Modified Large Sample Inference for the Ratio of Two Poisson Means and for Estimating Weighted Average of Poisson Means

• Activity Number: 354
• Type: Contributed
• Date/Time: Tuesday, July 31, 2012 : 10:30 AM to 12:20 PM
• Sponsor: Section on Statistical Computing
• Author(s): Jie Peng*+ and Kalimuthu Krishnamoorthy
• Companies: St. Ambrose University and University of Louisiana at Lafayette
• Keywords: Cox'sapproach ; Fiducial approach ; Conditional score method ; Type I error rates ; Power ; F distribution

Abstract

The problem of testing or estimating the ratio of two Poisson means is considered. A new approach based on the modified large sample (MLS) method for estimating variance components is proposed. It has been shown that the likelihood-score test, moment test and the Wilson score test based on the conditional approach are identical, and the Cox confidence interval (CI) based on an F distribution can be obtained via the conditional approach. Tests based on the MLS method, Cox's approach and the conditional score method are compared with respect to type I error rates and powers. Our numerical studies indicate that the MLS CIs control the type I error rates better than other methods in some situations. CIs that are based on the tests are described. Furthermore, test and CI for a weighted average of Poisson means based on the MLS method are developed and compared with those based on the fiducial approach. The methods are illustrated using a few examples.