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The lognormal distribution, environmental data, and radiological monitoring

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Abstract

The lognormal distribution has become a common choice to represent intrinsically positive and often highly skewed environmental data in statistical analysis. However the implications of its use are often not carefully considered. With an emphasis on radiological monitoring applications, this paper reviews what assuming lognormality means in terms of data analysis and interpretation. The relationship of using normal theory methods on log transformed data to multiplicative errors and hypothesis testing in the original scale is also discussed.

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References

  • Aitchison J., and Brown J. A. C.: 1957, The Lognormal Distribution with Special Reference to Its Use in Economics, Cambridge: Cambridge University Press.

    Google Scholar 

  • Bernarie, M. M.: 1971, ‘The Validity of the Log-normal Distribution of Pollutant Concentrations’, Paper SU-18D, Proceedings of the 2nd International Clean Air Conference (CE-Trans-7589).

  • Blackwood L. G.: 1991, ‘The Quality of Mean and Variance Estimates for Normal and Lognormal Data when the Underlying Distribution is misspecified’, Journal of Chemometrics, 5, 263–271.

    Google Scholar 

  • Crow E. L.: 1988, ‘Applications in Atmospheric Sciences’, Chapter 13 in Lognormal Distributions: Theory and Applications, (E. L.Crow and K.Shimizu, eds.), New York: Marcel Dekker, Inc.

    Google Scholar 

  • Crow E. L., and Shimizu K. (eds.): 1988, Lognormal Distributions: Theory and Applications, New York: Marcel Dekker, Inc.

    Google Scholar 

  • Dennis B. and Patil G. P.: 1988, ‘Applications in Ecology’, Chapter 12 in Lognormal Distributions: Theory and Applications, (E. L.Crow and K.Shimizu, eds.), New York: Marcel Dekker, Inc.

    Google Scholar 

  • Eberhardt, L. L., and Gilbert, R. O.: 1973, ‘Gamma and Lognormal Distributions as Models in Studying Food-Chain Kinetics’, Battelle, Pacific Northwest Laboratories, BNWL-1747.

  • Eberhardt, L. L., and Gilbert, R. O.: 1980, ‘Statistics and Sampling in Transuranic Studies’, in Transuranic Elements in the Environment (W. C. Hanson, ed.), DOE/TIC-22800 NTIS, pp. 173–186.

  • Erron B.: 1982, The Jackknife, the Bootstrap, and Other Resampling Plans, Philadelphia: Society for Industrial and Applied Mathematics.

    Google Scholar 

  • Finney D. J.: 1941, ‘On the Distribution of a Variate whose Logarithm is Normally Distributed’, Journal of the Royal Statistical Society, Supplement 7, 155–161.

    Google Scholar 

  • Georgopoulos P. G., and Seinfeld J. H.: 1982, ‘Statistical Distributions of Air Quality Concentrations’, Environmental Science and Technology 16, 401–416A.

    Google Scholar 

  • Gilbert R. O.: 1987, Statistical Methods for Environmental Pollution Monitoring, New York: Van Nostrand Reinhold Co.

    Google Scholar 

  • Gilliom R. J., and Helsel D. R.: 1986, ‘Estimation of Distributional Parameters for Censored Trace Level Water Quality Data. 1. Estimation Techniques’, Water Resources Research 22, 147–155.

    Google Scholar 

  • Johnson, T. R., and Symons, M. J.: 1980, ‘Extreme Values of Weibull and Lognormal Distributions Fitted to Ambient Air Quality Data’, presented at the 73rd Annual Meeting of the Air Pollution Control Association, Montreal, Quebec.

  • Koch G. S., and Link R. F.: 1981, Statistical Analysis of Geological Data, New York: Dover.

    Google Scholar 

  • Land C. E.: 1971, ‘Confidence Intervals for Linear Functions of the Normal Mean and Variance’, Annals of Mathematic Statistics 42, 1187–1205.

    PubMed  Google Scholar 

  • Land C. E.: 1972, ‘An Evaluation of Approximate Confidence Interval Estimation Methods for Lognormal Means’, Technometrics 14, 145–158.

    Google Scholar 

  • Land C. E.: 1988, ‘Hypothesis Tests and Interval Estimates’, Chapter 3 in Lognormal Distributions: Thoery and Applications, (E. L.Crow and K.Shimizu, eds.), New York: Marcel Dekker, Inc.

    Google Scholar 

  • Naus J. I.: 1969, ‘The Distribution of the Logarithm of the Sum of Two Lognormal Variates’, Journal of the American Statistical Association 64, 655–659.

    Google Scholar 

  • Shaban S. A.: 1981, ‘On the Estimation of the Ratio of Means and Other Characteristics of Two Log Normal Variates’, Biometrical Journal 23, 357–369.

    Google Scholar 

  • Shih W. J., and Binkowitz B.: 1987, ‘Median versus Geometric Mean for Lognormal Samples’, Journal of Statistical Computation and Simulation 28, 81–83.

    Google Scholar 

  • Shimizu K.: 1988, ‘Point Estimation’, Chapter 2 in Lognormal Distributions: Theory and Applications, (E. L.Crow and K.Shimizu, eds.), New York: Marcel Dekker, Inc.

    Google Scholar 

  • Shimizu K., and Crow E. L.: 1988, ‘History, Genesis, and Properties’, Chapter 1 in Lognormal Distributions: Theory and Applications, (E. L.Crow and K.Shimizu, eds.), New York: Marcel Dekker, Inc.

    Google Scholar 

  • Speer, D. R., and Waite, D. A.: 1975, ‘Statistical Distributions as Applied to Environmental Surveillance Data’, Battelle, Pacific Northwest Laboratories, BNWL-SA-5482.

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Work performed under the auspices of the U.S. Department of Energy, DOE Contract No. DE-AC-07-76ID01570.

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Blackwood, L.G. The lognormal distribution, environmental data, and radiological monitoring. Environ Monit Assess 21, 193–210 (1992). https://doi.org/10.1007/BF00399687

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