NAG C Library Function Document

nag_prob_f_dist (g01edc)

1

Purpose

2

Specification

3

Description

4

References

5

Arguments

1:    $\mathbf{tail}$ – Nag_TailProbabilityInput

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

$\mathbf{tail}=\mathrm{Nag\_LowerTail}$

The lower tail probability is returned, i.e., $P\left(F\le f:{\nu }_1,{\nu }_2\right)$.

$\mathbf{tail}=\mathrm{Nag\_UpperTail}$

The upper tail probability is returned, i.e., $P\left(F\ge f:{\nu }_1,{\nu }_2\right)$.

Constraint: $\mathbf{tail}=\mathrm{Nag\_LowerTail}$ or $\mathrm{Nag\_UpperTail}$.

2:    $\mathbf{f}$ – doubleInput

On entry: $f$, the value of the $F$ variate.

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

3:    $\mathbf{df1}$ – doubleInput

On entry: the degrees of freedom of the numerator variance, ${\nu }_1$.

Constraint: $\mathbf{df1}>0.0$.

4:    $\mathbf{df2}$ – doubleInput

On entry: the degrees of freedom of the denominator variance, ${\nu }_2$.

Constraint: $\mathbf{df2}>0.0$.

5:    $\mathbf{fail}$ – NagError *Input/Output

The NAG error argument (see Section 3.7 in How to Use the NAG Library and its Documentation).

6

Error Indicators and Warnings

On any of the error conditions listed below except NE_PROBAB_CLOSE_TO_TAIL nag_prob_f_dist (g01edc) returns $0.0$.

NE_ALLOC_FAIL

Dynamic memory allocation failed.
See Section 2.3.1.2 in How to Use the NAG Library and its Documentation for further information.

NE_BAD_PARAM

On entry, argument $〈\mathit{\text{value}}〉$ 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 2.7.6 in How to Use the NAG Library and its Documentation for further information.

NE_NO_LICENCE

Your licence key may have expired or may not have been installed correctly.
See Section 2.7.5 in How to Use the NAG Library and its Documentation 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, $\mathbf{df1}=〈\mathit{\text{value}}〉$ and $\mathbf{df2}=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{df1}>0.0$ and $\mathbf{df2}>0.0$.

NE_REAL_ARG_LT

On entry, $\mathbf{f}=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{f}\ge 0.0$.

7

Accuracy

8

Parallelism and Performance

9

Further Comments

10

Example

10.1

Program Text

Program Text (g01edce.c)

10.2

Program Data

Program Data (g01edce.d)

10.3

Program Results

Program Results (g01edce.r)