Performances of Several Univariate Tests of Normality: An EmpiricalStudy

[摘要] The problem of testing for normality is fundamental in both theoretical and empirical statistical research. This paper compares the performances of eighteen normality tests available in literature. Since a theoretical comparison is not possible, MonteCarlo simulation were done from various symmetric and asymmetric distributions for different sample sizes ranging from 10 to 1000. The performance of the test statistics are compared based on empirical Type I error rate and power of the test. The simulations results show that the Kurtosis Test is the most powerful for symmetric data and Shapiro Wilk test is the most powerful for asymmetric data.

[关键词] Chi-square;Kurtosis;Normality;Shapiro-wilk;Simulation study;Skewness;Type I and type errorsAMS Subject Classifications 2010: Primary 62F03;62F40