A new class of estimators for the shape parameter of a Pareto model

Abstract

The Pareto model, first used in socioeconomic problems, has successfully been applied in many other areas such as astronomy, biology, bibliometrics, demography, insurance, or risk management. Although there are several variants of this distribution, the current study focuses on the classic Pareto distribution, also known as the Pareto type I distribution. We propose a new class of estimators for the Pareto shape parameter, obtained through a modification of the probability weighted moment method, called the log generalized probability weighted moments method. In addition to the asymptotic distribution, Monte Carlo simulations were performed to analyze the finite sample behavior of the proposed new estimators. A comparison with the most used estimators, such as the moment, the maximum likelihood, the least squares, and the probability weighted moments estimators was also performed. In addition, the estimators were used to construct asymptotic confidence intervals. To illustrate an application of the different estimation methods to a real data set from a clinical trial complete the article. Results indicate an overall good performance of the new proposed class.

A New Class of Generalized Probability-Weighted Moment Estimators for the Pareto Distribution

“…Recently, Chen [39] introduced an extended class of GPWMs by evaluating the PWMs in (12) with g a suitable continuous function and r and s any real values. Mateus and Caeiro [40] considered the extended class of GPWMs with g(x) = ln(x) for a rescaled sample of the Pareto model. This approach, called log-generalized probability-weighted (LGPWM), uses one theoretical moment and only provides an estimator for the shape parameter of the Pareto distribution.…”

“…This approach, called log-generalized probability-weighted (LGPWM), uses one theoretical moment and only provides an estimator for the shape parameter of the Pareto distribution. For the estimation of the scale parameter, Mateus and Caeiro [40] used an estimator similar to the moment estimator, ĉM .…”