Variances and covariances underlying loading estimates and part-whole relationships

The effluent limit guidelines are usually based on loading estimates of chemicals discharged into the environment. The loading estimates, calculated as the product of flow times concentration, have underlying mathematical relationships in terms of variances and covariances. These relationships are presented by using the moment generating function technique. Estimators of loading means are compared. Cramer-Rao bounds for the variances of unbiased estimators of the loading means are presented. Mathematical details underlying several part-whole and ratio estimators are also presented. An understanding of these relationships should provide unbiased estimates of loading means, variances and covariances.