Bayesian and Non-Bayesian Interval Estimators for the Poisson Mean

Abstract

Seventeen different confidence intervals for the Poisson mean are compared using simulations and a real data application. The interval estimators include the Wald interval estimator, the score interval estimator, the exact interval estimator, the bootstrap interval estimator, the equal tails credible interval estimator, Jeffreys prior credible interval estimator, the HPD credible interval estimator and the relative surprise credible interval estimator. Recommendations for choosing among the seventeen intervals are given for different sample sizes and different Poisson means.

Keywords

• coverage length
• coverage probability
• Poisson distribution