An easy to use method to approximate Poisson confidence limits

Despite the ever larger choice of softwares and statistical packages allowing fast and accurate computation of binomial and Poisson confidence limits, there is always a need for a simple and reliable formula allowing non-computerized computations. The method proposed in this paper is derived from the Freeman and Tukey's variance stabilizing transformation for a random Poisson variable and adjusted for giving the best fit with the exact Poisson values. Despite its simplicity, allowing its use in any circumstances, this method provides very satisfactory results and a much better fit than classical formula based on the normal approximation, even if a continuity correction is used. It allows computation of Poisson confidence limits both for count or rates and proportions.