Affine Invariant Tests of Multivariate Normality
Overview
Various affine invariant multivariate normality tests are provided. It is designed to accompany the survey article Ebner, B. and Henze, N. (2020) doi:10.1007/s11749-020-00740-0 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).
- Added a
NEWS.mdfile to track changes to the package. - Added Pearson and Johnson four-moment approximations for BHEP critical values.
- Added p-values for all three calibration methods, returned as
pvalue. - Monte Carlo remains the default calibration method.
- Updated the result printer to display the calibration method and p-value.
- Added numerical safeguards for calculating limiting moments and fitting Johnson distributions.
From NEWS.md in the release
Install
Health
- OK13 OK2026-09-30
- NOTE11 OK, 2 NOTE2026-06-08
- ERROR11 OK, 1 NOTE, 1 ERROR2026-06-07
- NOTE12 OK, 2 NOTE2026-03-10
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- Help pages
- 45includes a package overview page
- Examples that run
- 89%33 run in a plain check · 4 only when donttest examples are enabled (R CMD check --as-cran)
- Exported functions with examples
- 90%
- Documented parameters
- 100%
- Return-value docs
- 100%
- Help pages citing references
- 87%
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Package metadata
- First published
- 2020-04-23
- Total releases
- 4 / 6 yrs
- License
- CC BY 4.0
- Minimum R
- ≥ 3.5.0
- Bundled data
- 4.5 KB / 3 files
- Download size
- 45 KB
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