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