From moments of sum to moments of product

JOURNAL OF MULTIVARIATE ANALYSIS

卷:99

Article

Kan, Raymond

关键词: moments of product;    product of random variables;    product of quadratic forms;   

DOI  :  10.1016/j.jmva.2007.01.013

来源: Elsevier

【 摘 要 】

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. (C) 2007 Elsevier Inc. All rights reserved.

【 授权许可】

Free