Package: mnt 1.3

mnt: Affine Invariant Tests of Multivariate Normality

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).

Authors:Lucas Butsch [aut], Bruno Ebner [aut, cre], Jaco Visagie [ctb], Johann Siemens [ctb]

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mnt.pdf |mnt.html✨
mnt/json (API)

# Install 'mnt' in R:
install.packages('mnt', repos = c('https://ebner-kit.r-universe.dev', 'https://cloud.r-project.org'))

Peer review:

Datasets:
  • Quantile09 - Simulated empirical 90% quantiles of the tests contained in package 'mnt'
  • Quantile095 - Simulated empirical 95% quantiles of the tests contained in package 'mnt'
  • Quantile099 - Simulated empirical 99% quantiles of the tests contained in package 'mnt'

On CRAN:

This package does not link to any Github/Gitlab/R-forge repository. No issue tracker or development information is available.

1.70 score 1 scripts 196 downloads 40 exports 2 dependencies

Last updated 4 years agofrom:d4ca733cff. Checks:OK: 3 NOTE: 4. Indexed: yes.

TargetResultDate
Doc / VignettesOKNov 08 2024
R-4.5-winOKNov 08 2024
R-4.5-linuxOKNov 08 2024
R-4.4-winNOTENov 08 2024
R-4.4-macNOTENov 08 2024
R-4.3-winNOTENov 08 2024
R-4.3-macNOTENov 08 2024

Exports:BHEPCScv.quanDEHTDEHUEHSHJGHJMHVHZKKurtMAKurtMASkewMKurtMQ1MQ2MRSSkewMSkewPUSRstandardtest.BHEPtest.CStest.DEHTtest.DEHUtest.EHStest.HJGtest.HJMtest.HVtest.HZtest.KKurttest.MAKurttest.MASkewtest.MKurttest.MQ1test.MQ2test.MRSSkewtest.MSkewtest.PUtest.SR

Dependencies:MASSpracma

Readme and manuals

Help Manual

Help pageTopics
Statistic of the BHEP-testBHEP
Statistic of the test of Cox and SmallCS
Monte Carlo simulation of quantiles for normality testscv.quan
Statistic of the DEH test based on harmonic oscillatorDEHT
Statistic of the DEH test based on a double estimation in PDEDEHU
Statistic of the EHS test based on a multivariate Stein equationEHS
Henze-Jiménes-Gamero test statisticHJG
statistic of the Henze-Jiménes-Gamero-Meintanis testHJM
statistic of the Henze-Visagie testHV
Statistic of the Henze-Zirkler testHZ
Koziols measure of multivariate sample kurtosisKKurt
multivariate kurtosis in the sense of Malkovich and AfifiMAKurt
multivariate skewness in the sense of Malkovich and AfifiMASkew
Mardias measure of multivariate sample kurtosisMKurt
first statistic of Manzotti and QuirozMQ1
second statistic of Manzotti und QuirozMQ2
multivariate skewness of Móri, Rohatgi and SzékelyMRSSkew
Mardias measure of multivariate sample skewnessMSkew
Print method for tests of multivariate normalityprint.mnt
Statistic of the Pudelko testPU
Simulated empirical 90% quantiles of the tests contained in package 'mnt'Quantile09
Simulated empirical 95% quantiles of the tests contained in package 'mnt'Quantile095
Simulated empirical 99% quantiles of the tests contained in package 'mnt'Quantile099
statistic of the Székely-Rizzo testSR
Empirical scaled residualsstandard
Baringhaus-Henze-Epps-Pulley (BHEP) testtest.BHEP
multivariate normality test of Cox and Smalltest.CS
Doerr-Ebner-Henze test of multivariate normality based on harmonic oscillatortest.DEHT
Doerr-Ebner-Henze test of multivariate normality based on a double estimation in a PDEtest.DEHU
Ebner-Henze-Strieder test of multivariate normality based on Fourier methods in a multivariate Stein equationtest.EHS
Henze-Jimenes-Gamero test of multivariate normalitytest.HJG
Henze-Jimenes-Gamero-Meintanis test of multivariate normalitytest.HJM
The Henze-Visagie test of multivariate normalitytest.HV
The Henze-Zirkler testtest.HZ
Test of normality based on Koziols measure of multivariate sample kurtosistest.KKurt
Test of normality based on multivariate kurtosis in the sense of Malkovich and Afifitest.MAKurt
Test of normality based on multivariate skewness in the sense of Malkovich and Afifitest.MASkew
Test of normality based on Mardias measure of multivariate sample kurtosistest.MKurt
Manzotti-Quiroz test 1test.MQ1
Manzotti-Quiroz test 2test.MQ2
Test of multivariate normality based on the measure of multivariate skewness of Mori, Rohatgi and Szekelytest.MRSSkew
Test of normality based on Mardias measure of multivariate sample skewnesstest.MSkew
Pudelko test of multivariate normalitytest.PU
Szekely-Rizzo (energy) testtest.SR