R Functions to Symbolically Compute the Central Moments of the Multivariate Normal Distribution

Abstract

The central moments of the multivariate normal distribution are functions of its n x n variance-covariance matrix Σ. These moments can be expressed symbolically as linear combinations of products of powers of the elements of Σ. A formula for these moments derived by differentiating the characteristic function is developed. The formula requires searching integer matrices for matrices whose n successive row and column sums equal the n exponents of the moment. This formula is implemented in R, with R functions to display moments in LaTeX and to evaluate moments at specified variance-covariance matrices included.