论文标题
$ n $维椭圆形分布的联合时刻的显式表达式
Explicit expressions for joint moments of $n$-dimensional elliptical distributions
论文作者
论文摘要
受斯坦因的引理的启发，我们为椭圆形分布的联合力矩提供了两个表达式。我们使用两种不同的方法来得出$ e [x_ {1}^{2} f（\ mathbf {x}）] $用于满足某些规律性条件的任何可测量函数$ f $。然后，通过应用此结果，我们获得了新的公式，以期期望正态分布的随机变量的产品，并且还提供了$ e [x_ {1}^{2} f（\ Mathbf {x}）$的简化表达式，用于多变量学生 - $ t $ t $ t $，logistic-logistic- logistic和laplace发行。
Inspired by Stein's lemma, we derive two expressions for the joint moments of elliptical distributions. We use two different methods to derive $E[X_{1}^{2}f(\mathbf{X})]$ 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 $E[X_{1}^{2}f(\mathbf{X})]$ for multivariate Student-$t$, logistic and Laplace distributions.
