Small-sample interval estimation of Bernoulli and Poisson parameters

To find an interval estimate for the parameter of the Bernoulli or the Poisson distribution usually requires the sample size to be large so that the normal approximation may be used. Small-sample intervals have been proposed earlier, but the procedures have required tables and are inexact. In this note we give a simple procedure for finding a small-sample confidence interval with minimum interval width. We also give a geometric interpretation to the minimization problem.