Likelihood analysis for the ratio of means of two independent log-normal distributions

Existing methods for comparing the means of two independent skewed log-normal distributions do not perform well in a range of small-sample settings such as a small-sample bioavailability study. In this article, we propose two likelihood-based approaches - the signed log-likelihood ratio statistic and modified signed log-likelihood ratio statistic - for inference about the ratio of means of two independent log-normal distributions. More specifically, we focus on obtaining p-values for testing the equality of means and also constructing confidence intervals for the ratio of means. The performance of the proposed methods is assessed through simulation studies that show that the modified signed log-likelihood ratio statistic is nearly an exact approach even for very small samples. The methods are also applied to two real-life examples.