RFunctions to Symbolically Compute the Central Moments of the Multivariate Normal Distribution | Zendy

Kem F. Phillips | Zendy

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RFunctions to Symbolically Compute the Central Moments of the Multivariate Normal Distribution

Author(s) -

Kem F. Phillips

Publication year - 2010

Publication title -

journal of statistical software

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 7.636

H-Index - 145

ISSN - 1548-7660

DOI - 10.18637/jss.v033.c01

Subject(s) - mathematics , moment (physics) , multivariate statistics , multivariate normal distribution , covariance , distribution (mathematics) , variance (accounting) , matrix (chemical analysis) , method of moments (probability theory) , matrix t distribution , integer (computer science) , function (biology) , normal distribution , covariance matrix , combinatorics , central moment , moment generating function , mathematical analysis , statistics , probability distribution , computer science , physics , materials science , accounting , classical mechanics , estimator , evolutionary biology , business , composite material , biology , programming language

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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