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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.
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.
The skew normal distribution; Student's t-distribution, useful for estimating unknown means of Gaussian populations. The noncentral t-distribution; The skew t distribution; The Champernowne distribution; The type-1 Gumbel distribution; The Tracy–Widom 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
In statistics, the folded-t and half-t distributions are derived from Student's t-distribution by taking the absolute values of variates. This is analogous to the folded-normal and the half-normal statistical distributions being derived from the normal distribution.
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 ...
In probability and statistics, the skewed generalized "t" distribution is a family of continuous probability distributions. The distribution was first introduced by Panayiotis Theodossiou [1] in 1998. The distribution has since been used in different applications.