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The moments of the multivariate normal

Published online by Cambridge University Press:  17 April 2009

C.S. Withers
C.S. Withers
Affiliation:
Applied Mathematics Division, Department of Scientific and Industrial Research, PO Box 1335, Wellington, New Zealand.
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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.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 32 , Issue 1 , August 1985 , pp. 103 - 107
Copyright
Copyright © Australian Mathematical Society 1985

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