Anil K. Bera, Antonio F. Galvao, Liang Wang, Zhijie Xiao, A NEW CHARACTERIZATION OF THE NORMAL DISTRIBUTION AND TEST FOR NORMALITY, Econometric Theory, Vol. 32, No. 5 (October 2016), pp. 1216-1252 ...

These tests often employ advanced metrics, such as weighted L2-statistics and comparisons via the moment generating function, to sensitively detect departures from normality.

The use of the plots usually centers on detecting irregular tail behavior or outliers. Along with the normal plot, we develop tests for various departures from normality, especially for skewness and ...