Definition:Student's t-Distribution/Degrees of Freedom
< Definition:Student's t-Distribution(Redirected from Definition:Degrees of Freedom of Student's t-Distribution)
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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