Definition:Student's t-Distribution/Degrees of Freedom

Definition

Let $X$ be a continuous random variable with a Student's $t$-distribution :

$\map {f_X} x = \dfrac {\map \Gamma {\frac {k + 1} 2} } {\sqrt {\pi k} \map \Gamma {\frac k 2} } \paren {1 + \dfrac {x^2} k}^{-\frac {k + 1} 2}$

for some $k \in \R_{>0}$.

The parameter $k$ is the number of degrees of freedom of $\StudentT k$.

Also see

• Results about Student's $t$-distribution can be found here.

Source of Name

This entry was named for William Sealy Gosset.

Sources

• 2014: Christopher Clapham and James Nicholson: The Concise Oxford Dictionary of Mathematics (5th ed.) ... (previous) ... (next): t-distribution