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Introduction and Historical Remarks

In: Handbook of Tables for Order Statistics from Lognormal Distributions with Applications

Author

Listed:
  • N. Balakrishnan

    (McMaster University, Department of Mathematics and Statistics)

  • William W. S. Chen

    (Internal Revenue Service)

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.

Suggested Citation

  • N. Balakrishnan & William W. S. Chen, 1999. "Introduction and Historical Remarks," Springer Books, in: Handbook of Tables for Order Statistics from Lognormal Distributions with Applications, chapter 1, pages 1-4, Springer.
    • Handle: RePEc:spr:sprchp:978-1-4615-5309-0_1
    DOI: 10.1007/978-1-4615-5309-0_1
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