Abstract
Several characteristics of confidence intervals for a binomial parameter are considered. In particular confidence intervals when zero success is observed are of our interest. There have been proposed two constructing methods for such cases, which seems to be troublesome. In order to resolve the confict we examine the methods from the viewpoint of coverage probabilities of the central and shortest confidence intervals. After a brief review of several constructing methods of confidence intervals, a simple iterative procedure to find the shortest interval is introduced. Then, in terms of actual coverage probabilities, we examine the properties of several intervals. Some guidelines for selecting appropriate interval are provided.
