NAG Library Routine Document

g01edf  (prob_f)

1

Purpose

2

Specification

3

Description

4

References

5

Arguments

1:     $\mathbf{tail}$ – Character(1)Input

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

$\mathbf{tail}=\text{'L'}$

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

$\mathbf{tail}=\text{'U'}$

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

Constraint: $\mathbf{tail}=\text{'L'}$ or $\text{'U'}$.

2:     $\mathbf{f}$ – Real (Kind=nag_wp)Input

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

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

3:     $\mathbf{df1}$ – Real (Kind=nag_wp)Input

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

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

4:     $\mathbf{df2}$ – Real (Kind=nag_wp)Input

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

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

5:     $\mathbf{ifail}$ – IntegerInput/Output

On entry: ifail must be set to $0$, $-1\text{ or }1$. If you are unfamiliar with this argument you should refer to Section 3.4 in How to Use the NAG Library and its Documentation for details.

For environments where it might be inappropriate to halt program execution when an error is detected, the value $-1\text{ or }1$ is recommended. If the output of error messages is undesirable, then the value $1$ is recommended. Otherwise, because for this routine the values of the output arguments may be useful even if $\mathbf{ifail}\ne \mathbf{0}$ on exit, the recommended value is $-1$. When the value $-\mathbf{1}\text{ or }1$ is used it is essential to test the value of ifail on exit.

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

6

Error Indicators and Warnings

$\mathbf{ifail}=1$

On entry, $\mathbf{tail}=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{tail}=\text{'L'}$ or $\text{'U'}$.

$\mathbf{ifail}=2$

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

$\mathbf{ifail}=3$

On entry, $\mathbf{df1}=〈\mathit{\text{value}}〉$ and $\mathbf{df2}=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{df1}>0.0$ and $\mathbf{df2}>0.0$.

$\mathbf{ifail}=4$

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.

$\mathbf{ifail}=-99$

An unexpected error has been triggered by this routine. Please contact NAG.

See Section 3.9 in How to Use the NAG Library and its Documentation for further information.

$\mathbf{ifail}=-399$

Your licence key may have expired or may not have been installed correctly.

See Section 3.8 in How to Use the NAG Library and its Documentation for further information.

$\mathbf{ifail}=-999$

Dynamic memory allocation failed.

See Section 3.7 in How to Use the NAG Library and its Documentation for further information.

7

Accuracy

8

Parallelism and Performance

9

Further Comments

10

Example

10.1

Program Text

Program Text (g01edfe.f90)

10.2

Program Data

Program Data (g01edfe.d)

10.3

Program Results

Program Results (g01edfe.r)