NORMAL Distribution: Origin of the name

The NORMAL distribution has been studied under various names for nearly 300 years. Some names were derived from ERROR, e.g. the law of error, the law of facility of errors and the law of frequency of errors. Some were derived from persons associated with the distribution, e.g. Laplaceís second law and the GAUSSIAN law. Stigler remarks in his "Stiglerís law of eponymy" (see EPONYMY) that as the distribution has never been called after Abraham De Moivre, who worked on it in 1733, we may conclude that he was its originator. (See also Symbols Associated with the Normal Distribution on the Symbols in Probability and Statistics page.)

According to Kruskal & Stigler, the term normal was used, apparently independently, by Charles S. Peirce (1873) in an appendix to a report of the US Coast Survey (reprinted in Stigler (1980, vol. 2), Wilhelm Lexis Theorie der Massenerscheinungen in der menschlichen Gesellschaft (1877) and Francis Galton 'Typical laws of heredity' (1877).

Of the three, Galton had most influence on the development of Statistics in Britain and, through his Ďdescendantsí Karl Pearson and R. A. Fisher, on Statistics worldwide. In the 1877 article Galton used the phrase "deviated normally" only once (p. 513)--his name for the distribution was "the law of deviation." However in the 1880s he began using the term "normal" systematically: chapter 5 of his Natural Inheritance (1889) is entitled "Normal Variability" and Galton refers to the "normal curve of distributions" or simply the "normal curve." Galton does not explain why he uses the term "normal" but the sense of conforming to a norm ( = "A standard, model, pattern, type." (OED)) seems implied.

Karl Pearson wrote, in his "Contributions to the Mathematical Theory of Evolution," Philosophical Transactions of the Royal Society of London. A, 185, (1894) p. 72, "A frequency-curve, which for practical purposes, can be represented by the error curve, will for the remainder of this paper be termed a normal curve." Later Pearson seemed to imply that he had introduced the term: "Many years ago I called the Laplace-Gaussian curve the normal curve ..." (Biometrika, 13, (1920), p. 25). While Pearson did not introduce the term, it is fair to say that his "consistent and exclusive use of this term in his epoch-making publications led to its adoption throughout the statistical community." (DSB) Curiously a main theme in Pearsonís scientific work was that data did not Ďnormallyí follow this distribution and that alternative distributions had to be devised. (See the entry on Pearson curves.)

Once the basic normal terminology was adopted NORMAL appeared in many expressions. These must have seemed more or less obvious to their creators and were probably re-invented many times.

Normal correlation appears in W. F. Sheppard, "On the application of the theory of error to cases of normal distribution and normal correlation," Phil. Trans. A, 192, (1899) page 101, and Proc. Roy. Soc. 62, page 170 (1898) [James A. Landau].

Normal curve appears in Galtonís Natural Inheritance (1889)--see above.

Normal distribution appears in Karl Pearsonís 1897 "Contributions to the Mathematical Theory of Evolution. II. Skew Variation in Homogeneous Material," Philosophical Transactions of the Royal Society of London. A, 186, (1895), pp. 343-414: "A random selection from a normal distribution" (OED2).

Normal deviate is found in 1925 in R. A. Fisher, Statistical Methods for Research Workers p. 47:  "Table I. shows that the normal deviate falls outside the range +/-1.598193 in 10 per cent of cases" (OED2).

Normal law is found in Francis Galtonís "Results Derived from the Natality Table of Korosi by Employing the Method of Contours or Isogens," Proceedings of the Royal Society, 55, (1894), p. 23 (JSTOR search).

Normal population appears in Karl Pearsonís "Contributions to the Mathematical Theory of Evolution," Philosophical Transactions of the Royal Society of London. A, 185. (1894), p. 104. [JSTOR search].

Normal sample is found in R. A. Fisher's The Goodness of Fit of Regression Formulae and the Distribution of Regression Coefficients. Journal of the Royal Statistical Society, 85, No. 4. (1922), p. 599 [JSTOR search]

Normal universe is found in W. A. Shewhart & F. W. Winters "Small Samples--New Experimental Results" Journal of the American Statistical Association, 23, (Jun., 1928), p. 145. [JSTOR search].

Normal variate was in wide use in the 1930s and is found in Joseph Pepper's "Studies in the Theory of Sampling," Biometrika, 21, (1929), p. 239. [JSTOR search]

Normality appears in Karl Pearson "Contributions to the Mathematical Theory of Evolution. II. Skew Variation in Homogeneous Material," Philosophical Transactions of the Royal Society of London. A, 186, (1895), p. 386. [JSTOR search]

(This entry was contributed by John Aldrich drawing on Kruskal & Stigler "Normative Terminology" in Stigler (1999), Hald (1998, p. 356) and Walker (p. 185).

Reference: http://members.aol.com/jeff570/n.html )