Abstract
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.
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References
AndersonT.W.: 1958, An Introduction to Multivariate Analysis, John Wiley, New York.
DolanD.M., YuiA.K., and GeistR.D.: 1981, ‘Evaluation of River Load Estimation Methods for Total Phosphorus’, J. Great Lakes Res. 7 (3), 207–214.
El-ShaarawiA.H., KuntzK.W., and SylvestreA.: 1985, ‘Estimation of Loading by Numerical Integration’, pp. 469–478 in. Development in Water Science. Statistical Aspects of Water Quality Monitoring. Vol. 27. Elsevier Science Pub., New York.
GoodmanL.A.: 1960, ‘On the Exact Variance of Products’, J. Am. Stat. Assoc. 55, 708–713.
E.P.A. Development Document for Effluent Limitations Guidelines and Standards for Organic Chemicals, Plastics and Synthetic Fibres. Point Source Category. Vols. 1 and 2. Oct. 1987. PB88-171335. National Technical Information Service. Springfield, VA 22161, U.S.A.
KendallM.G.: 1946, The Advanced Theory of Statistics, Vols. 1 and 2, Charles Griffin and Co., London.
LindgrenB.W.: 1976, Statistical Theory, Macmillan Publishing Co., Inc., New York.
MOE: MISA Effluent Monitoring Regulations for the Petroleum Refining Sector: 1988, Ontario Ministry of the Environment. Queen's Printer for Ontario, Toronto.
MoodA.M., GraybillF.A., and BoesD.C.: 1974, Introduction to the Theory of Statistics, McGraw-Hill, New York.
PearsonK.: 1897, ‘Mathematical Contributions to the Theory of Evolution.-On a Form of Spurious Correlation which may Arise when Indices are used in the Measurement of Organs’, Proc. Royal Soc. 60, 489–498.
PressS.J.: 1972, Applied Multivariate Analysis, Holt Rinehart and Winston Inc., New York.
SearleS.R.: 1969, ‘Correlation Between Means of Parts and Wholes’, Am. Stat. 4, 24.
SrivastavaM.S. and CarterE.M.: 1983, An Introduction to Applied Multivariate Statistics, North Holland, New York.
ThompsonM.E. and BischopingK.: 1985, ‘On the Estimation of Monthly Phosphorus Loadings’, pp. 460–468 in. Developments in Water Science. Statistical Aspects of Water Quality Monitoring. Vol. 27. Elsevier Science Pub., New York.
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Sharma, A., Selliah, J. Variances and covariances underlying loading estimates and part-whole relationships. Environ Monit Assess 23, 243–267 (1992). https://doi.org/10.1007/BF00406964
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DOI: https://doi.org/10.1007/BF00406964