Comparison of Frequentist Methods for Estimating the Total Weight of Consignments of Drugs

A topic in forensic statistics is the estimation of the total weight of consignments of drugs based on subsamples of which a certain fraction may not contain drugs at all. The frequentist approach to this concentrates on obtaining confidence intervals for the total weight, based on estimation of the fraction of drugs and the mean and variance of the weights of drug units. The current study shows that the resulting confidence intervals are basically unreliable, since they are based on an underestimation of the variation of the underlying statistical process. Two alternatives are given that yield asymptotically correct results. These are not reliable for small subsamples either, though, because of the inherent multimodal behaviour of the sample mean. In cases where a relatively large fraction of the consignment contains no drugs, the confidence intervals reported in the literature should not be used in practice.