From moments of sum to moments of product

Authors:
Raymond Kan
Affiliations:
Joseph L. Rotman School of Management, University of Toronto, 105St. George Street, Toronto, Ont., Canada M5S 3E6
Venue:
Journal of Multivariate Analysis
Year:
2008

Citing 4
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Abstract

We provide an identity that relates the moment of a product of random variables to the moments of different linear combinations of the random variables. Applying this identity, we obtain new formulae for the expectation of the product of normally distributed random variables and the product of quadratic forms in normally distributed random variables. In addition, we generalize the formulae to the case of multivariate elliptically distributed random variables. Unlike existing formulae in the literature, our new formulae are extremely efficient for computational purposes.