Examining Tail Index Estimators in New Pareto Distribution: Monte Carlo Simulations and Income Data Applications

Abstract

An evolved form of Pareto distribution, the new Pareto-type distribution, offers an alternative model for data with heavy-tailed characteristics. This investigation examines and discusses fourteen diverse estimators for the tail index of the new Pareto-type, including estimators such as maximum likelihood, method of moments, maximum product of spacing, its modified version, ordinary least squares, weighted least squares, percentile, Kolmogorov-Smirnov, Anderson-Darling, its modified version, Cramér-von Mises, and Zhang's variants of the previous three. Using Monte Carlo simulations, the effectiveness of these estimators is compared both with and without the presence of outliers. The findings show that, without outliers, the maximum product of spacing, its modified version, and maximum likelihood are the most effective estimators. In contrast, with outliers present, the top performers are Cramér-von Mises, ordinary least squares, and weighted least squares. The study further introduces a graphical method called the new Pareto-type quantile plot for validating the new Pareto-type assumptions and outlines a stepwise process to identify the optimal threshold for this distribution. Concluding the study, the new Pareto-type distribution is employed to model the high-end household income data from Italy and Malaysia, leveraging all the methodologies proposed.