# Chapter 5 Distribution-Free Statistical Intervals

## Objectives and Overview

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, such as the normal distribution used in Chapters 3 and 4, for their construction. Moreover, as implied by the term distribution-free, the statistical properties of these procedures, such as their coverage probabilities, do not depend on the underlying distribution. This is in contrast to nonparametric methods, such as those presented in some subsequent chapters, whose construction does not depend on the underlying distribution, but whose statistical properties do. The subtle difference between distribution-free and nonparametric procedures is discussed further at the beginning of Chapter 11. In either case, the important assumption that sampling is random from the population (or process) of interest, and, more generally, the assumptions discussed in Chapter 1, still pertain.

The topics discussed in this chapter are distribution-free:

• Confidence intervals for a distribution quantile, such as the median (Section 5.2).
• Tolerance intervals to contain at least a specified proportion of a distribution (Section 5.3).
• Prediction intervals to contain a specified ordered observation in a future sample (Section 5.4).
• Prediction intervals to contain at least ...

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