NAG FL Interface
g01ecf (prob_​chisq)

1 Purpose

2 Specification

3 Description

4 References

5 Arguments

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

On entry: indicates whether the upper or lower tail probability is required.

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

The lower tail probability is returned, i.e., $P(X\le x:\nu )$.

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

The upper tail probability is returned, i.e., $P(X\ge x:\nu )$.

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

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

On entry: $x$, the value of the ${\chi }^2$ variate with $\nu$ degrees of freedom.

Constraint: $\mathbf{x}\ge 0.0$.

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

On entry: $\nu$, the degrees of freedom of the ${\chi }^2$-distribution.

Constraint: $\mathbf{df}>0.0$.

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

On entry: ifail must be set to $0$, $\mathrm{-1}$ 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 $\mathrm{-1}$ means that an error message is printed while a value of $1$ means that it is not.

If halting is not appropriate, the value $\mathrm{-1}$ or $1$ is recommended. If message printing is undesirable, then the value $1$ is recommended. Otherwise, the value $\mathrm{-1}$ 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: $\mathbf{tail}=\text{'L'}$ or $\text{'U'}$.

$\mathbf{ifail}=2$

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

$\mathbf{ifail}=3$

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

$\mathbf{ifail}=4$

The series used to calculate the gamma probabilities has failed to converge. The result returned should represent an approximation to the solution.

$\mathbf{ifail}=-99$

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