Symbols:T/Student's t-Distribution
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Student's $t$-Distribution
- $\StudentT k$
Symbol used for Student's $t$-Distribution.
Let $X$ be a continuous random variable on a probability space $\struct {\Omega, \Sigma, \Pr}$.
Let $\Img X = \R$.
$X$ is said to have a Student's $t$-distribution with $k$ degrees of freedom if and only if it has probability density function:
- $\map {f_X} x = \dfrac {\map \Gamma {\frac {k + 1} 2} } {\sqrt {\pi k} \map \Gamma {\frac k 2} } \paren {1 + \dfrac {x^2} k}^{-\frac {k + 1} 2}$
for some $k \in \R_{>0}$.
This is written:
- $X \sim \StudentT k$
The $\LaTeX$ code for \(X \sim \StudentT k\) is X \sim \StudentT k
.
Sources
- 1989: Ephraim J. Borowski and Jonathan M. Borwein: Dictionary of Mathematics ... (previous) ... (next): t: 3.