期刊名称：Journal of Statistical Theory and Applications (JSTA)
电子版ISSN：1538-7887
出版年度：2018
卷号：17
期号：4
页码：63-76
DOI：10.2991/jsta.2018.17.4.7
语种：English
出版社：Atlantis Press
摘要：Many statistical procedures assume that the underling distribution is normal. In this paper, we consider the popular and powerful tests for normality and investigate the power values of these tests to detect deviations from normality. The family of fourparameter generalized lambda distributions (FMKL) for its high flexibility is considered as alternative distributions. We then compare the power values of normality tests against these alternatives and for different sample sizes. The considered tests are Kolmogorov-Smirnov, Anderson-Darling, Kuiper, Jarque-Bera, Cramer von Mises, Shapiro-Wilk and Vasicek. These tests are popular tests which are commonly used in practice and statistical software. The tests are described and then power values of the tests are compared against FMKL family by Monte Carlo simulation. The results are discussed and interpreted. Finally, we apply some real data examples to show the behavior of the tests in practice.
关键词：Test of normality;Monte Carlo simulation;Power of test;The generalized lambda distribution
