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Affine Invariant Tests of Multivariate Normality

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Overview

About

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).

Changes in 1.4
  • Added a NEWS.md file 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

CRAN checks
13OK
Slowest check: 1.6 min · r-oldrel-windows-x86_64
Status changes
  • OK13 OK2026-09-30
  • NOTE11 OK, 2 NOTE2026-06-08
  • ERROR11 OK, 1 NOTE, 1 ERROR2026-06-07
  • NOTE12 OK, 2 NOTE2026-03-10
Advisories

none known

Documentation

In release 1.4
READMEYes · 189 wordsVignettesNoNEWSYes · 67% structured · mentions 1.4Citation fileNoWebsitenot declared in DESCRIPTION
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%

Downloads

2.9K
CRAN downloads in the past year
Rank #15,126 · ~8/day · ~243/mo
Daily download trend is not available in this view yet.
33630 days
80890 days
2.9K1 year
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Also on73 r2u6 autocran

Dependencies

Declared dependencies
4 external dependencies (excludes base and recommended)

Installing mnt adds 5 packages (4 with compiled code, 1.4 MB of source tarballs). Heaviest: Rmpfr 647 KB, pracma 389 KB, gmp 163 KB.

Depends (1)
R >= 3.5.0
Imports (6)
LinkingTo (0)
none
Suggests (0)
none
Enhances (0)
none
Reverse dependencies
0direct
0indirect

Nothing depends on this yet.

Datasets

People & History

People (4)
Author, Maintainer since 1.0 (2020)
Contributor
Contributor
Releases (4)

Pick two releases to compare their code metrics.

  • 1.4Latest
    record
    2026-09-25 · current release · diff ↗
  • R
    R 4.6.0 released · 2026-04-24
  • R
    R 4.5.0 released · 2025-04-11
  • R
    R 4.4.0 released · 2024-04-24
  • R
    R 4.3.0 released · 2023-04-21
  • R
    R 4.2.0 released · 2022-04-22
  • R
    R 4.1.0 released · 2021-05-18
  • 1.3
    record
    2020-07-31 · diff ↗ ·
    added 2 exports
    EHS, test.EHS
  • 1.2
    record
    2020-04-26 · diff ↗
  • R
    R 4.0.0 released · 2020-04-24
  • 1.0
    record
    2020-04-23
  • R
    R 3.6.0 released · 2019-04-26

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

Cite

Cite this package

Run in R for the authors' preferred citation:

citation("mnt")
Ebner, B., Butsch, L., Siemens, J., & Visagie, J. (2026). mnt: Affine Invariant Tests of Multivariate Normality (Version 1.4) [Computer software]. https://doi.org/10.32614/CRAN.package.mnt

This package has no citation file, so citation() returns this entry built from DESCRIPTION.

Cite the R Observatory

For a number measured here: a download total, a coverage figure, an archival date.

APA

Balamuta, J. J. (2026). R Observatory: Metrics for mnt version 1.4 [Data set]. HJJB, LLC. Data release v2026-10-25. https://doi.org/10.5281/zenodo.21843040

From data release v2026-10-25, which the citation names so these numbers can be found later. More on citing and the projects behind them.

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