Explicit expressions for joint moments of n-dimensional elliptical distributions

07/18/2020

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by   Baishuai Zuo, et al.

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Inspired by Stein's lemma, we derive two expressions for the joint moments of elliptical distributions. We use two different methods to derive E[X_1^2f(𝐗)] for any measurable function f satisfying some regularity conditions. Then, by applying this result, we obtain new formulae for expectations of product of normally distributed random variables, and also present simplified expressions of E[X_1^2f(𝐗)] for multivariate Student-t, logistic and Laplace distributions.