Statistical Intervals, 2nd Edition

Chapter 12 Likelihood-Based Statistical Intervals

Objectives and Overview

Previous chapters dealt with statistical intervals for complete samples (i.e., no censoring or truncation) from common statistical distributions, focusing on the normal distribution (Chapters 3 and 4), the binomial distribution (Chapter 6), and the Poisson distribution (Chapter 7). In addition, Chapter 5 provided methods for constructing distribution-free intervals. This chapter and subsequent chapters describe and illustrate more general methods for constructing statistical intervals that can be applied to many other distributions and to more complicated models and types of data.

The following topics are discussed in this chapter:

• The motivation for likelihood-based inference and model selection (Sections 12.1).
• The construction of a likelihood function and maximum likelihood (ML) estimation for a parametric model for different types of data (Section 12.2).
• Likelihood-based confidence intervals for a single-parameter distribution, illustrated by the exponential distribution (Section 12.3).
• Likelihood and ML estimators for location-scale and log-location-scale distributions, illustrated by the lognormal and Weibull distributions (Section 12.4).
• Likelihood-based confidence intervals for location-scale and log-location-scale distributions, illustrated by the lognormal and Weibull distributions (Section 12.5).
• Confidence intervals based on computationally simpler Wald approximations of the likelihood-based ...