Editing Student's t-distribution (section)

==History==
[[File:William_Sealy_Gosset.jpg|thumb|upright|Statistician [[William Sealy Gosset]], known as "Student"]]

In statistics, the {{mvar|t}}&nbsp;distribution was first derived as a [[posterior distribution]] in 1876 by [[Friedrich Robert Helmert|Helmert]]<ref name=HFR1>{{cite journal |vauthors=Helmert FR |year=1875 |title=Über die Berechnung des wahrscheinlichen Fehlers aus einer endlichen Anzahl wahrer Beobachtungsfehler |language=de |journal=[[Zeitschrift für Angewandte Mathematik und Physik]] |volume=20 |pages=300–303}}</ref><ref name=HFR2>{{cite journal |vauthors=Helmert FR |year=1876 |title=Über die Wahrscheinlichkeit der Potenzsummen der Beobachtungsfehler und uber einige damit in Zusammenhang stehende Fragen |language=de |journal=[[Zeitschrift für Angewandte Mathematik und Physik]] |volume=21 |pages=192–218 }}</ref><ref name=HFR3>{{cite journal |vauthors=Helmert FR |year=1876 |title=Die Genauigkeit der Formel von Peters zur Berechnung des wahrscheinlichen Beobachtungsfehlers directer Beobachtungen gleicher Genauigkeit |language=de |trans-title=The accuracy of Peters' formula for calculating the probable observation error of direct observations of the same accuracy |journal=[[Astronomische Nachrichten]] |volume=88 |issue=8–9 |pages=113–132 |bibcode=1876AN.....88..113H |doi=10.1002/asna.18760880802 |url=https://zenodo.org/record/1424695}}</ref> and [[Jacob Lüroth|Lüroth]].<ref name=L1876>{{cite journal |vauthors=Lüroth J |date=1876 |title=Vergleichung von zwei Werten des wahrscheinlichen Fehlers |language=de |journal=[[Astronomische Nachrichten]] |volume=87 |issue=14 |pages=209–220 |bibcode=1876AN.....87..209L |doi=10.1002/asna.18760871402 |url=https://zenodo.org/record/1424693}}</ref><ref>{{Cite journal |vauthors=Pfanzagl J, Sheynin O |year=1996 |title=Studies in the history of probability and statistics. XLIV. A forerunner of the {{mvar|t}}&nbsp;distribution |journal=[[Biometrika]] |volume=83 |issue=4 |pages=891–898 |doi=10.1093/biomet/83.4.891 |mr=1766040 }} <!-- abstract = "The t-distribution first occurred in a paper by Lüroth (1876) on the classical theory of errors in connection with a Bayesian result." --></ref><ref>{{Cite journal |vauthors=Sheynin O |year=1995 |title=Helmert's work in the theory of errors |journal=[[Archive for History of Exact Sciences]] |volume=49 |issue=1 |pages=73–104 |doi=10.1007/BF00374700 |s2cid=121241599}}</ref> As such, Student's t-distribution is an example of [[Stigler's law of eponymy|Stigler's Law of Eponymy]]. The {{mvar|t}}&nbsp;distribution also appeared in a more general form as [[Pearson distribution|Pearson type&nbsp;IV]] distribution in [[Karl Pearson]]'s 1895 paper.<ref>{{cite journal |last=Pearson |first=K. |year=1895 |title=Contributions to the Mathematical Theory of Evolution. II. Skew Variation in Homogeneous Material |journal=Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences |volume=186 |issue=374 |pages=343–414 |doi=10.1098/rsta.1895.0010 |doi-access=free |bibcode=1895RSPTA.186..343P |issn=1364-503X|url=https://zenodo.org/record/1432104 }}</ref>

In the English-language literature, the distribution takes its name from [[William Sealy Gosset]]'s 1908 paper in ''[[Biometrika]]'' under the pseudonym "Student" during his work at the [[Guinness Brewery]] in [[Dublin, Ireland]].<ref>{{cite journal |author="Student" <nowiki>[</nowiki>[[pen name|pseu.]] [[William Sealy Gosset]]<nowiki>]</nowiki> |year=1908 |title=The probable error of a mean |journal=[[Biometrika]] |volume=6 |issue=1 |pages=1–25 |doi=10.1093/biomet/6.1.1 |jstor=2331554 |hdl=10338.dmlcz/143545  |url=http://www.york.ac.uk/depts/maths/histstat/student.pdf}}</ref> One version of the origin of the pseudonym is that Gosset's employer preferred staff to use pen names when publishing scientific papers instead of their real name, so he used the name "Student" to hide his identity. Another version is that Guinness did not want their competitors to know that they were using the {{mvar|t}}&nbsp;test to determine the quality of raw material.<ref>{{cite journal |vauthors=Wendl MC |author-link=Michael Christopher Wendl |date=2016 |title=Pseudonymous fame |journal=[[Science (journal)|Science]] |volume=351 |issue=6280 |page =1406 |doi=10.1126/science.351.6280.1406 |pmid=27013722 |bibcode=2016Sci...351.1406W}}</ref><ref>{{cite book |vauthors=Mortimer RG |year=2005 |title=Mathematics for Physical Chemistry |edition=3rd |publisher=Elsevier |isbn=9780080492889 |location=Burlington, MA |pages=[https://archive.org/details/mathematicsforph00mort_321/page/n339 326] |oclc=156200058 |url=https://archive.org/details/mathematicsforph00mort_321 |url-access=registration}}</ref>

Gosset worked at Guinness and was interested in the problems of small samples – for example, the chemical properties of barley where sample sizes might be as few as 3. Gosset's paper refers to the distribution as the "frequency distribution of standard deviations of samples drawn from a normal population". It became well known through the work of [[Ronald Fisher]], who called the distribution "Student's distribution" and represented the test value with the letter {{mvar|t}}.<ref name="Fisher 1925 90–104">{{cite journal |vauthors=Fisher RA |author-link=Ronald Fisher |year=1925 |title=Applications of 'Student's' distribution |journal=Metron |volume=5 |pages=90–104 |url=http://www.sothis.ro/user/content/4ef6e90670749a86-student_distribution_1925.pdf |url-status=dead |archive-url=https://web.archive.org/web/20160305130235/http://www.sothis.ro/user/content/4ef6e90670749a86-student_distribution_1925.pdf |archive-date=5 March 2016}}</ref><ref>{{cite book |vauthors=Walpole RE, Myers R, Myers S, Ye K |year=2006 |title=Probability & Statistics for Engineers & Scientists |edition=7th |publisher=Pearson |isbn=9788177584042 |location=New Delhi, IN |page=237 |oclc=818811849 }}</ref>