A Simple Measure of the Efficiency of a Buehler Confidence Limit

ABSTRACT

The Buehler 1 − α upper confidence limit for a scalar parameter θ is as small as possible, subject to the constraints that (a) its coverage probability never falls below 1 − α and (b) it is a non decreasing function of a pre-specified designated statistic T. This confidence limit finds important applications in the analysis of discrete data arising in, among others, the fields of reliability, epidemiology, finance, dose-response analysis, and the pharmaceutical industry. The efficiency of the Buehler 1 − α limit depends greatly on T. We present an easy-to-compute, single-number measure of the inefficiency of this Buehler limit. We also derive the large sample properties of a relative inefficiency measure when T is an approximate 1 − γ upper limit where . A numerical example, illustrating the application of these large sample properties, is also presented.

Key Words:

• Confidence limit
• Discrete data
• Reliability