Upper and Lower Bound Distributions that Give Simultaneous Confidence Intervals for Quantiles
提出一种新方法，为未知分布的分位数构建参数置信区间，使得所有区间同时包含对应百分位数的联合概率至少为预设值，并可用于构造容差分布。
Abstract We propose a new method for constructing parametric confidence intervals for quantiles of an unknown distribution. These confidence intervals are constructed so that the joint probability that all intervals simultaneously contain their respective percentiles is at least a preset value. Thus we may also use the set of either upper or lower confidence limits to define an upper (or lower) bound distribution function, which we call an upper (or lower) tolerance distribution because this distribution may also be used to construct tolerance intervals for the unknown distribution. We derive tolerance distributions with exact coverage probability for iid samples from distributions in the location-scale family. Tolerance distributions can also be used for best- and worst-case analyses, as we illustrate by considering bounds on the distribution of the time interval between the onset of infectiousness and development of detectable antibody in individuals newly infected with the human immunodeficiency virus (HIV), the virus that causes acquired immune deficiency syndrome (AIDS).