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

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  • Phillips, Kem

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.

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  • Phillips, Kem, 2010. "R Functions to Symbolically Compute the Central Moments of the Multivariate Normal Distribution," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 33(c01).
    • Handle: RePEc:jss:jstsof:v:033:c01
    DOI: http://hdl.handle.net/10.18637/jss.v033.c01
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    1. Kuonen, Diego, 2003. "Numerical Integration in S-PLUS or R: A Survey," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 8(i13).
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    1. Yu, Haiyan & Yang, Ching-Chi & Yu, Ping, 2023. "Constrained optimization for stratified treatment rules in reducing hospital readmission rates of diabetic patients," European Journal of Operational Research, Elsevier, vol. 308(3), pages 1355-1364.

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