A basic statistical problem: Confidence interval for the Bernoulli parameter (Q1072294)

This paper summarizes and compares in a unified way 11 different methods (obtained through Neyman, Bayesian or fiducial approach) proposed in the literature for setting confidence intervals (CI) for the parameter \(\pi\in [0,1]\) of the Bernoulli distribution based on a random sample \(X_ 1,...,X_ n\) from this distribution, i.e., \(P(X_ i=1)=\pi =1- P(X_ i=0)\), \(1\leq i\leq n\). Based on this comparison, a practical procedure for obtaining a CI for \(\pi\) is proposed.