Confidence interval of mean is often used when quoting statistics. The same rigor is often missing when quoting percentiles and tolerance or percentile intervals. This article derives the expression for confidence in percentiles of a sample population. Confidence intervals of median is compared to those of mean for a few sample distributions. The concept of assurance from reliability engineering is then extended to percentiles. The assurance level of sorted samples simply matches the confidence and percentile levels. Numerical method to compute assurance using Brent's optimization method is provided as an open-source python package.

翻译：在引用统计数据时，通常使用均值的置信区间。然而，在引用百分位数以及容差或百分位数区间时，往往缺乏同样的严谨性。本文推导了样本总体百分位数置信度的表达式，并通过若干样本分布比较了中位数置信区间与均值置信区间的差异。随后，将可靠性工程中的"保证度"概念扩展到百分位数领域。排序样本的保证水平简单地与置信度和百分位数水平相匹配。最后提供了基于Brent优化方法计算保证度的数值方法，并以开源Python软件包形式发布。