Ibrahim, Kamarulzaman & Hussain, Saiful Izzuan, 2021. "Measuring income inequality: A robust semi-parametric approach," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 562(C).
    3. Silvia De Nicol`o & Maria Rosaria Ferrante & Silvia Pacei, 2021. "Mind the Income Gap: Bias Correction of Inequality Estimators in Small-Sized Samples," Papers 2107.08950, arXiv.org, revised May 2023.
    4. Frederico Caeiro & Mina Norouzirad, 2024. "Comparing Estimation Methods for the Power–Pareto Distribution," Econometrics, MDPI, vol. 12(3), pages 1-28, July.
    5. Safari, Muhammad Aslam Mohd & Masseran, Nurulkamal & Ibrahim, Kamarulzaman & Hussain, Saiful Izzuan, 2019. "A robust and efficient estimator for the tail index of inverse Pareto distribution," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 517(C), pages 431-439.
    6. Felix Koenig, 2023. "Technical Change and Superstar Effects: Evidence from the Rollout of Television," American Economic Review: Insights, American Economic Association, vol. 5(2), pages 207-223, June.
    7. Beran, Jan & Schell, Dieter, 2012. "On robust tail index estimation," Computational Statistics & Data Analysis, Elsevier, vol. 56(11), pages 3430-3443.
    8. Safari, Muhammad Aslam Mohd & Masseran, Nurulkamal & Ibrahim, Kamarulzaman, 2018. "A robust semi-parametric approach for measuring income inequality in Malaysia," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 512(C), pages 1-13.
    9. Frederico Caeiro & Ayana Mateus, 2023. "A New Class of Generalized Probability-Weighted Moment Estimators for the Pareto Distribution," Mathematics, MDPI, vol. 11(5), pages 1-17, February.
    10. Frank A. Cowell & Philippe Kerm, 2015. "Wealth Inequality: A Survey," Journal of Economic Surveys, Wiley Blackwell, vol. 29(4), pages 671-710, September.
    11. Safari, Muhammad Aslam Mohd & Masseran, Nurulkamal & Ibrahim, Kamarulzaman, 2018. "Optimal threshold for Pareto tail modelling in the presence of outliers," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 509(C), pages 169-180.
    12. Jan Beran & Dieter Schell & Milan Stehlík, 2014. "The harmonic moment tail index estimator: asymptotic distribution and robustness," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 66(1), pages 193-220, February.
    13. Muhammad Aslam Mohd Safari & Nurulkamal Masseran & Muhammad Hilmi Abdul Majid, 2020. "Robust Reliability Estimation for Lindley Distribution—A Probability Integral Transform Statistical Approach," Mathematics, MDPI, vol. 8(9), pages 1-21, September.

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