NAG Library Routine Document

g08edf  (randtest_gaps)

1

Purpose

2

Specification

3

Description

4

References

5

Arguments

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

On entry: indicates the type of call to g08edf.

$\mathbf{cl}=\text{'S'}$

This is the one and only call to g08edf (single call mode). All data are to be input at once. All test statistics are computed after the counting of gaps is complete.

$\mathbf{cl}=\text{'F'}$

This is the first call to the routine. All initializations are carried out before the counting of gaps begins. The final test statistics are not computed since further calls will be made to g08edf.

$\mathbf{cl}=\text{'I'}$

This is an intermediate call during which the counts of gaps are updated. The final test statistics are not computed since further calls will be made to g08edf.

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

This is the last call to g08edf. The test statistics are computed after the final counting of gaps is complete.

Constraint: $\mathbf{cl}=\text{'S'}$, $\text{'F'}$, $\text{'I'}$ or $\text{'L'}$.

2:     $\mathbf{n}$ – IntegerInput

On entry: $n$, the length of the current sequence of observations.

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

3:     $\mathbf{x}\left(\mathbf{n}\right)$ – Real (Kind=nag_wp) arrayInput

On entry: the sequence of observations.

4:     $\mathbf{m}$ – IntegerInput

On entry: the maximum number of gaps to be sought. If $\mathbf{m}\le 0$ then there is no limit placed on the number of gaps that are found.

m should not be changed between calls to g08edf.

Constraint: if $\mathbf{cl}=\text{'S'}$, $\mathbf{m}\le \mathbf{n}$.

5:     $\mathbf{maxg}$ – IntegerInput

On entry: $k$, the length of the longest gap for which tabulation is desired.

maxg must not be changed between calls to g08edf.

Constraints:

• $\mathbf{maxg}>1$;
• if $\mathbf{cl}=\text{'S'}$, $\mathbf{maxg}\le \mathbf{n}$.

6:     $\mathbf{rlo}$ – Real (Kind=nag_wp)Input

On entry: the lower limit of the interval to be used to define the gaps, $r_l$.

rlo must not be changed between calls to g08edf.

7:     $\mathbf{rup}$ – Real (Kind=nag_wp)Input

On entry: the upper limit of the interval to be used to define the gaps, $r_u$.

rup must not be changed between calls to g08edf.

Constraint: $\mathbf{rup}>\mathbf{rlo}$.

8:     $\mathbf{totlen}$ – Real (Kind=nag_wp)Input

On entry: the total length of the interval which contains all possible numbers that may arise in the sequence.

Constraint: $\mathbf{totlen}>0.0$ and $\mathbf{rup}-\mathbf{rlo}<\mathbf{totlen}$.

9:     $\mathbf{ngaps}$ – IntegerInput/Output

On entry: if $\mathbf{cl}=\text{'S'}$ or $\text{'F'}$, ngaps need not be set.

If $\mathbf{cl}=\text{'I'}$ or $\text{'L'}$, ngaps must contain the value returned by the previous call to g08edf.

On exit: the number of gaps actually found, $\mathit{ngaps}$.

10:   $\mathbf{ncount}\left(\mathbf{maxg}\right)$ – Integer arrayInput/Output

On entry: if $\mathbf{cl}=\text{'S'}$ or $\text{'F'}$, ncount need not be set.

If $\mathbf{cl}=\text{'I'}$ or $\text{'L'}$, ncount must contain the values returned by the previous call to g08edf.

On exit: the counts of gaps of the different lengths, $c_{\mathit{i}}$, for $\mathit{i}=1,2,\dots ,k$.

11:   $\mathbf{ex}\left(\mathbf{maxg}\right)$ – Real (Kind=nag_wp) arrayOutput

On exit: if $\mathbf{cl}=\text{'S'}$ or $\text{'L'}$ (i.e., if it is a final exit) then ex contains the expected values of the counts.

Otherwise the elements of ex are not set.

12:   $\mathbf{chi}$ – Real (Kind=nag_wp)Output

On exit: if $\mathbf{cl}=\text{'S'}$ or $\text{'L'}$ (i.e., if it is a final exit) then chi contains the ${\chi }^2$ test statistic, $X^2$, for testing the null hypothesis of randomness.

Otherwise chi is not set.

13:   $\mathbf{df}$ – Real (Kind=nag_wp)Output

On exit: if $\mathbf{cl}=\text{'S'}$ or $\text{'L'}$ (i.e., if it is a final exit) then df contains the degrees of freedom for the ${\chi }^2$ statistic.

Otherwise df is not set.

14:   $\mathbf{prob}$ – Real (Kind=nag_wp)Output

On exit: if $\mathbf{cl}=\text{'S'}$ or $\text{'L'}$ (i.e., if it is a final exit) then prob contains the upper tail probability associated with the ${\chi }^2$ test statistic, i.e., the significance level.

Otherwise prob is not set.

15:   $\mathbf{ifail}$ – 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, $\mathbf{cl}=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{cl}=\text{'S'}$, $\text{'F'}$, $\text{'I'}$ or $\text{'L'}$.

$\mathbf{ifail}=2$

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

$\mathbf{ifail}=3$

On entry, $\mathbf{m}=〈\mathit{\text{value}}〉$ and $\mathbf{n}=〈\mathit{\text{value}}〉$.
Constraint: if $\mathbf{cl}=\text{'S'}$, $\mathbf{m}\le \mathbf{n}$.

$\mathbf{ifail}=4$

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

On entry, $\mathbf{maxg}=〈\mathit{\text{value}}〉$ and $\mathbf{n}=〈\mathit{\text{value}}〉$.
Constraint: if $\mathbf{cl}=\text{'S'}$, $\mathbf{maxg}\le \mathbf{n}$.

$\mathbf{ifail}=5$

On entry, $\mathbf{rlo}=〈\mathit{\text{value}}〉$, $\mathbf{rup}=〈\mathit{\text{value}}〉$ and $\mathbf{totlen}=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{rup}-\mathbf{rlo}<\mathbf{totlen}$.

On entry, $\mathbf{rlo}=〈\mathit{\text{value}}〉$ and $\mathbf{rup}=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{rup}>\mathbf{rlo}$.

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

$\mathbf{ifail}=6$

No gaps were found. Try using a longer sequence, or increase the size of the interval $\mathbf{rup}-\mathbf{rlo}$.

$\mathbf{ifail}=7$

The expected frequency in class $i=〈\mathit{\text{value}}〉$ is zero. The value of $\left(\mathbf{rup}-\mathbf{rlo}\right)/\mathbf{totlen}$ may be too close to $0.0\text{ or }1.0$. or maxg is too large relative to the number of gaps found.

$\mathbf{ifail}=8$

The number of gaps requested were not found, only $〈\mathit{\text{value}}〉$ out of the requested $〈\mathit{\text{value}}〉$ where found.
All statistics are returned and may still be of use.

$\mathbf{ifail}=9$

The expected frequency of at least one class is less than one.
This implies that the ${\chi }^2$ may not be a very good approximation to the distribution of the test statistics.
All statistics are returned and may still be of use.

$\mathbf{ifail}=-99$

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 (g08edfe.f90)

10.2

Program Data

Program Data (g08edfe.d)

10.3

Program Results

Program Results (g08edfe.r)