Are You All Normal? It Depends!

The assumption of normality has underlain much the development statistics, including spatial and many tests have been proposed. In this work, we focus on multivariate setting first review recent advances in for i.i.d. data, with emphasis skewness kurtosis approaches. We show through simulation studies that some these cannot be used directly testing data. further briefly few existing univariate under dependence (time or space), then propose a new test data by accounting dependence. utilises union-intersection principle to decompose null hypothesis into intersections hypotheses projection it rejects if any individual is rejected. are conducted using Jarque–Bera type statistic accounts also good control I error high empirical power, especially large sample sizes. illustrate our bivariate wind over Arabian Peninsula.