A MATLAB package for multivariate normality test

Abstract

A MATLAB package testing for multivariate normality (TMVN) is implemented as an interactive and graphical tool to examine multivariate normality (MVN). Monte Carlo simulation studies have failed to find a uniformly most powerful MVN test, which requires a rather extensive statistical inference procedure. TMVN contains several competitive MVN tests and provides a flexible and extensive testing environment for univariate or multivariate data analyses. Simulated results provide information of which test may possess more power for the selected non-MVN alternatives. Fisher's Iris data are used to show how TMVN can be used in practice.

Keywords:

• MATLAB
• multivariate normality
• Monte Carlo simulation
• graphical user interface

Acknowledgements

The author gratefully acknowledges the referees for their comments, which enhanced the presentation of this paper.

Notes

The TMVN package can be downloaded from the website http://web.ntpu.edu.tw/∼ccw/software. This package contains some open-source programmes by other authors. I would like to express my gratitude to those who contribute to this package and have tried my best to retain the copyright notices. Please inform the author if any copyright notice is neglected, or inappropriately made.

Notes

1. The n×p matrix Y is a standardized transformation of the original data matrix X such that n⁻¹Y′Y=I_p. Doornik and Hassen [9] show how to derive the transformed matrix Y.

2. The formula for WH(b_{1, p}) is modified from Equation (3.7) in [34] by

• where f=p(p+1)(p+2)/6.

3. Affine invariant means invariant under full-rank linear transformations of the data.

4. The BHEP(h_S) and BHEP(h_L) designate the BHEP tests suitable for short-tailed and long-tailed alternatives, respectively.