Multivariate Normality Test


Multivariate normal distribution or multivariate Gaussian distribution is a generalization of the one-dimensional (univariate

) normal distribution to higher dimensions. A random vector is said to be multivariate normally distributed if every linear combination of its components has a univariate normal distribution.

If X and Y are normally distributed and independent, this implies they are "jointly normally distributed", i.e., the pair (XY) must have bivariate normal distribution. However, a pair of jointly normally distributed variables need not be independent.

The fact that a set of random variables X1, X2, , Xi, each has a normal distribution does not imply that the they have a joint normal distribution.

This function performs the Shapiro-Wilk test for multivariate normality.


Below is a sample input window:



Below is a sample output:


Multivariate normality test for:








Shapiro-Wilk normality test


data: Z

W = 0.5889, p-value < 2.2e-16