ANALÝZA SÍLY VYBRANÝCH KLASICKÝCH A ROBUSTNÍCH TESTŮ NORMALITY PROTI BIMODÁLNÍMU ROZDĚLENÍ

Abstract

The aim of this paper is to compare the power of selected normality tests to detect a bimodal distribution. We use some classical normality tests (the Shapiro-Wilk test, the Lilliefors test, the Anderson-Darling test, the classical Jarque-Bera test and the Jarque-Bera-Urzua test), some robust normality tests (the robust Jarque-Bera test and the Medcouple test) and the modified Jarque-Bera tests, where the median instead of the mean is used in the classical Jarque-Bera test statistic. The results of simulation study show that the Anderson-Darling and the Shapiro-Wilk tests outperform the others, especially in small sample sizes. On the other hand the classical Jarque-Bera, the Jarque-Bera-Urzua and robust Jarque-Bera tests are biased, especially in small sample sizes again. Finally, the modification of the Jarque-Bera test leads to increase of power against bimodal distribution.