Editing Chi-squared distribution (section)

== History ==
This distribution was first described by the German geodesist and statistician [[Friedrich Robert Helmert]] in papers of 1875–6,{{sfn|Hald|1998|pp=633–692|loc=27. Sampling Distributions under Normality}}<ref>[[F. R. Helmert]], "[http://gdz.sub.uni-goettingen.de/dms/load/img/?PPN=PPN599415665_0021&DMDID=DMDLOG_0018 Ueber die Wahrscheinlichkeit der Potenzsummen der Beobachtungsfehler und über einige damit im Zusammenhange stehende Fragen]", ''Zeitschrift für Mathematik und Physik'' [http://gdz.sub.uni-goettingen.de/dms/load/toc/?PPN=PPN599415665_0021 21], 1876, pp. 192–219</ref> where he computed the sampling distribution of the sample variance of a normal population. Thus in German this was traditionally known as the ''Helmert'sche'' ("Helmertian") or "Helmert distribution".

The distribution was independently rediscovered by the English mathematician [[Karl Pearson]] in the context of [[goodness of fit]], for which he developed his [[Pearson's chi-squared test]], published in 1900, with computed table of values published in {{Harv|Elderton|1902}}, collected in {{Harv|Pearson|1914|pp=xxxi–xxxiii, 26–28|loc=Table XII}}.
The name "chi-square" ultimately derives from Pearson's shorthand for the exponent in a [[multivariate normal distribution]] with the Greek letter [[Chi (letter)|Chi]], writing {{mvar|−½χ<sup>2</sup>}} for what would appear in modern notation as {{math|−½'''x'''<sup>T</sup>Σ<sup>−1</sup>'''x'''}} (Σ being the [[covariance matrix]]).<ref>R. L. Plackett, ''Karl Pearson and the Chi-Squared Test'', International Statistical Review, 1983, [https://www.jstor.org/stable/1402731?seq=3 61f.]
See also Jeff Miller, [http://jeff560.tripod.com/c.html Earliest Known Uses of Some of the Words of Mathematics].</ref> The idea of a family of "chi-squared distributions", however, is not due to Pearson but arose as a further development due to Fisher in the 1920s.{{sfn|Hald|1998|pp=633–692|loc=27. Sampling Distributions under Normality}}