摘要
设(X_(1),X_(2),X_(3))为中心化的高斯随机变量,其协方差矩阵的对角线元素均为1,该文借助于超几何函数的性质及因式分解得到了E[|X_(1)^(4)X^(3)_(2)X^(3)_(3)|]≥E|X_(1)^(4)X_(2)^(3)X_(3)^(3)|,等号成立当且仅当X_(1),X_(2),X_(3)相互独立.从而补充了现有文献中三维高斯乘积不等式的结果.
Let(X_(1),X_(2),X_(3))be a centered Gaussian random vector with D(Xi)=1,i=1,2,3.By means of the properties of hypergeometric function and factorization,we prove that E[|X_(1)^(4)X_(3)2X_(3)3|]≥E|X_(1)^(4)X_(2)^(3)X_(3)^(3)|,and the equal sign holds if and only if X_(1),X_(2),X_(3) are independent.This complements the results of the three dimensional Gauss product inequality in the existing literature.
作者
马丽
陈蓬颖
韩新方
Li Ma;Pengying Chen;Xinfang Han(Department of Mathematics and Statistics,Hainan Normal University,Haikou 571158;Key Laboratory of Data Science and Intelligence Education(Hainan Normal University),Ministry of Education,Haikou 571158)
出处
《数学物理学报(A辑)》
北大核心
2025年第3期960-971,共12页
Acta Mathematica Scientia
基金
海南省自然科学基金(122MS056,124MS056)。
关键词
高斯乘积不等式
正态分布
超几何函数
因式分解
Gauss Product Inequality
normal Distribution
hypergeometric Function
factorization
