The paper by Jürgen A. Doornik and Henrik Hansen introduces an omnibus test for univariate and multivariate normality, based on skewness and kurtosis. The test is designed to be easy to use and to control the size well, addressing the limitations of existing tests such as the one proposed by Bowman and Shenton (1975). The authors derive a transformed version of skewness and kurtosis that are closer to standard normal distributions, simplifying the implementation of the test statistic. They also propose a multivariate version of the test, which is scale-invariant and invariant to variable ordering. The paper compares the size and power of the proposed test with four other multivariate normality tests: Small's (1980) test, Mardia's (1970) test, Mudholkar et al.'s (1992) test, and the multivariate Shapiro-Wilk test. The comparisons are conducted using Monte Carlo simulations under various alternative distributions, including the Johnson system of distributions. The results show that the proposed test has better size control and higher power against certain alternatives compared to the other tests. The authors conclude that their test is simple, has correct size, and has good power properties, making it a preferred choice for testing univariate and multivariate normality. They also suggest that the test could be used in conjunction with Mardia's test for enhanced performance.The paper by Jürgen A. Doornik and Henrik Hansen introduces an omnibus test for univariate and multivariate normality, based on skewness and kurtosis. The test is designed to be easy to use and to control the size well, addressing the limitations of existing tests such as the one proposed by Bowman and Shenton (1975). The authors derive a transformed version of skewness and kurtosis that are closer to standard normal distributions, simplifying the implementation of the test statistic. They also propose a multivariate version of the test, which is scale-invariant and invariant to variable ordering. The paper compares the size and power of the proposed test with four other multivariate normality tests: Small's (1980) test, Mardia's (1970) test, Mudholkar et al.'s (1992) test, and the multivariate Shapiro-Wilk test. The comparisons are conducted using Monte Carlo simulations under various alternative distributions, including the Johnson system of distributions. The results show that the proposed test has better size control and higher power against certain alternatives compared to the other tests. The authors conclude that their test is simple, has correct size, and has good power properties, making it a preferred choice for testing univariate and multivariate normality. They also suggest that the test could be used in conjunction with Mardia's test for enhanced performance.