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

Constraint: $0.0 \leq p < 1.0$ .
2: $df1$ – Real (Kind=nag_wp) Input: On entry: the degrees of freedom of the numerator variance, $ν_{1}$ .

Constraint: $df1 > 0.0$ .
3: $df2$ – Real (Kind=nag_wp) Input: On entry: the degrees of freedom of the denominator variance, $ν_{2}$ .

Constraint: $df2 > 0.0$ .
4: $ifail$ – 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 g01fdf may return useful information.

If on exit

ifail = 1

2

4

, then g01fdf returns

0.0

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

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

$ifail = 2$: On entry, $df1 = ⟨ value ⟩$ and $df2 = ⟨ value ⟩$ .
Constraint: $df1 > 0.0$ and $df2 > 0.0$ .

$ifail = 3$: The solution has failed to converge. However, the result should be a reasonable approximation. Alternatively, g01fef can be used with a suitable setting of the argument tol.

$ifail = 4$: The probability is too close to $0.0$ or $1.0$ . The value of $f_{p}$ cannot be computed. This will only occur when the large sample approximations are used.

$ifail = - 99$: 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 result should be accurate to five significant digits.

g01fdf is not threaded in any implementation.

For higher accuracy g01fef can be used along with the transformations given in Section 3.

This example reads the lower tail probabilities for several

F

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

g01fd: FL CL CPP AD