Student's t-Distribution | t distribution and gamma distribution
Astatisticaldistribution[1]publishedbyWilliamGossetin1908.Hisemployer,GuinnessBreweries,requiredhimtopublishunderapseudonym,sohechose"Student."Givenindependentmeasurements,let(1)whereisthepopulationmean[2],isthesamplemean[3],andistheestimator[4]forpopulationstandarddeviation[5](i.e.,thesamplevariance[6])definedby(2)Students-distributionisdefinedasthedistributionoftherandomvariablewhichis(veryloosely)the"best"thatwecandonotknowing.TheStudents-distributionwithdegreesoffreedomisimplementedinthe...
A statistical distribution[1] published by William Gosset in 1908. His employer, Guinness Breweries, required him to publish under a pseudonym, so he chose "Student." Given independent measurements , let
(1)
where is the population mean[2], is the sample mean[3], and is the estimator[4] for population standard deviation[5] (i.e., the sample variance[6]) defined by
(2)
Students -distribution is defined as the distribution of the random variable which is (very loosely) the "best" that we can do not knowing .
The Students -distribution with degrees of freedom is implemented in the Wolfram Language[7] as StudentTDistribution[8][n].
If , and the distribution becomes the normal distribution[9]. As increases, Students -distribution approaches the normal distribution[10].
Students -distribution can be derived by transforming Students z-distribution[11] using
(3)
and ...