Modified method on the means for several log-normal distributions

Among statistical inferences, one of the main interests is drawing the inferences about the log-normal means since the log-normal distribution is a well-known candidate model for analyzing positive and right-skewed data. In the past, the researchers only focused on one or two log-normal populations or used the large sample theory or quadratic procedure to deal with several log-normal distributions. In this article, we focus on making inferences on several log-normal means based on the modification of the quadratic method, in which the researchers often used the vector of the generalized variables to deal with the means of the symmetric distributions. Simulation studies show that the quadratic method performs well only for symmetric distributions. However, the modified procedure fits both symmetric and skew distribution. The numerical results show that the proposed modified procedure can provide the confidence interval with coverage probabilities close to the nominal level and the hypothesis testing performed with satisfactory results.