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,σ2) with Y ~ N(μ,σ2) where μ and σ2 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 and Kotz (1970). 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 and his law of proportionate effect is given in equation (1) below.
KeywordsLognormal Distribution Central Limit Theorem Analogue Machine Normal Curve Important Special Case
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