Prior-free probabilistic interval estimation for binomial proportion

The interval estimation of a binomial proportion has been one of the most important problems in statistical inference. The modified Wilson interval, Agresti-Coull interval, and modified Jeffreys interval have good coverage probabilities among the existing methods. However, as approximation approaches, they still behave poorly under some circumstances. In this paper, we propose an exact and efficient randomized plausible interval based on the inference model and suggest the practical use of its non-randomized approximation. The randomized plausible interval is proven to have the exact coverage probability. Moreover, our non-randomized approximation is competitive with the existing approaches confirmed by the simulation studies. Three examples including a real data analysis are illustrated to portray the usefulness of our method.