NAG FL Interface
g01ebf (prob_​students_​t)

1 Purpose

2 Specification

3 Description

4 References

5 Arguments

1: $\mathbf{tail}$ – Character(1) Input

On entry: indicates which tail the returned probability should represent.

$\mathbf{tail}=\text{'U'}$

The upper tail probability is returned, i.e., $P\left(T\ge t:\nu \right)$.

$\mathbf{tail}=\text{'S'}$

The two tail (significance level) probability is returned, i.e., $P\left(T\ge \left|t\right|:\nu \right)+P\left(T\le -\left|t\right|:\nu \right)$.

$\mathbf{tail}=\text{'C'}$

The two tail (confidence interval) probability is returned, i.e., $P\left(T\le \left|t\right|:\nu \right)-P\left(T\le -\left|t\right|:\nu \right)$.

$\mathbf{tail}=\text{'L'}$

The lower tail probability is returned, i.e., $P\left(T\le t:\nu \right)$.

Constraint: $\mathbf{tail}=\text{'U'}$, $\text{'S'}$, $\text{'C'}$ or $\text{'L'}$.

2: $\mathbf{t}$ – Real (Kind=nag_wp) Input

On entry: $t$, the value of the Student's $t$ variate.

3: $\mathbf{df}$ – Real (Kind=nag_wp) Input

On entry: $\nu$, the degrees of freedom of the Student's $t$-distribution.

Constraint: $\mathbf{df}\ge 1.0$.

4: $\mathbf{ifail}$ – Integer Input/Output

On entry: ifail must be set to $0$, $-1$ or $1$ to set behaviour on detection of an error; these values have no effect when no error is detected.

A value of $0$ causes the printing of an error message and program execution will be halted; otherwise program execution continues. A value of $-1$ means that an error message is printed while a value of $1$ means that it is not.

If halting is not appropriate, the value $-1$ or $1$ is recommended. If message printing is undesirable, then the value $1$ is recommended. Otherwise, the value $0$ is recommended. When the value $-\mathbf{1}$ or $\mathbf{1}$ is used it is essential to test the value of ifail on exit.

On exit: $\mathbf{ifail}=\mathbf{0}$ unless the routine detects an error or a warning has been flagged (see Section 6).

6 Error Indicators and Warnings

$\mathbf{ifail}=1$

On entry, $\mathbf{tail}=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{tail}=\text{'L'}$, $\text{'U'}$, $\text{'S'}$ or $\text{'C'}$.

$\mathbf{ifail}=2$

On entry, $\mathbf{df}=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{df}\ge 1.0$.

$\mathbf{ifail}=-99$

An unexpected error has been triggered by this routine. Please contact NAG.

See Section 7 in the Introduction to the NAG Library FL Interface for further information.

$\mathbf{ifail}=-399$

Your licence key may have expired or may not have been installed correctly.

See Section 8 in the Introduction to the NAG Library FL Interface for further information.

$\mathbf{ifail}=-999$

Dynamic memory allocation failed.

See Section 9 in the Introduction to the NAG Library FL Interface for further information.

7 Accuracy

8 Parallelism and Performance

9 Further Comments

10 Example

10.1 Program Text

10.2 Program Data

10.3 Program Results