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We apply the optimal transport distance to construct two goodness of t tests for (univariate) normality. The derived statistics are then compared with those used by the Shapiro-Wilk, the Anderson-Darling and the Cramervon Mises tests. In particular, we preform Monte Carlo experiments, involving computations of the test power against some selected alternatives and wide range of sample sizes, which show e ciency of the obtained test procedures.

On Some Goodness of Fit Tests for Normality Based on the Optimal Transport Distance