Shortest Confidence Intervals for Families of Distributions Involving Truncation Parameters

Abstract

Statistical inferences for probability distributions involving truncation parameters have received recent attention in the literature. One aspect of these inferences is the question of shortest confidence intervals for parameters or parametric functions of these models. The topic is a classical one, and the approach follows the usual theory. In all literature treatments the authors consider specific models and derive confidence intervals (not necessarily shortest). All of these models can, however, be considered as special cases of a more general one. The use of this model enables one to obtain easily shortest confidence intervals and unify the different approaches. In addition, it provides a useful technique for classroom presentation of the topic.

Key Words:

• One-parameter family of densities
• Pivotal quantity method
• Two-parameter family of densities