$tail = Nag_LowerTail$: The lower tail probability is returned, i.e., $P (F \leq f : ν_{1}, ν_{2})$ .
$tail = Nag_UpperTail$: The upper tail probability is returned, i.e., $P (F \geq f : ν_{1}, ν_{2})$ .

Constraint:

tail = Nag_LowerTail

Nag_UpperTail

2: $f$ – double Input

On entry:

f

, the value of the

F

variate.

Constraint:

f \geq 0.0

3: $df1$ – double Input

On entry: the degrees of freedom of the numerator variance,

ν_{1}

Constraint:

df1 > 0.0

4: $df2$ – double Input

On entry: the degrees of freedom of the denominator variance,

ν_{2}

Constraint:

df2 > 0.0

5: $fail$ – NagError * Input/Output

The NAG error argument (see Section 7 in the Introduction to the NAG Library CL Interface).

6 Error Indicators and Warnings

Note: on any of the error conditions listed below except

fail . code =

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_BAD_PARAM: On entry, argument $⟨ value ⟩$ had an illegal value.
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 $1.0$ . f is too far out into the tails for the probability to be evaluated exactly. The result tends to approach $1.0$ if $f$ is large, or $0.0$ if $f$ is small. The result returned is a good approximation to the required solution.
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, $f = ⟨ value ⟩$ .
Constraint: $f \geq 0.0$ .

7 Accuracy

The result should be accurate to five significant digits.

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

g01edc is not threaded in any implementation.

For higher accuracy g01eec can be used along with the transformations given in Section 3.

This example reads values from, and degrees of freedom for, a number of

F

-distributions and computes the associated lower tail probabilities.

g01ed: FL CL CPP AD PY MB