search for


Testing for multivariate normality based on generalization of empirical distribution function
Journal of the Korean Data & Information Science Society 2024;35:217-28
Published online March 31, 2024;
© 2024 Korean Data and Information Science Society.

Namhyun Kim1

1Department of Science, Hongik University
Correspondence to: This work was supported by 2023 Hongik University Research Fund.
1 Professor, Department of Science, Hongik University, Seoul 04066, Korea. E-mail:
Received February 22, 2024; Revised March 16, 2024; Accepted March 18, 2024.
This is an Open Access article distributed under the terms of the Creative Commons Attribution Non-Commercial License ( which permits unrestricted non-commercial use, distribution, and reproduction in any medium, provided the original work is properly cited.
Testing multivariate normality is a topic of ongoing practical and theoretical interest in statistical inference. We generalize goodness-of-fit test statistics based on the empirical distribution function to test multivariate normality. Kesmen et al. (2021) defined a multivariate empirical distribution function and generalized the Kolmogorov-Smirnov statistic to multivariate cases. In this paper the Cramér-von Mises statistic and the Anderson-Darling statistic are generalized by the same way. Through simulation study, the Anderson-Darling statistic showed the best power among three of them. Since the statistics run very simply even in multivariate cases, they could be easily applied in practical situation.
Keywords : Empirical distribution function, goodness-of-fit tests, multivariate normality