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COMPARISON OF INTERVAL ESTIMATION METHODS FOR A BINOMIAL PROPORTION
We compare different confidence and credible intervals for the probability of success in a binomial model with respect to the coverage probability and expected length. The comparison is motivated by the similarity of a confidence interval proposed by Agresti and Coull (The American Statistician, 1998) and a Bayesian credible interval based on a Beta(2,2) prior distribution. Keeping in mind that confidence intervals are random and that credible intervals are numeric, we perform the comparison under the same paradigm, considering the Bayesian intervals (central and HPD) as realizations of random intervals or the latter as numeric intervals. The intervals are compared via simulation studies that show a better performance of the Wilson (score) and HPD intervals with uniform prior distribution and some advantages of Bayesian intervals with respect to the expected and posterior length.
Binomial distribution, coverage probability, expected length, Highest posterior density (HPD) intervals.
Tuany Paula Castro, Julio Motta Singer, Carlos Daniel Paulino