Negatively dependent bounded random variable probabilityinequalities and the strong law of large numbers

[摘要] LetX1,…,Xnbe negatively dependent uniformly bounded random variables with d.f.F(x). In this paper we obtain bounds for the probabilitiesP(|∑i=1nXi|≥nt)andP(|ξˆpn−ξp|>ϵ)whereξˆpnis thesamplepth quantile andξpis thepth quantile ofF(x). Moreover, we show thatξˆpnis a strongly consistent estimator ofξpunder mild restrictions onF(x)in the neighborhood ofξp. We also show thatξˆpnconverges completely toξp.

[学科分类] 应用数学