Using goodness-of-fit tests to detect normality for mesokurtic data

Abstract

The normality assumption is crucial in statistical inference and modelling. It is therefore important to determine if a sample comes from a normal distribution. Consequently, numerous goodness-of-fit hypothesis tests have been developed. The practical use of a specific test depends on its availability in the statistical software package considered. The field of application will also contribute to the choice of test. For instance, the Jarque-Bera test is popular in econometrics and finance. Various power comparison and simulation studies of goodness-of- t tests for normality can be found in the literature. Typically, these studies select alternative distributions whose levels of skewness and kurtosis deviate from that of the normal distribution. I.e., symmetric and asymmetric distributions exhibiting leptokurtosis or platykurtosis are included in these simulation studies. In this mini-dissertation, the focus is on mesokurtic distributions whose levels of skewness and kurtosis are equivalent to that of the normal distribution, but with different distributional shapes compared to the normal distribution.