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Parameter estimation of the Pareto distribution using least squares approaches blended with different rank methods and its applications in modeling natural catastrophes

Author

Listed:
  • Shahzad Hussain

    (Government College University)

  • Sajjad Haider Bhatti

    (Government College University)

  • Tanvir Ahmad

    (Government College University)

  • Muhammad Ahmed Shehzad

    (Bahauddin Zakariya University)

Abstract

The current article evaluates least-squares-based approaches for estimating parameters of the two-parameter Pareto distribution. The algebraic expressions for least squares (LS), relative least squares (RLS) and weighted least squares (WLS) estimators are derived by generating empirical cumulative distribution function (CDF) using mean rank, median rank and symmetrical CDF methods. The performance of the estimation approaches is evaluated through Monte Carlo simulations for different combinations of parameter values and sample sizes. The performance of the regression-based methods is then compared with one another and with the traditional maximum likelihood (ML) estimation method. Our simulation results unveil that among the regression-based methods, RLS has an improved or better performance compared to the other two regression-based approaches for samples of all sizes. Moreover, RLS performs better than the ML method for small samples. Among the rank methods used for generating empirical CDF, it is observed that the mean rank method outperformed other two rank methods. The simulation results are further corroborated by the application of all the methods on two real-life datasets representing damages caused by natural catastrophes.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:nathaz:v:107:y:2021:i:2:d:10.1007_s11069-021-04654-4
    DOI: 10.1007/s11069-021-04654-4
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    References listed on IDEAS

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    1. 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.
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