Maximum likelihood estimation with poisson (counting) statistics for waste drum inspection

摘要

This note provides a preliminary look at the issues involved in waste drum inspection when emission levels are so low that central limit theorem arguments do not apply and counting statistics, rather than the usual Gaussian assumption, must be considered. At very high count rates the assumption of Gaussian statistics is reasonable, and the maximum likelihood arguments that we discuss below for low count rates would lead to the usual approach of least squares fits. Least squares is not the the best technique for low counts, and we will develop the maximum likelihood estimators for the low count case.