Editing Normal distribution (section)

=== Naming ===
Today, the concept is usually known in English as the '''normal distribution''' or '''Gaussian distribution'''.  Other less common names include Gauss distribution, Laplace–Gauss distribution, the law of error, the law of facility of errors, Laplace's second law, and Gaussian law.

Gauss himself apparently coined the term with reference to the "normal equations" involved in its applications, with normal having its technical meaning of orthogonal rather than usual.<ref>Jaynes, Edwin J.; ''Probability Theory: The Logic of Science'', [http://www-biba.inrialpes.fr/Jaynes/cc07s.pdf Ch. 7].</ref> However, by the end of the 19th century some authors{{NoteTag|Besides those specifically referenced here, such use is encountered in the works of [[Charles Sanders Peirce|Peirce]], [[Galton]] ({{harvtxt |Galton |1889 |loc = chapter V }}) and [[Wilhelm Lexis|Lexis]] ({{harvtxt | Lexis |1878 }}, {{harvtxt |Rohrbasser |Véron |2003 }}) c. 1875.{{Citation needed |date=June 2011 }} }} had started using the name ''normal distribution'', where the word "normal" was used as an adjective&nbsp;– the term now being seen as a reflection of the fact that this distribution was seen as typical, common&nbsp;– and thus normal. [[Charles Sanders Peirce|Peirce]] (one of those authors) once defined "normal" thus: "...the 'normal' is not the average (or any other kind of mean) of what actually occurs, but of what ''would'', in the long run, occur under certain circumstances."<ref>Peirce, Charles S. (c. 1909 MS), ''[[Charles Sanders Peirce bibliography#CP|Collected Papers]]'' v. 6, paragraph 327.</ref> Around the turn of the 20th century [[Karl Pearson|Pearson]] popularized the term ''normal'' as a designation for this distribution.<ref>{{harvtxt |Kruskal |Stigler |1997 }}.</ref>
{{Blockquote|Many years ago I called the Laplace–Gaussian curve the ''normal'' curve, which name, while it avoids an international question of priority, has the disadvantage of leading people to believe that all other distributions of frequency are in one sense or another 'abnormal'. |{{harvtxt |Pearson |1920 }}}}

Also, it was Pearson who first wrote the distribution in terms of the standard deviation ''σ'' as in modern notation. Soon after this, in year 1915, [[Ronald Fisher|Fisher]] added the location parameter to the formula for normal distribution, expressing it in the way it is written nowadays:
<math display=block> df = \frac{1}{\sqrt{2\sigma^2\pi}} e^{-(x - m)^2/(2\sigma^2)} \, dx.</math>

The term ''standard normal distribution'', which denotes the normal distribution with zero mean and unit variance came into general use around the 1950s, appearing in the popular textbooks by P.&nbsp;G. Hoel (1947) ''Introduction to Mathematical Statistics'' and A.&nbsp;M. Mood (1950) ''Introduction to the Theory of Statistics''.<ref>{{cite web|title=Earliest Uses... (Entry Standard Normal Curve)|url=http://jeff560.tripod.com/s.html}}</ref><ref>{{harvtxt|Hoel|1947}} introduces the terms ''standard normal curve'' [https://archive.org/details/in.ernet.dli.2015.263186/page/n41/mode/2up?q=%22standard+normal+curve%22 (p. 33)] and ''standard normal distribution'' [https://archive.org/details/in.ernet.dli.2015.263186/page/n77/mode/2up?q=%22standard+normal+distribution%22 (p. 69)].</ref><ref>{{harvtxt|Mood|1950}} explicitly defines the ''standard normal distribution'' [https://archive.org/details/introductiontoth0000alex/page/112/mode/2up?q=%22standard+normal+distribution%22 (p. 112)].</ref>