Affine Invariant Tests of Multivariate Normality
Koziols measure of multivariate sample kurtosis
multivariate kurtosis in the sense of Malkovich and Afifi
Statistic of the BHEP-test
Statistic of the test of Cox and Small
Monte Carlo simulation of quantiles for normality tests
Statistic of the DEH test based on harmonic oscillator
Statistic of the DEH test based on a double estimation in PDE
Statistic of the EHS test based on a multivariate Stein equation
Henze-Jiménes-Gamero test statistic
statistic of the Henze-Jiménes-Gamero-Meintanis test
statistic of the Henze-Visagie test
Statistic of the Henze-Zirkler test
multivariate skewness in the sense of Malkovich and Afifi
Mardias measure of multivariate sample kurtosis
first statistic of Manzotti and Quiroz
second statistic of Manzotti und Quiroz
multivariate skewness of Móri, Rohatgi and Székely
Mardias measure of multivariate sample skewness
Print method for tests of multivariate normality
Statistic of the Pudelko test
statistic of the Székely-Rizzo test
Empirical scaled residuals
Baringhaus-Henze-Epps-Pulley (BHEP) test
multivariate normality test of Cox and Small
Doerr-Ebner-Henze test of multivariate normality based on harmonic osc...
Doerr-Ebner-Henze test of multivariate normality based on a double est...
Ebner-Henze-Strieder test of multivariate normality based on Fourier m...
Henze-Jimenes-Gamero test of multivariate normality
Henze-Jimenes-Gamero-Meintanis test of multivariate normality
The Henze-Visagie test of multivariate normality
The Henze-Zirkler test
Test of normality based on Koziols measure of multivariate sample kurt...
Test of normality based on multivariate kurtosis in the sense of Malko...
Test of normality based on multivariate skewness in the sense of Malko...
Test of normality based on Mardias measure of multivariate sample kurt...
Manzotti-Quiroz test 1
Manzotti-Quiroz test 2
Test of multivariate normality based on the measure of multivariate sk...
Test of normality based on Mardias measure of multivariate sample skew...
Pudelko test of multivariate normality
Szekely-Rizzo (energy) test
Various affine invariant multivariate normality tests are provided. It is designed to accompany the survey article Ebner, B. and Henze, N. (2020) <arXiv:2004.07332> titled "Tests for multivariate normality -- a critical review with emphasis on weighted L^2-statistics". We implement new and time honoured L^2-type tests of multivariate normality, such as the Baringhaus-Henze-Epps-Pulley (BHEP) test, the Henze-Zirkler test, the test of Henze-Jiménes-Gamero, the test of Henze-Jiménes-Gamero-Meintanis, the test of Henze-Visage, the Dörr-Ebner-Henze test based on harmonic oscillator and the Dörr-Ebner-Henze test based on a double estimation in a PDE. Secondly, we include the measures of multivariate skewness and kurtosis by Mardia, Koziol, Malkovich and Afifi and Móri, Rohatgi and Székely, as well as the associated tests. Thirdly, we include the tests of multivariate normality by Cox and Small, the 'energy' test of Székely and Rizzo, the tests based on spherical harmonics by Manzotti and Quiroz and the test of Pudelko. All the functions and tests need the data to be a n x d matrix where n is the samplesize (number of rows) and d is the dimension (number of columns).