In this paper, we discuss asymptotic infimum coverage probability (ICP) of eight widely used confidence intervals for proportions, including the Agresti–Coull (A–C) interval (Am Stat 52:119–126, <CitationRef CitationID="CR2">1998</CitationRef>) and the Clopper–Pearson (C–P) interval (Biometrika 26:404–413, <CitationRef CitationID="CR5">1934</CitationRef>). For the A–C...</citationref></citationref>