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

Kem Phillips

Journal of Statistical Software, 2010, vol. 033, issue c01

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.

Date: 2010-02-02
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Persistent link: https://EconPapers.repec.org/RePEc:jss:jstsof:v:033:c01

DOI: 10.18637/jss.v033.c01

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