The New Palgrave Dictionary of Economics

Living Edition
| Editors: Palgrave Macmillan

Lognormal Distribution

  • P. E. Hart
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DOI: https://doi.org/10.1057/978-1-349-95121-5_1089-2
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Abstract

If there is a number, ϴ, such that Y = loge(X – ϴ) is normally distributed, the distribution of X is lognormal. The important special case of ϴ = 0 gives the two parameter lognormal distribution, X ~ Λ(μ, σ 2) with Y ~ N(μ, σ 2), where μ and σ 2 denote the mean and variance of loge X. The classic work on the subject is by Aitchison and Brown (1957). A useful survey is provided by Johnson et al. (1994, ch. 14). They also summarize the history of this distribution: the pioneer contributions by Galton (1879) on its genesis, and by McAlister (1879) on its measures of location and dispersion, were followed by Kapteyn (1903), who studied its genesis in more detail and also devised an analogue machine to generate it. Gibrat’s (1931) study of economic size distributions was a most important development because of his law of proportionate effect. Since then there has been an immense number of applications of the lognormal distribution in the natural, behavioural and social sciences.

Keywords

Central limit theorems Gibrat’s Law Lognormal distribution 

JEL Classifications

C1 
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Bibliography

  1. Aitchison, J., and J.A.C. Brown. 1957. The lognormal distribution. Cambridge: Cambridge University Press.Google Scholar
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  7. Kapteyn, J.C. 1903. Skew frequency curves in biology and statistics. Astronomical Laboratory, Groningen: Noordhoff.Google Scholar
  8. McAlister, D. 1879. The law of the geometric mean. Proceedings of the Royal Society of London 29: 367–375.CrossRefGoogle Scholar

Copyright information

© The Author(s) 2008

Authors and Affiliations

  • P. E. Hart
    • 1
  1. 1.