Likelihood-ratio tests for normality

There are many variety of tests for normality in the literature. Some are either too simple to be powerful or too difficult to apply. Most of them only suit for certain situations due to various kinds of biases. Powerful omnibus tests of normality based on the likelihood ratio are proposed. In terms of power for testing normality, they outperform the best tests in the literature, including the Shapiro-Wilk and Anderson-Darling tests.