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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]
Download QR code; Print/export Download as PDF; Printable version; In other projects ... The phrase "T distribution" may refer to Student's t-distribution in ...
where is the beta function, is the location parameter, > is the scale parameter, < < is the skewness parameter, and > and > are the parameters that control the kurtosis. and are not parameters, but functions of the other parameters that are used here to scale or shift the distribution appropriately to match the various parameterizations of this distribution.
Once the t value and degrees of freedom are determined, a p-value can be found using a table of values from Student's t-distribution. If the calculated p-value is below the threshold chosen for statistical significance (usually the 0.10, the 0.05, or 0.01 level), then the null hypothesis is rejected in favor of the alternative hypothesis.
Central t-distribution: the central t-distribution can be converted into a location/scale family. 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
The multivariate t-distribution, a generalization of the Student's t-distribution. The negative multinomial distribution , a generalization of the negative binomial distribution . The Dirichlet negative multinomial distribution , a generalization of the beta negative binomial distribution .
T-coloring-- T distribution-- T-duality-- T-group (mathematics)-- T-norm-- T-norm fuzzy logics-- T puzzle-- T-schema-- T-spline-- T-square (fractal)-- T-statistic-- T-structure-- T-symmetry-- T-table-- T-theory-- T(1) theorem-- T.C. Mits-- T1 process-- T1 space-- Table of bases-- Table of Clebsch–Gordan coefficients-- Table of congruences-- Table of costs of operations in elliptic curves ...
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]