Modified large sample confidence intervals for Poisson distributions: Ratio, weighted average, and product of means

Interval estimation procedures for the ratio of two Poisson means, weighted average of Poisson rates, and product of powers of Poisson means are considered. We propose a confidence interval (CI) based on the modified large sample (MLS) approach, and compare with the Cox CIs and the Wilson-score CIs. Our numerical studies indicate that the MLS CI is comparable with the Cox CI, and offers improvement in some cases. We also provide MLS CI for a weighted sum of Poisson means and compare with the available approximate CIs. The methods are illustrated using two examples.