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

Marcin Mazur,

Piotr Kościelniak


We apply the optimal transport distance to construct two goodness of fit tests for (univariate) normality. The derived statistics are then compared with those used by the Shapiro-Wilk, the Anderson-Darling and the Cramer-von 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 efficiency of the obtained test procedures.

Słowa kluczowe: Goodness of fit test (for normality), optimal transport distance, Wasserstein distance, autoencoder-based generative model.

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