Optimal confidence intervals for the geometric parameter

Abstract

This article discusses optimal confidence estimation for the geometric parameter and shows how different criteria can be used for evaluating confidence sets within the framework of tail functions theory. The confidence interval obtained using a particular tail function is studied and shown to outperform others, in the sense of having smaller width or expected width under a specified weight function. It is also shown that it may not be possible to find the most powerful test regarding the parameter using the Neyman-Pearson lemma. The theory is illustrated by application to a fecundability study.