Confidence bands for the CDF when sampling from a finite population

We develop two methods for obtaining a confidence band for the cumulative distribution function (CDF) based on a simple random sample from a finite population of known size. The methods are exact when the population contains no repeated values, and conservative otherwise. The first method consists of using a Kolmogorov–Smirnov-type band, and the second method consists of combining together separate, equal-coverage-probability confidence intervals for each ordered population value. Confidence bands obtained using either method yield simultaneous confidence intervals for all ordered population values. Coverage probabilities are computed using a new recursive algorithm.