<p>a n x d matrix of d dimensional data vectors.</p>

data

<p>This function returns the value of the first statistic of Manzotti and Quiroz (2001).</p>

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-Jim<c3><a9>nes-Gamero, the test of Henze-Jim<c3><a9>nes-Gamero-Meintanis, the test of Henze-Visage, the D<c3><b6>rr-Ebner-Henze test based on harmonic oscillator and the D<c3><b6>rr-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 M<c3><b3>ri, Rohatgi and Sz<c3><a9>kely, as well as the associated tests. Thirdly, we include the tests of multivariate normality by Cox and Small, the 'energy' test of Sz<c3><a9>kely 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).

MQ1: first statistic of Manzotti and Quiroz

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