位置刻度分布族中参数的两步置信区间(英文)

Two-stage Approach to Fixed-width Confidence Intervals for the Parameters in Location and Scale Family of Distributions

寻找一些分布中的参数的具有预先给定宽度和预先给定覆盖概率的置信区间是令人感兴趣的.对于位置刻度分布族中位置参数和刻度参数,这种类型的置信区间的存在性问题已在文献中被解决.本文利用两步抽样,具体地构造出这样的固定宽度置信区间.此外,对于Cauchy分布,第一阶段的最优抽样量和一些统计量的分位点也被计算出.所得到的结果具有应用价值.

Finding confidence intervals with prescribed width and prescribed coverage probability for some parameters in distributions is of great interest. The existence of the intervals of this type for the location parameter μ, and scale parameter σ of the family of location and scale F((x-μ)/σ) has been solved in literatures. This paper concretely constructs fixed-width confidence intervals for these parameters by two-stage procedures. Further, for Cauchy distribntion, the optimal sample size of the first stage and the quantiles of some statistics' are also proposed by numerical computations. The results obtained have values of application.