Modified frequentist determination of confidence intervals for Poisson distribution

We propose modified frequentist definitions for the determination of confidence intervals for the case of Poisson statistics. We require that 1-β^{'} \geq \sum_{n=o}^{n_{obs}+k} P(n|λ) \geq α^{'}. We show that this definition is equivalent to the Bayesian method with prior π(λ) \sim λ^{k}. Other generalizations are also considered. In particular, we propose modified symmetric frequentist definition which corresponds to the Bayes approach with the prior function π(λ) \sim 1/2(1 + \frac{n_{obs}}λ). Modified frequentist definitions for the case of nonzero background are proposed.

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