The Sampling Distribution of the Total Correlation for Multivariate Gaussian Random Variables

The sampling distribution of the total correlation (TC) for a d-dimensional standardized multivariate Gaussian random variable with an identity covariance matrix is derived. It is shown to be the distribution of a sum of generalized beta random variables. It is also shown that, for large dimension and sample size, a central limit theorem holds, providing a Gaussian approximation to the sampling distribution for high dimensional data.