论文标题
多元高斯，伽马和正偏分布的产品不平等现象
Product Inequalities for Multivariate Gaussian, Gamma, and Positively Upper Orthant Dependent Distributions
论文作者
论文摘要
高斯产品不平等是关于高斯随机向量矩的重要猜想。虽然所有试图证明高斯产品不平等的尝试都没有成功，但近几十年来已经得出了许多部分结果，我们在这里为问题提供了进一步的结果。最重要的是，在非负相关的情况下，我们为多元伽马分布建立了高斯产品不平等的强大版本，从而扩大了Genest和Ouimet最近得出的结果[5]。此外，我们表明高斯产品不等式与所有具有正分量的随机向量的非负指数相关，只要下面的载体是肯定的上部矫正依赖性的。最后，我们表明，具有负指数的高斯产品不平等直接遵循高斯相关性不平等。
The Gaussian product inequality is an important conjecture concerning the moments of Gaussian random vectors. While all attempts to prove the Gaussian product inequality in full generality have been unsuccessful to date, numerous partial results have been derived in recent decades and we provide here further results on the problem. Most importantly, we establish a strong version of the Gaussian product inequality for multivariate gamma distributions in the case of nonnegative correlations, thereby extending a result recently derived by Genest and Ouimet [5]. Further, we show that the Gaussian product inequality holds with nonnegative exponents for all random vectors with positive components whenever the underlying vector is positively upper orthant dependent. Finally, we show that the Gaussian product inequality with negative exponents follows directly from the Gaussian correlation inequality.
