2010
DOI: 10.18637/jss.v033.c01
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RFunctions 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 × 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… Show more

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Cited by 5 publications
(5 citation statements)
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“…For n = 4, more than one hundred moments need to be computed. The computational complexity to numerically compute the central moments of the multivariate normal distribution is discussed in [68]; see also [3, p. 49], [38, proposition 1], [62, p. 46], and the matrix derivative formula in [92]. The above formulae also show that we cannot expect to have a semi-circle-type law as in (1.7) for any covariance matrix.…”
Section: Description Of the Modelsmentioning
confidence: 99%
“…For n = 4, more than one hundred moments need to be computed. The computational complexity to numerically compute the central moments of the multivariate normal distribution is discussed in [68]; see also [3, p. 49], [38, proposition 1], [62, p. 46], and the matrix derivative formula in [92]. The above formulae also show that we cannot expect to have a semi-circle-type law as in (1.7) for any covariance matrix.…”
Section: Description Of the Modelsmentioning
confidence: 99%
“…which only depends on the central third order moments of the latent field x since all the other mixed moments are zero (see [26] for more details on moments of a multivariate Gaussian distribution). Thus, the overall skewness for the linear combination vector Ax can easily be evaluated as…”
Section: Moments Matchingmentioning
confidence: 99%
“…Existing methods for calculating the higher-order moments for normal distributions rely on the characteristic function [49], [50]. The main bottleneck of these methods is enumerating an integers matrix.…”
Section: A Gaussian Mixture Modelmentioning
confidence: 99%