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Comparing Estimation Methods for the Power–Pareto Distribution

Author

Listed:
  • Frederico Caeiro

    (Department of Mathematics and Center for Mathematics and Applications (NOVA Math), NOVA School of Science and Technology (NOVA FCT), 2829-516 Caparica, Portugal)

  • Mina Norouzirad

    (Center for Mathematics and Applications (NOVA Math), NOVA School of Science and Technology (NOVA FCT), 2829-516 Caparica, Portugal)

Abstract

Non-negative distributions are important tools in various fields. Given the importance of achieving a good fit, the literature offers hundreds of different models, from the very simple to the highly flexible. In this paper, we consider the power–Pareto model, which is defined by its quantile function. This distribution has three parameters, allowing the model to take different shapes, including symmetrical and left- and right-skewed. We provide different distributional characteristics and discuss parameter estimation. In addition to the already-known Maximum Likelihood and Least Squares of the logarithm of the order statistics estimation methods, we propose several additional methods. A simulation study and an application to two datasets are conducted to illustrate the performance of the estimation methods.

Suggested Citation

  • Frederico Caeiro & Mina Norouzirad, 2024. "Comparing Estimation Methods for the Power–Pareto Distribution," Econometrics, MDPI, vol. 12(3), pages 1-28, July.
    • Handle: RePEc:gam:jecnmx:v:12:y:2024:i:3:p:20-:d:1433083
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    References listed on IDEAS

    as
    1. 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.
    2. Hai-Lin Lu & Shin-Hwa Tao, 2007. "The Estimation of Pareto Distribution by a Weighted Least Square Method," Quality & Quantity: International Journal of Methodology, Springer, vol. 41(6), pages 913-926, December.
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