Testing the mean of skewed distributions applying the maximum likelihood estimator. Issue 1 (1st January 2019) - Tzeng, I-Shiang; Chen, Li-Shya
Abstract: The sample moment can be used to estimate the population third central moment, μ 3, 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 μ 3 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.