NAG Library Routine Document

g01gdf  (prob_f_noncentral)

1

Purpose

2

Specification

3

Description

4

References

5

Arguments

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

On entry: $f$, the deviate from the noncentral $F$-distribution.

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

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

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

Constraint: $0.0<\mathbf{df1}\le {10}^6$.

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

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

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

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

On entry: $\lambda$, the noncentrality parameter.

Constraint: $0.0\le \mathbf{rlamda}\le -2.0\log \left(U\right)$ where $U$ is the safe range parameter as defined by x02amf.

5:     $\mathbf{tol}$ – Real (Kind=nag_wp)Input

On entry: the relative accuracy required by you in the results. If g01gdf is entered with tol greater than or equal to $1.0$ or less than $10\times \mathit{machine precision}$ (see x02ajf), the value of $10\times \mathit{machine precision}$ is used instead.

6:     $\mathbf{maxit}$ – IntegerInput

On entry: the maximum number of iterations to be used.

Suggested value: $500$. See g01gcf and g01gef for further details.

Constraint: $\mathbf{maxit}\ge 1$.

7:     $\mathbf{ifail}$ – 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, $\mathbf{df1}=〈\mathit{\text{value}}〉$.
Constraint: $0.0<\mathbf{df1}\le {10}^6$.

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

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

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

On entry, $\mathbf{maxit}=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{maxit}\ge 1$.

On entry, $\mathbf{rlamda}=〈\mathit{\text{value}}〉$.
Constraint: $0.0\le \mathbf{rlamda}\le -2.0\times \log \left(U\right)$, where $U$ is the safe range parameter as defined by x02amf.

$\mathbf{ifail}=2$

The solution has failed to converge in $〈\mathit{\text{value}}〉$ iterations. Consider increasing maxit or tol.

$\mathbf{ifail}=3$

The required probability cannot be computed accurately. This may happen if the result would be very close to zero or one. Alternatively the values of df1 and f may be too large. In the latter case you could try using a normal approximation, see Abramowitz and Stegun (1972).

$\mathbf{ifail}=4$

The required accuracy was not achieved when calculating the initial value of the central $F$ or ${\chi }^2$ probability. You should try a larger value of tol. If the ${\chi }^2$ approximation is being used then g01gdf returns zero otherwise the value returned should be an approximation to the correct value.

$\mathbf{ifail}=-99$

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 (g01gdfe.f90)

10.2

Program Data

Program Data (g01gdfe.d)

10.3

Program Results

Program Results (g01gdfe.r)