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Based on the canonical correlation analysis we derive series representationsof the probability density function (PDF) and the cumulative distributionfunction (CDF) of the information density of arbitrary Gaussian random vectorsas well as a general formula to calculate the central moments. Using thegeneral results we give closed-form expressions of the PDF and CDF and explicitformulas of the central moments for important special cases. Furthermore, wederive recurrence formulas and tight approximations of the general seriesrepresentations, which allow very efficient numerical calculations with anarbitrarily high accuracy as demonstrated with an implementation in Pythonpublicly available on GitLab. Finally, we discuss the (in)validity of Gaussianapproximations of the information density.

On the Distribution of the Information Density of Gaussian Random Vectors: Explicit Formulas and Tight Approximations