Efficient estimation of Pareto model using modified maximum likelihood estimators

Abstract

In this article, we propose some modifications to the maximum likelihood estimation for estimating the parameters of the Pareto distribution and evaluate the performance of these modified estimators in comparison with the existing maximum likelihood estimators. Total Relative Deviation (TRD), Total Mean Square Error (TMSE), and Stein Loss Function (SLF) were used as performance indicators of goodness of fit analysis. The modified and traditional estimators were compared for different sample sizes and different parameter combinations using a Monte Carlo simulation in R-language. We concluded that the modified maximum likelihood estimator based on expectation of empirical Cumulative Distribution Function (CDF) of first-order statistic performed much better than the traditional ML estimator and other modified estimators based on median and coefficient of variation. The superiority of the mentioned estimator was independent of sample size and choice of true parameter values. The simulation results were further corroborated by employing the proposed estimation strategies for two real-life datasets.