  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.
