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 (X, Y) 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
W = 0.5889, p-value < 2.2e-16