关于定数截尾失效率参数比的最优置信区间(Ⅱ)——最优置信区间与UMAU置信区间的等价性

用UMAU置信区间对参数进行估计,这种方法是通过构造的区间包含“错误值的概率尽可能小”来刻画精度的。也就是说,当参数真值为θ,θ′与θ不等时,Pθ(θ(X)≤θ′≤θ(X))应尽可能的小。引用一种更富有直观性的刻画精度的方法来考虑区间长度,提出了具有一致最小平均长度的置信区间的概念。通过相关引理证明了两种区间的等价性。进一步完善了最优区间估计的理论,为定数截尾失效率参数比的最优置信区间估计提供了理论依据。

The Best Confidence Interval of Failure Rate Parameters Proportion on Censored Data(Ⅱ) : Equivalence of the Best Confidence Interval and UMAU Confidence Interval

The parameter being estimated by using UMAU confidence interval,this method can describe precision by making an interval,which includes the smaller probability of wrong value.That is to say,when the true value of parameter is θ and unequal with θ′,P_θ(θ(X)≤θ′≤θ(X)) should be small.The interval length was considered by a more direct method to describe precision,giving the conception of possessing uniformly minimum mean length confidence interval(the best confidence interval).The equivalence of two different confidence intervals was posed by some correlative knowledge.The theory of the best interval estimation is improved,which provides the theory base for application,such as studying about the best confidence interval estimation of failure rate parameters proportion on censored data.