Comparison of Confidence Intervals for a Poisson Mean – Further Considerations

Abstract

I make recommendations in choosing a confidence interval for the Poisson mean, from twelve different methods, that are based on four general principles: actual coverage should closely match the nominal coverage; narrower expected widths of confidence intervals are better; the right and left non-coverage should be fairly balanced; and some investigators may prefer closed-form intervals. The interval chosen depends on the relative importance the investigator places on each of these principles. The confidence intervals are examined through graphs of their coverage probability, interval widths and shapes.

Keywords:

• Confidence interval
• Coverage probability
• Discrete data
• Expected length
• Expected shape
• Poisson mean

Mathematics Subject Classification:

• Primary 62F25