Acceptance Regions and Their Application in Lifetime Estimation

Abstract

In the first part of this paper, a general method is proposed for determining confidence bounds based on so-called acceptance regions. This method can be applied, if the observed random variables are discrete and may-adopt at most a finite number of realizations.

This concept has the following advantages:

• Contrary to asymptotic confidence bounds, the inclusion probability of the confidence bounds based on acceptance regions is never less than the given confidence level.

• The confidence bounds based on acceptance regions may be determined in a way that they are optimal with respect to any quality indicator which may be chosen out of a large class of quality indicators including, e.g., all convex combinations of the realizations of the confidence bounds.

The second part of this paper is an application of this concept to a problem of lifetime estimation, namely the determination of a lower confidence bound for the expectation of a Weibull distribution based on a left- and right-censored sample.