A Robust Wald-type Test for Testing the Equality of Two Means from Log-Normal Samples

TL;DR

This paper introduces a robust Wald-type test for comparing the means of two independent log-normal distributions, emphasizing its robustness against outliers and its solid theoretical properties, validated through simulations and real data.

Contribution

It develops a new robust testing procedure using minimum density power divergence estimators for log-normal means, improving performance over existing methods especially with outliers.

Findings

The proposed test is robust against outliers.

It outperforms existing methods in simulations.

The test has desirable asymptotic properties.

Abstract

The log-normal distribution is one of the most common distributions used for modeling skewed and positive data. It frequently arises in many disciplines of science, specially in the biological and medical sciences. The statistical analysis for comparing the means of two independent log-normal distributions is an issue of significant interest. In this paper we present a robust test for this problem. The unknown parameters of the model are estimated by minimum density power divergence estimators (Basu et al 1998, Biometrika, 85(3), 549-559). The robustness as well as the asymptotic properties of the proposed test statistics are rigorously established. The performance of the test is explored through simulations and real data analysis. The test is compared with some existing methods, and it is demonstrated that the proposed test outperforms the others in the presence of outliers.