Is the highest density interval the shortest confidence interval?

Mohammadpour, Adel; Kazemzadeh Gharechopogh, Hossein

doi:10.22060/ajmc.2025.23615.1273

Is the highest density interval the shortest confidence interval?

Articles in Press

Document Type : Short Contribution

Authors

Adel Mohammadpour

Hossein Kazemzadeh Gharechopogh

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