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 ...