On fitting the Lomax distribution: a comparison between minimum distance estimators and other estimation techniques

TL;DR

This paper compares various estimation methods for the Lomax distribution's parameters, highlighting their performance differences through extensive simulations and practical application, and offering recommendations based on sample size.

Contribution

It provides a comprehensive comparison of traditional, bias-adjusted, moment-based, and minimum distance estimators for the Lomax distribution, including practical guidance.

Findings

Minimum distance estimators perform well with small samples.

Bias-reduced maximum likelihood estimators are suitable for large samples.

No single estimator is best across all scenarios.

Abstract

In this paper we investigate the performance of a variety of estimation techniques for the scale and shape parameter of the Lomax distribution. These methods include traditional methods such as the maximum likelihood estimator and the method of moments estimator. A version of the maximum likelihood estimator adjusted for bias is also included. Furthermore, alternative moment-based estimation techniques such as the $L$-moment estimator and the probability weighted moments estimator are included along with three different minimum distance estimators. The finite sample performances of each of these estimators is compared via an extensive Monte Carlo study. We find that no single estimator outperforms its competitors uniformly. We recommend one of the minimum distance estimators for use with smaller samples, while a bias reduced version of maximum likelihood estimation is recommended for use with larger samples. In addition, the desirable asymptotic properties of traditional maximum likelihood estimators make them appealing for larger samples. We also include a practical application demonstrating the use of the techniques on observed data.