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Folded-t Distribution
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. Definitions The folded non-standardized ''t'' distribution is the distribution of the absolute value of the non-standardized ''t'' distribution with \nu degrees of freedom; its probability density function is given by: :g\left(x\right)\;=\;\frac\left\lbrace \left +\frac\frac\right+\left +\frac\frac\right \right\rbrace \qquad(\mbox\quad x \geq 0). The half-''t'' distribution results as the special case of \mu=0, and the standardized version as the special case of \sigma=1. If \mu=0, the folded-''t'' distribution reduces to the special case of the half-''t'' distribution. Its probability density function then simplifies to :g\left(x\right)\;=\;\frac \left(1+\frac\frac\right)^ \qquad(\mbox\quad x \geq 0). Th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Student's T-distribution
In probability and statistics, Student's ''t''-distribution (or simply the ''t''-distribution) is any member of a family of continuous probability distributions that arise when estimating the mean of a normally distributed population in situations where the sample size is small and the population's standard deviation is unknown. It was developed by English statistician William Sealy Gosset under the pseudonym "Student". The ''t''-distribution plays a role in a number of widely used statistical analyses, including Student's ''t''-test for assessing the statistical significance of the difference between two sample means, the construction of confidence intervals for the difference between two population means, and in linear regression analysis. Student's ''t''-distribution also arises in the Bayesian analysis of data from a normal family. If we take a sample of n observations from a normal distribution, then the ''t''-distribution with \nu=n-1 degrees of freedom can be de ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
