Introduction and Historical Remarks

Abstract

More than a century ago, Galton (1879) pointed out that if X ₁,X ₂,…, X _n are independent positive random variables, and then logT _n =, when appropriately standardized for mean and variance, will tend to a standard normal variable as n → ∞. Then, the limiting distribution of the variable T _n would then be lognormal. In a follow-up article, McAlister (1879) derived expressions for the mean, median, mode, variance and some percentiles of the log-normal distribution. Kapteyn (1903) and Kapteyn and van Uven (1916) displayed the use of the lognormal distribution in biological problems and also presented a graphical method for estimation the parameters of the distribution using sample quantiles. While Wicksell (1917) obtained formulas for higher order moments, van Uven (1917a,b) discussed transformations to normality from a more general point of view.