Abstract:
The subject of assessing whether a data set is from a specific distribution has
received a good deal of attention. This topic is critically important for the normal
distribution. Often the distributions of the test statistics are intractable.
Here we consider simulation based distributions for several commonly used
normality test statistics, such as, Anderson-Darling A2 test, Chi-square test,
Shapiro-Wilk W test, Shapiro-Francia W′ test, D’Agostino-Pearson test, and
Jarque-Bera test. Practitioners are used to with the Chi-square test because all
other tests are dependent on specialized tables and/or software. Here, we give
algorithms, how those specialized tables can be generated and then the respective
tests can be implemented without much difficulty. A power comparison is
also performed using simulation.
