Abstract
A LARGE part of statistical theory is based on the assumption that measurements are distributed in normal probability curves and that the variance is constant. The normal curve was discovered by de Moivre in 1753 and developed as a useful mathematical tool by Laplace, Gauss, Maxwell and others. It has a number of interesting properties, and various attempts were once made to establish a law of Nature known as the ‘normal law of errors’, which implied that measurements ought always to be distributed in this way. These attempts were undeservedly successful. The use of the adjective ‘normal’ in connexion with this law implies more than is justified by the facts, whereas in fact the adjective is established by custom and provides a convenient label for distributions of this type.
This is a preview of subscription content, access via your institution
Access options
Subscribe to this journal
Receive 51 print issues and online access
$199.00 per year
only $3.90 per issue
Buy this article
- Purchase on SpringerLink
- Instant access to full article PDF
Prices may be subject to local taxes which are calculated during checkout
Similar content being viewed by others
References
Poincaré, H. (1892), quoted from Mellor, J. W., "Higher Mathematics for Students of Chemistry and Physics" (Longmans, Green and Co., 1922).
Cramér, H., "Random Variables and Probability Distributions", Cambridge Tract. Math., 36 (1937).
Bagnold, R. A., "The Physics of Blown Sand and Desert Dunes" (London: Methuen, 1941).
Kapteyn, J. C., "Skew Frequency Curves in Biology and Statistics" (Groningen: Noordhoff, 1903).
Kapteyn, J. C., Rec Trav. Bot. Neerland, 13, 105 (1916).
Curtiss, J. H., Ann. Math. Statist., 14, 107 (1943).
Fisher, R. A., and Yates, F., "Statistical Tables" (Edinburgh:Oliver and Boyd., 1938).
Gaddum, J. H., Med. Res. Coun. Spec. Rep., 183 (1933).
Irwin, J. O., J. Roy. Stat. Soc., Suppl. 4, 1 (1937).
Bliss, C. I., Quart. J. Pharm., 11, 192 (1938).
Ferguson, G. A., Psychometrika, 7, 19 (1942).
Finney, D. J., Psychometrika, 9, 31 (1944).
Galton, F., Proc. Roy. Soc, 29, 365 (1879).
Williams, C. B., Ann. Appl. Biol., 24, 404 (1937).
Williams, C. B., Trans. Roy. Entom. Soc. Lond., 90, 227 (1940).
Finney, D. J., J. Roy. Stat. Soc, Suppl. 7, 155 (1941).
Wightman, E. P., Trivelli, E. P. H., and Sheppard, S. E., J. Phys. Chem., 28, 529 (1924).
Bliss, C. I., and Cattell, M., Ann. Rev. Physiol., 5, 479 (1943)
Withell, E. R., J. Hyg., 42, 124 (1942).
Hemmingsen, A. M., Vidensk Medd. fra Dansk naturh. Foren., 98, 125 (1933).
Snedecor, G. W., "Statistical Methods" (Iowa State College Press, 1940).
Croxton, F. E., and Cowden, D. T., "Applied General Statistics" (New York:Prentice-Hall, 1939).
Brew, J. D., J. Dairy Sci., 12, 304 (1929).
Wechsler, D., "The Range of Human Capacities" (Baillière, Tindall and Cox., 1935).
Cooper, F. A., J. Soc Chem. Ind., 56, 447 T (1937).
Cochran, W. G., Empire J. Exp. Agric, 6, 157 (1938).
Williams, C. B., Biometrika, 31, 356 (1940).
Gaddum, J. H., Proc. Roy. Soc, B, 121, 598 (1937).
Fisher, Arne, "The Mathematical Theory of Probabilities" (The Macmillan Company, 1922).
Yuan, P. T., Ann. Math. Statist., 4, 30 (1933).
Nagelschmidt, G., Med. Res. Coun. Spec. Rep. 244 (1943).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
GADDUM, J. Lognormal Distributions. Nature 156, 463–466 (1945). https://doi.org/10.1038/156463a0
Issue date:
DOI: https://doi.org/10.1038/156463a0
This article is cited by
-
Mechanisms for log normal concentration distributions in the environment
Scientific Reports (2021)
-
A Simple Unsupervised Classification Workflow for Defining Geological Domains Using Multivariate Data
Mining, Metallurgy & Exploration (2021)
-
The scales of human mobility
Nature (2020)
-
Distribution of postpartum blood loss: modeling, estimation and application to clinical trials
Reproductive Health (2018)
-
Dripplons as localized and superfast ripples of water confined between graphene sheets
Nature Communications (2018)
