Central t-Distribution

Definition

Let

• $W$ : Random variable from $N(\delta ,1)$¹
• $V$ : Random variable from ${\chi }^2(r)$²
• $W$ and $V$ be independent

Suppose

$$T=\frac{W}{\sqrt{V/r}}$$

If $\delta =0$

Then

• We say $T$ has a central $t$-distribution

Note

$T$ is said to have a noncentral $t$-distribution with $r$ degrees of freedom and noncentraility parameter $\delta$.

Footnotes

1. 3.4 The Normal Distribution ↩

2. 3.3.1 The Chi-square Distribution ↩