Comparison of some Different Methods for Hypothesis Test of Means of Log-normal Populations

TL;DR

This paper compares various statistical methods for hypothesis testing of means in log-normal populations, focusing on their size and power through simulation studies.

Contribution

It evaluates and compares the effectiveness of F-test, likelihood ratio test, generalized p-value, and computational approaches for log-normal mean comparisons.

Findings

F-test and likelihood ratio test perform well in certain conditions.

Generalized p-value approach offers a viable alternative.

Simulation results highlight differences in test size and power.

Abstract

The log-normal distribution is used to describe the positive data, that it has skewed distribution with small mean and large variance. This distribution has application in many sciences for example medicine, economics, biology and alimentary science, ect. Comparison of means of several log-normal populations always has been in focus of researchers, but the test statistic are not easy to derive or extremely complicated for this comparisons. In this paper, the different methods exist for this testing that we can point out F-test, likelihood ratio test, generalized p-value approach and computational approach test. In this line with help of simulation studies, in this methods we compare and evaluate size and power test.