Distribution‐Free Statistical Intervals
William Q. Meeker, Gerald J. Hahn, Luis Alberto Escobar · Wiley series in probability and statistics · 2017
This chapter shows how to calculate "distribution-free" two-sided statistical intervals and one-sided statistical bounds. Such intervals and bounds, which are based on order statistics, do not require the assumption of a particular underlying distribution. The topics discussed in the chapter are distribution-free: confidence intervals for a distribution quantile, tolerance intervals to contain at least a specified proportion of a distribution, and prediction intervals to contain a specified ordered observation in a future sample. The chapter outlines the basic notation that is used in calculating the distribution-free intervals and bounds. The notation pertains to probability distributions that relate to dichotomous outcomes—that is, populations that contain units that belong to one category or another. The chapter also shows how to obtain distribution-free two-sided confidence intervals and one-sided confidence bounds for a distribution quantile. It provides some initial comments about coverage probabilities, and presents methods and examples showing how to calculate such intervals and bounds.