Win-probabilities for comparing two Poisson variables

ABSTRACT

This article considers the problem of choosing between two possible treatments which are each modeled with a Poisson distribution. Win-probabilities are defined as the probabilities that a single potential future observation from one of the treatments will be better than, or at least as good as, a potential future observation from the other treatment. Using historical data from the two treatments, it is shown how estimates and confidence intervals can be constructed for the win-probabilities. Extensions to situations with three or more treatments are also discussed. Some examples and illustrations are provided, and the relationship between this methodology and standard inference procedures on the Poisson parameters is discussed.

Keywords:

• Confidence intervals
• Gamma distribution
• Normal approximation
• Poisson distribution
• Poisson process
• Two-sample problem
• Win-probabilities.

MATHEMATICS SUBJECT CLASSIFICATION:

• Primary 62E15; Secondary 62N05

Acknowledgment

I would like to sincerely thank the reviewer for the helpful and insightful comments and suggestions that have resulted in a much improved version of this manuscript.