Introduction and Historical Remarks

N. Balakrishnan and William W. S. Chen
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N. Balakrishnan: McMaster University, Department of Mathematics and Statistics
William W. S. Chen: Internal Revenue Service

Chapter 1 in Handbook of Tables for Order Statistics from Lognormal Distributions with Applications, 1999, pp 1-4 from Springer

Abstract: 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.

Keywords: Order Statistic; Shape Parameter; Lognormal Distribution; High Order Moment; Standard Normal Variable (search for similar items in EconPapers)
Date: 1999
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DOI: 10.1007/978-1-4615-5309-0_1

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