Statistical Intervals, 2nd Edition

Appendix E Pivotal Methods for Constructing Parametric Statistical Intervals

Introduction

This appendix outlines some of the most useful methods for defining particular statistical interval procedures. In particular, we present pivotal quantities that lead to well-known interval procedures for the normal distribution. We also present pivotal quantities for the more general location-scale distributions and indicate how methods for location-scale distributions can usually be applied directly to log-location-scale distributions and, in an approximate manner, to obtain statistical intervals and bounds for other parametric distributions or when the data are censored.

The topics discussed in this appendix are:

• Pivotal quantities and their use to construct confidence intervals (Section E.1).
• Examples of normal distribution pivotal quantities (Section E.2).
• How to obtain confidence intervals for the mean, the standard deviation, quantiles, and tail probabilities of a normal distribution using pivotal quantities (Section E.3).
• Examples of pivotal methods to construct confidence intervals to compare means and sample variances for data coming from two normal distributions (Section E.4).
• The use of pivotal quantities to obtain tolerance intervals for normally distributed data (Section E.5).
• Examples of pivotal methods to construct prediction intervals to predict the mean or the sample standard deviation for data coming from a normal distribution. Also, examples of pivotal methods to construct ...