Multivariate normal distribution

Use the multivariate normal distribution to describe a group of variables that are correlated.Some multivariate analyses, such as factor analysis and MANOVA, assume that the data follow a multivariate normal distribution. For example, you perform a study to determine optimum conditions for extruding plastic film. You are interested in three correlated responses: tear resistance, gloss, and opacity. This group of variables follows a multivariate normal distribution.

The multivariate normal distribution is defined by a vector of means and the variance-covariance matrix. It is an extension of the univariate normal distribution for applications with a group of variables that may be correlated.

A vector follows a multivariate normal distribution if the following conditions are met:
  • Linear combinations of the components of the vector are normally distributed.
  • All subsets of the components of X have a multivariate normal distribution.
  • The conditional distributions of the components are multivariate normal.
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