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From moments of sum to moments of product. (English) Zbl 1133.60307

Summary: 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.

MSC:

60E10 Characteristic functions; other transforms
62H10 Multivariate distribution of statistics
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