AUT Journal of Mathematics and Computing

AUT Journal of Mathematics and Computing

Is the highest density interval the shortest confidence interval?

Articles in Press

Document Type : Short Contribution

Authors
Adel Mohammadpour
Hossain Kazemzadeh
Department of Mathematics and Computer Science, Amirkabir University of Technology (Tehran Polytechnic), Iran
10.22060/ajmc.2025.23615.1273
Abstract
The highest posterior density credible interval, known as the highest density interval, is the shortest interval for any continuous unimodal posterior distribution. However, this unique property, does not hold in the frequentist setting. In this note, we unveil the necessary and sufficient conditions under which a highest density interval is also the shortest confidence interval within the scale-exponential family of distributions.
Keywords
Shortest confidence intervals
Highest posterior density
Highest density interval
Scale-exponential family
Subjects
AUT Journal of Mathematics and Computing

Articles in Press, Accepted Manuscript
Available Online from 28 June 2026