ABSTRACT
A generalization of the univariate normal distribution to more than one variable is the multivariate normal distribution. Much of the basic statistical theory underlying statistical inference in factor analysis and structural equation modeling is based on the multivariate normal distribution. Some of the reason for this is that it is often an excellent approximation to many real-world distributions, while at the same time mathematically tractable. It also lends itself well to linear functional relations among variables because linear transformations of multivariate, normally distributed, variables are variables that also have multivariate normal distributions. And sampling distributions of many multivariate statistics, including those of factor analysis, behave approximately as multivariate normal distributions because of the effect described by the central limit theorem.
