More on Shortest and Equal Tails Confidence Intervals

Abstract

An interesting topic in mathematical statistics is that of constructing confidence intervals. Two types of intervals, both based on the method of pivotal quantity, are available: the Shortest Confidence Interval (SCI) and the Equal Tails Confidence Interval (ETCI). The aims of this article are: (i) to clarify and comment on methods of finding such intervals; (ii) to investigate the relationship between these types of intervals; (iii) to point out that confidence intervals with the shortest length do not always exist, even when the distribution of the pivotal quantity is symmetric; and finally, (iv) to give similar results when the Bayesian approach is used.

Keywords:

• Bayes
• Credible set
• Monotonicity
• Pivotal quantity
• Unimodal

Mathematics Subject Classification:

• 62F25
• 62F15

Acknowledgment

The authors wish to thank Professor Takis Papaioannou and the anonymous referee for their helpful comments and suggestions on an earlier draft of this article.