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

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.

Automated summary

The article evaluates least-squares-based approaches for estimating parameters of the two-parameter Pareto distribution. Results indicate that RLS performs the best among regression-based methods for all sample sizes, and the mean rank method outperforms others in generating CDF.