1: $p$ – Real (Kind=nag_wp) Input: On entry: $p$ , the lower tail probability from the required $χ^{2}$ -distribution.

Constraint: $0.0 \leq p < 1.0$ .
2: $df$ – Real (Kind=nag_wp) Input: On entry: $ν$ , the degrees of freedom of the $χ^{2}$ -distribution.

Constraint: $df > 0.0$ .
3: $ifail$ – 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 $ifail \neq 0$ on exit. When the value $- 1$ or $1$ is used it is essential to test the value of ifail on exit.

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

6 Error Indicators and Warnings

If on entry

ifail = 0

−1

, explanatory error messages are output on the current error message unit (as defined by x04aaf).

Errors or warnings detected by the routine:

Note: in some cases g01fcf may return useful information.

ifail = 1

2

3

5

on exit, then g01fcf returns

0.0

$ifail = 1$: On entry, $p = ⟨ value ⟩$ .
Constraint: $p < 1.0$ .

On entry, $p = ⟨ value ⟩$ .
Constraint: $p \geq 0.0$ .

$ifail = 4$: The algorithm has failed to converge in $⟨ value ⟩$ iterations. The result should be a reasonable approximation.

$ifail = 5$: The series used to calculate the gamma function has failed to converge. This is an unlikely error exit.

$ifail = - 99$: 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.

$ifail = - 399$: 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.

$ifail = - 999$: Dynamic memory allocation failed.
See Section 9 in the Introduction to the NAG Library FL Interface for further information.

7 Accuracy

The results should be accurate to five significant digits for most argument values. Some accuracy is lost for

p

close to

0.0

g01fcf is not threaded in any implementation.

For higher accuracy the relationship described in Section 3 may be used and a direct call to g01fff made.

This example reads lower tail probabilities for several

χ^{2}

-distributions, and calculates and prints the corresponding deviates until the end of data is reached.

g01fc: FL CL CPP AD