T Distribution

T Distribution

Definition

([@Ost20], Definition 7.5.1) Let $T$ be a random variable with outcome set $\mathbb{R}$ and PDF

$f(x)=\frac{\Gamma ((n+1)/2)}{\Gamma (n/2)\sqrt{\pi n}}{\left(\frac{1}{1+t^2/n}\right)}^{\frac{n+1}{2}},$

Then $T$ is called a t random variable and said to be distributed according to a t distribution with $n$ degrees of freedom, for which we write $T\sim t(n)$.

References

D. Ostwald - The general linear model 20_21