Testing the mean of skewed distributions applying the maximum likelihood estimator. Issue 1 (1st January 2019)

• Record Type: Journal Article
• Authors: Tzeng, I-Shiang; Chen, Li-Shya
• Editors: Zou, Guohua
• Is Part Of: Cogent mathematics & statistics. Volume 6:Issue 1(2019)
• Publication Date: 2019-01-01
• Subjects: Johnson's modified t-test -- third central moment -- statistical powers -- student's t-test; Mathematics -- Periodicals; Statistics -- Periodicals; Mathematics; Statistics; Periodicals; 510
• DOI: 10.1080/25742558.2019.1588191
• Languages: English
• ISSNs: 2574-2558

Abstract

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.