1: $p$ – double Input: On entry: $p$ , the lower tail probability from the required $F$ -distribution.

Constraint: $0.0 \leq p < 1.0$ .
2: $df1$ – double Input: On entry: the degrees of freedom of the numerator variance, $ν_{1}$ .

Constraint: $df1 > 0.0$ .
3: $df2$ – double Input: On entry: the degrees of freedom of the denominator variance, $ν_{2}$ .

Constraint: $df2 > 0.0$ .
4: $fail$ – NagError * Input/Output: The NAG error argument (see Section 7 in the Introduction to the NAG Library CL Interface).

6 Error Indicators and Warnings

If on exit

fail . code =

0.0

On any of the error conditions listed below except $fail . code =$ NE_SOL_NOT_CONV g01fdc returns $0.0$ .
NE_ALLOC_FAIL: Dynamic memory allocation failed.
See Section 3.1.2 in the Introduction to the NAG Library CL Interface for further information.
NE_INTERNAL_ERROR: An internal error has occurred in this function. Check the function call and any array sizes. If the call is correct then please contact NAG for assistance.
See Section 7.5 in the Introduction to the NAG Library CL Interface for further information.
NE_NO_LICENCE: Your licence key may have expired or may not have been installed correctly.
See Section 8 in the Introduction to the NAG Library CL Interface for further information.
NE_PROBAB_CLOSE_TO_TAIL: 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.
NE_REAL_ARG_GE: On entry, $p = ⟨ value ⟩$ .
Constraint: $p < 1.0$ .
NE_REAL_ARG_LE: On entry, $df1 = ⟨ value ⟩$ and $df2 = ⟨ value ⟩$ .
Constraint: $df1 > 0.0$ and $df2 > 0.0$ .
NE_REAL_ARG_LT: On entry, $p = ⟨ value ⟩$ .
Constraint: $p \geq 0.0$ .
NE_SOL_NOT_CONV: The solution has failed to converge. However, the result should be a reasonable approximation. Alternatively, g01fec can be used with a suitable setting of the argument tol.

7 Accuracy

The result should be accurate to five significant digits.

Background information to multithreading can be found in the Multithreading documentation.

g01fdc is not threaded in any implementation.

For higher accuracy g01fec 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 PY MB