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In probability theory and statistics, Student's t distribution (or simply the t distribution) is a continuous probability distribution that generalizes the standard normal distribution. Like the latter, it is symmetric around zero and bell-shaped.
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.
Multivariate normal distribution, which is the limiting case of the multivariate Student's t-distribution when . Chi distribution , the pdf of the scaling factor in the construction the Student's t-distribution and also the 2-norm (or Euclidean norm ) of a multivariate normally distributed vector (centered at zero).
The normal distribution, also called the Gaussian or the bell curve. ... The multivariate t-distribution, a generalization of the Student's t-distribution.
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
The noncentral t-distribution generalizes Student's t-distribution using a noncentrality parameter.Whereas the central probability distribution describes how a test statistic t is distributed when the difference tested is null, the noncentral distribution describes how t is distributed when the null is false.
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 ...
A Student's t-distribution with one degree of freedom (v = 1) is a Cauchy distribution with location parameter x = 0 and scale parameter γ = 1. A Burr distribution with parameters c = 1 and k (and scale λ) is a Lomax distribution with shape k (and scale λ.)