Inferences on the Means of Two Log-Normal Distributions: A Computational Approach Test

Abstract

In this article, we propose a novel approach for testing the equality of two log-normal populations using a computational approach test (CAT) that does not require explicit knowledge of the sampling distribution of the test statistic. Simulation studies demonstrate that the proposed approach can perform hypothesis testing with satisfying actual size even at small sample sizes. Overall, it is superior to other existing methods. Also, a CAT is proposed for testing about reliability of two log-normal populations when the means are the same. Simulations show that the actual size of this new approach is close to nominal level and better than the score test. At the end, the proposed methods are illustrated using two examples.

Keywords:

• Actual size
• Hypothesis test
• Log-normal distribution
• Reliability

Mathematics Subject Classification:

• 62F03
• 62F30
• 62F40

Acknowledgments

The authors would like to thank the referee for its comments and suggestions which have contributed to improving the manuscript.