**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. *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 **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

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 Galton’s Natural
Inheritance (1889)--see above.

*Normal distribution* appears in Karl Pearson’s 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: "

*Normal law* is found in Francis Galton’s
"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 Pearson’s "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

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