NAG FL Interface
g01fbf (inv_​cdf_​students_​t)

1 Purpose

2 Specification

3 Description

4 References

5 Arguments

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

On entry: indicates which tail the supplied probability represents.

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

The upper tail probability, i.e., $P(T\ge t_p:\nu )$.

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

The lower tail probability, i.e., $P(T\le t_p:\nu )$.

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

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

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

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

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

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

On entry: $p$, the probability from the required Student's $t$-distribution as defined by tail.

Constraint: $0.0<\mathbf{p}<1.0$.

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 $-1$ is recommended since useful values can be provided in some output arguments even when $\mathbf{ifail}\ne \mathbf{0}$ on exit. 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, $\mathbf{p}=⟨\mathit{\text{value}}⟩$.
Constraint: $\mathbf{p}<1.0$.

On entry, $\mathbf{p}=⟨\mathit{\text{value}}⟩$.
Constraint: $\mathbf{p}>0.0$.

$\mathbf{ifail}=3$

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

$\mathbf{ifail}=5$

The solution has failed to converge. However, the result should be a reasonable approximation.

$\mathbf{ifail}=-99$

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

9.1 Internal Changes

10 Example

10.1 Program Text

10.2 Program Data

10.3 Program Results