Modified frequentist determination of confidence intervals for poisson distribution

We propose modified frequentist definition for the determination of confidence intervals for the case of Poisson statistics. Namely, we require that $1-{\beta }^{\prime }⩾{\sum }_{n=0}^{n=n_{obs}+k}P\left(n|\lambda \right)⩾{\alpha }^{\prime }$. We show that this definition is equivalent to the Bayesian method with prior π(λ) ∼ λ^k. We also propose modified frequentist definition for the case of nonzero background.