Non-Parametric Estimation. I. Validation of Order Statistics

Previous work on non-parametric estimation has concerned three problems: (i) confidence intervals for an unknown quantile, (ii) population tolerance limits, (iii) confidence bands of an unknown cumulative distribution function (cdf). For problem (iii) a solution has been available which is valid for any cdf whatever, but for (i) and (ii) it has heretofore assumed that the population has continuous probability density. This paper validates the existing solutions of (i) and (ii) assuming only a continuous cdf. It then modifies these solutions so that they are valid for any cdf whatever.