The moments of the multivariate normal

C.S. Withers

doi:10.1017/S000497270000976X

Abstract

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Explicit expressions are given for the noncentral moments of the multivariate normal. Finding the general moment is shown to be equivalent to finding the general derivative of the density of the multivariate normal, that is to finding an expression for the multivariate Hermite polynomial.

References

[1]Isserlis, L., “On a formula for the product moment coefficient of any order of a normal frequency distribution in any number of variables”, Biometrika 12 (1918), 134–139.Google Scholar

[2]Withers, C.S., “A chain rule for differentiation giving simple expressions for the multivariate Hermite polynomials”, Bull. Austral. Math. Soc. 30 (1983), 247–250.Google Scholar

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