Efficient estimation of Pareto model using modified maximum likelihood estimators

Abstract

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