Symbols:T/Student's t-Distribution

Student's $t$-Distribution

$\StudentT k$

Symbol used for Student's $t$-Distribution.

Student's $t$-distribution is the probability distribution of a random variable which is proportional to the ratio of:

a standard normal distribution

and:

the square root of a $\chi$-squared variable with $k$ degrees of freedom.

Let $S = \set {x_1, x_2, \ldots, x_n}$ be a sample of size $n$ from a normal distribution with expectation $\mu$.

The statistic:

$t := \dfrac {\overline x - \mu} {s / \sqrt n}$

where:

$\overline x$ is the mean of $S$

$s^2 := \ds \sum_{i \mathop = 1}^n \dfrac {\paren {x_i - \overline x}^2} {n - 1}$

has a Student's $t$-distribution with $n - 1$ degrees of freedom.

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.