Improved confidence intervals when the sample is counted an integer times longer than the blank

Abstract

Past computer solutions for confidence intervals in paired counting are extended to the case where the ratio of the sample count time to the blank count time is taken to be an integer, IRR. Previously, confidence intervals have been named Neyman-Pearson confidence intervals; more correctly they should have been named Neyman confidence intervals or simply confidence intervals. The technique utilized mimics a technique used by Pearson and Hartley to tabulate confidence intervals for the expected value of the discrete Poisson and Binomial distributions. The blank count and the contribution of the sample to the gross count are assumed to be Poisson distributed. The expected value of the blank count, in the sample count time, is assumed known. The net count, OC, is taken to be the gross count minus the product of IRR with the blank count. The probability density function (PDF) for the net count can be determined in a straightforward manner.