A new prediction interval for binomial random variable based on inferential models

Abstract The prediction interval (PI) is useful to predict future observations based on the information available in a given sample and has many practical applications. The Score, Bayesian and Fiducial PIs are well-known existing methods. Recently, two PIs based on the inferential model (IM) have been established. However, they have either poor or conservative behavior of the coverage probability in some cases. In this paper, we propose a new PI from the randomized IM for the binomial random variable. Our non-randomized approximation has the better coverage probability and stability, which is confirmed by the simulation studies. Moreover, our ideas can be applied to other discrete populations.

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