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Efficient estimation of Pareto model: Some modified percentile estimators

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  • Sajjad Haider Bhatti
  • Shahzad Hussain
  • Tanvir Ahmad
  • Muhammad Aslam
  • Muhammad Aftab
  • Muhammad Ali Raza

Abstract

The article proposes three modified percentile estimators for parameter estimation of the Pareto distribution. These modifications are based on median, geometric mean and expectation of empirical cumulative distribution function of first-order statistic. The proposed modified estimators are compared with traditional percentile estimators through a Monte Carlo simulation for different parameter combinations with varying sample sizes. Performance of different estimators is assessed in terms of total mean square error and total relative deviation. It is determined that modified percentile estimator based on expectation of empirical cumulative distribution function of first-order statistic provides efficient and precise parameter estimates compared to other estimators considered. The simulation results were further confirmed using two real life examples where maximum likelihood and moment estimators were also considered.

Suggested Citation

  • Sajjad Haider Bhatti & Shahzad Hussain & Tanvir Ahmad & Muhammad Aslam & Muhammad Aftab & Muhammad Ali Raza, 2018. "Efficient estimation of Pareto model: Some modified percentile estimators," PLOS ONE, Public Library of Science, vol. 13(5), pages 1-15, May.
    • Handle: RePEc:plo:pone00:0196456
    DOI: 10.1371/journal.pone.0196456
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    Cited by:

    1. Shahzad Hussain & Sajjad Haider Bhatti & Tanvir Ahmad & Muhammad Ahmed Shehzad, 2021. "Parameter estimation of the Pareto distribution using least squares approaches blended with different rank methods and its applications in modeling natural catastrophes," Natural Hazards: Journal of the International Society for the Prevention and Mitigation of Natural Hazards, Springer;International Society for the Prevention and Mitigation of Natural Hazards, vol. 107(2), pages 1693-1708, June.
    2. 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.
    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. 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.
    5. Silius M. Vandeskog & Thordis L. Thorarinsdottir & Ingelin Steinsland & Finn Lindgren, 2022. "Quantile based modeling of diurnal temperature range with the five‐parameter lambda distribution," Environmetrics, John Wiley & Sons, Ltd., vol. 33(4), June.

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