非负WOD随机变量的第k小矩不等式

Moment inequalities of the k-minimum for nonnegative widely orthant dependent random variables

设{x_n,n≥1}为正数序列,{ξ_n,n≥1}为非负的WOD随机变量序列,其分布满足适当的条件.首先利用WOD随机变量的定义建立最小值min1≤i≤nx_iξ_i的一个指数不等式.利用此指数不等式,进一步研究非负WOD随机变量的第k小(E(k-min1≤i≤n|x_iξ_i|~p))^(1/p)的矩不等式,其中p>0,k=1,2,…,n.本文中所得结果推广独立变量和NOD变量的相应结果.

Let {x_n,n≥1} be a sequence of positive numbers and {ξ_n,n≥1} be a sequence ofnonnegative widely orthant dependent(WOD) random variables satisfying certain distribution conditions.Anexponential inequality for the minimum min1≤i≤nx_iξ_i is established by using the definition of WOD random variables.In addition,the moment inequalities of thek-th minimum(E(k-min1≤i≤n|x_iξ_i|~p))^(1/p) for nonnegative WOD random variables are established,wherep>0,k=1,2,…,n.Our results generalize the correspondingones for independent random variables and negatively orthant dependent(NOD) random variables.