设{Xn;n≥1}是一列同分布的NA序列,μ=EX1〉0,σ^2=VarX1〈∞.在适当的条件下证明了{[(^nПk=1)Sk ]/n!μ^n}1/γσn→de^N,n→∞,其中Sk=^k∑i=1Xi,γ=σ/μ,σn^2=Var{[1/γ(^n∑k=1)](^Sk/kμ-1)},N是标准正态随机变量.
Let {Xn;n≥1} be a sequence of negatively associated identically distributed random variables,μ=EX1〉0,σ^2=VarX1〈∞. Under suitable conditions it is proved that {[(^nПk=1)Sk ]/n!μ^n}1/γσn→de^N,n→∞,where Sk=^k∑i=1Xi,γ=σ/μ,σn^2=Var{[1/γ(^n∑k=1)](^Sk/kμ-1)} and N is a standard normal random variable.