Standardized likelihood ratio test for comparing several log-normal means and confidence interval for the common mean.

Standardized likelihood ratio test (SLRT) for testing the equality of means of several log-normal distributions is proposed. The properties of the SLRT and an available modified likelihood ratio test (MLRT) and a generalized variable (GV) test are evaluated by Monte Carlo simulation and compared. Evaluation studies indicate that the SLRT is accurate even for small samples, whereas the MLRT could be quite liberal for some parameter values, and the GV test is in general conservative and less powerful than the SLRT. Furthermore, a closed-form approximate confidence interval for the common mean of several log-normal distributions is developed using the method of variance estimate recovery, and compared with the generalized confidence interval with respect to coverage probabilities and precision. Simulation studies indicate that the proposed confidence interval is accurate and better than the generalized confidence interval in terms of coverage probabilities. The methods are illustrated using two examples.