Likelihood-based confidence intervals for a log-normal mean

To construct a confidence interval for the mean of a log-normal distribution in small samples, we propose likelihood-based approaches - the signed log-likelihood ratio and modified signed log-likelihood ratio methods. Extensive Monte Carlo simulation results show the advantages of the modified signed log-likelihood ratio method over the signed log-likelihood ratio method and other methods. In particular, the modified signed log-likelihood ratio method produces a confidence interval with a nearly exact coverage probability and highly accurate and symmetric error probabilities even for extremely small sample sizes. We then apply the methods to two sets of real-life data.