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In statistics, the t distribution was first derived as a posterior distribution in 1876 by Helmert [19] [20] [21] and Lüroth. [22] [23] [24] As such, Student's t-distribution is an example of Stigler's Law of Eponymy. The t distribution also appeared in a more general form as Pearson type IV distribution in Karl Pearson's 1895 paper. [25]
Student's T Distribution; Earliest known uses of some of the words of mathematics: S under the heading of "Student's t-distribution", describes briefly how Student's z became t. O'Connor, John J.; Robertson, Edmund F., "William Sealy Gosset", MacTutor History of Mathematics Archive, University of St Andrews
Most frequently, t statistics are used in Student's t-tests, a form of statistical hypothesis testing, and in the computation of certain confidence intervals. The key property of the t statistic is that it is a pivotal quantity – while defined in terms of the sample mean, its sampling distribution does not depend on the population parameters, and thus it can be used regardless of what these ...
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Student's t-test is a statistical test used to test whether the difference between the response of two groups is statistically significant or not. It is any statistical hypothesis test in which the test statistic follows a Student's t-distribution under the null hypothesis.
This family of distributions is used in data modeling to capture various tail behaviors. The location/scale generalization of the central t-distribution is a different distribution from the noncentral t-distribution discussed in this article. In particular, this approximation does not respect the asymmetry of the noncentral t-distribution.
The phrase "T distribution" may refer to Student's t-distribution in univariate probability theory, Hotelling's T-square distribution in multivariate statistics.
One common method of construction of a multivariate t-distribution, for the case of dimensions, is based on the observation that if and are independent and distributed as (,) and (i.e. multivariate normal and chi-squared distributions) respectively, the matrix is a p × p matrix, and is a constant vector then the random variable = / / + has the density [1]