随机变量的负超可加相依及其应用

Negatively Superadditive Dependence of Random Variables with Applications

摘要: 一个随机向量 X=（X₁, X₂,..., X_m）称为负超可加相依（NSD），如果对每个超可加函数ϕ， Eϕ（X₁, X₂,..., X_m）≤5 Eϕ（Y₁, Y₂,..,Y_m）其中Y₁, Y₂,..,Y_m相互独立且对任意i,Y_i \stackreld= X_i 本文研究了NSD的基本性质，给出了NSD判定的三个结构性定理，并且这些定理可用来证明许多著名的多元分布具有NSD性质，本文还给出了NSD的许多概率不等式。

Abstract: A random vector X =（X₁,X₂,...,X_m） is said to be negatively superadditive dependent （NSD） if for every superadditive function ϕ, Eϕ（X₁, X₂,..., X_m）≤5 Eϕ（Y₁, Y₂,..,Y_m） where Y₁, Y₂,..,Y_m are independent with Y_i \stackreld= X_i for each i. Some basic properties and three structural theorems of NSD are derived and applied to show that a number of well-known multivariate distributions possess the NSD property. Applications are also presented.