A new powerful version of the BUS test of normality

In this paper we introduce a modified version of the BUS test, which we call NBUS (New Borovkov–Utev Statistic). This latter defines a family of goodness of fit tests that can be used to detect normality against alternative hypothesis of which all moments up to the fifth exist. The test statistic depends on empirical moments and real parameters that have to be chosen appropriately. The good abilities of the NBUS with respect to BUS and other powerful normality tests are illustrated by means of a Monte Carlo experiment for finite samples. Besides, we show how an adaptation of NBUS for testing departing from normality due only to kurtosis, leads to comparable performances with classical tests based on the fourth moment.