On the Confidence Limits of Bernoulli Parameter in Any Sequential Case

设(xn,n≥1)是独立同分布的随机变量列，xn=0或1且P(xn=1)=p(n≥1),这里p是未知的.设τ是(xn，n≥1)的任何有限停止时间.对任何序贯样本(x1,x2,…,xτ)和γ∈(0,1)，本文给出了p的γ水平最优置信下限和最优置信上限，还讨论了一些有关的问题.Let x1,x2,… be independent identically distributed(i.i.d.) random variables,in which xn=0 or 1 and the probability of ｛xn=1｝ is p.Here p is unknown.Let τ be any finite stopping time for(xn,n1).For any sequential sample(x1,x2，…,xτ) and γ∈(0,1),we have given an optimal confidence limit of p with confidence level γ.Some related problems are also discussed.国家自然科学基金011-81