Testing the mean of skewed distributions applying the maximum likelihood estimator

Abstract

Abstract The sample moment can be used to estimate the population third central moment, , in the Johnson’s modified t-statistic for skewed distributions. However, moment estimator is non-unique and insufficient for the parameter of population. In this paper, we display the maximum likelihood estimator (MLE) of in modified t-statistic as parent distributions are asymmetrical. A Monte Carlo study shows that the MLE procedure is more powerful than Student’s t-test and ordinary Johnson’s modified t-test for a variety of positively skewed distributions with small sample sizes.