NAG Toolbox: nag_nonpar_randtest_triplets (g08ec)

Purpose

Syntax

Description

References

Parameters

Compulsory Input Parameters

1:     $\mathrm{cl}$ – string (length ≥ 1)

Indicates the type of call to nag_nonpar_randtest_triplets (g08ec).

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

This is the one and only call to nag_nonpar_randtest_triplets (g08ec) (single call mode). All data are to be input at once. All test statistics are computed after counting of the triplets is complete.

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

This is the first call to the function. All initializations are carried out and the counting of triplets begins. The final test statistics are not computed since further calls will be made to nag_nonpar_randtest_triplets (g08ec).

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

This is an intermediate call during which counts of the triplets are updated. The final test statistics are not computed since further calls will be made to nag_nonpar_randtest_triplets (g08ec).

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

This is the last call to nag_nonpar_randtest_triplets (g08ec). The test statistics are computed after the final counting of the triplets is complete.

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

2:     $\mathrm{x}\left(\mathbf{n}\right)$ – double array

The sequence of observations.

Constraint: $0.0\le \mathbf{x}\left(\mathit{i}\right)\le 1.0$, for $\mathit{i}=1,2,\dots ,n$.

3:     $\mathrm{ncount}\left(\mathit{ldc},\mathit{ldc},\mathbf{msize}\right)$ – int64int32nag_int array

ldc, the first dimension of the array, must satisfy the constraint $\mathit{ldc}\ge \mathbf{msize}$.

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 nag_nonpar_randtest_triplets (g08ec).

Optional Input Parameters

1:     $\mathrm{n}$ – int64int32nag_int scalar

Default: the dimension of the array x.

$n$, the number of observations.

Constraints:

• if $\mathbf{cl}=\text{'S'}$, $\mathbf{n}\ge 3$;
• otherwise $\mathbf{n}\ge 1$.

2:     $\mathrm{msize}$ – int64int32nag_int scalar

Default: the first dimension of the array ncount and the third dimension of the array ncount. (An error is raised if these dimensions are not equal.)

$m$, the size of the count matrix to be formed.

msize must not be changed between calls to nag_nonpar_randtest_triplets (g08ec).

Constraint: $\mathbf{msize}\ge 2$.

Output Parameters

1:     $\mathrm{ncount}\left(\mathit{ldc},\mathit{ldc},\mathbf{msize}\right)$ – int64int32nag_int array

Is an msize by msize by msize matrix containing the counts of the number of triplets, $c_{jkl}$, for $\mathit{j}=1,2,\dots ,m$, $\mathit{k}=1,2,\dots ,m$ and $\mathit{l}=1,2,\dots ,m$.

2:     $\mathrm{ex}$ – double scalar

If $\mathbf{cl}=\text{'S'}$ or $\text{'L'}$ (i.e., if it is a final exit) then ex contains the expected number of counts for each element of the count matrix.

Otherwise ex is not set.

3:     $\mathrm{chi}$ – double scalar

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.

4:     $\mathrm{df}$ – double scalar

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.

5:     $\mathrm{prob}$ – double scalar

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.

6:     $\mathrm{ifail}$ – int64int32nag_int scalar

$\mathbf{ifail}=\mathbf{0}$ unless the function detects an error (see Error Indicators and Warnings).

Error Indicators and Warnings

Cases prefixed with W are classified as warnings and do not generate an error of type NAG:error_n. See nag_issue_warnings.

   $\mathbf{ifail}=1$

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

   $\mathbf{ifail}=2$

Constraint: if $\mathbf{cl}=\text{'S'}$, $\mathbf{n}\ge 3$, otherwise $\mathbf{n}\ge 1$.

   $\mathbf{ifail}=3$

Constraint: $\mathbf{msize}\ge 2$.

   $\mathbf{ifail}=4$

Constraint: $\mathit{ldc}\ge \mathbf{msize}$.

   $\mathbf{ifail}=5$

On entry, at least one element of x is out of range.
Constraint: $0\le \mathbf{x}\left(\mathrm{i}\right)\le 1$, for $i=1,2,\dots ,\mathbf{n}$.

   $\mathbf{ifail}=6$

No triplets were found because less than $3$ observations were provided in total.

W  $\mathbf{ifail}=7$

msize is too large relative to the number of triplets, therefore the expected value for at least one cell is less than or equal to $5.0$.

   $\mathbf{ifail}=-99$

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

   $\mathbf{ifail}=-399$

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

   $\mathbf{ifail}=-999$

Dynamic memory allocation failed.

Accuracy

Further Comments

Example

Open in the MATLAB editor: g08ec_example

function g08ec_example


fprintf('g08ec example results\n\n');

% Initialize the base generator to a repeatable sequence
seed  = [int64(324213)];
genid = int64(1);
subid = int64(1);
[state, ifail] = g05kf( ...
                        genid, subid, seed);
m      = 2;
ncount = zeros(m, m, m, 'int64');
n      = int64(100);
nsampl = 5;
cl     = 'F';

for i=1:nsampl
  % Generate a sample from U(0,1)
  [state, x, ifail] = g05sq( ...
                             n, 0, 1, state);
  % Process the sample
  [ncount, ex, chi, df, prob, ifail] = ...
  g08ec( ...
         cl, x, ncount);
  % Adjust CL
  cl = 'I';
  if i==nsampl-1
     cl = 'L';
  end
end

for k = 1:m
  mtitle = sprintf('k = %2d',k);
  [ifail] = x04ea('General', ' ', reshape(ncount(:,:,k),m,m), mtitle);
  fprintf('\n');
end

fprintf('\nExpected value = %8.2f\n', ex);
fprintf('Chisq          = %10.4f\n', chi);
fprintf('DF             = %7.1f\n', df);
fprintf('Probability    = %10.4f\n', prob);

g08ec example results

 k =  1
     1  2
 1  22 25
 2  18 17

 k =  2
     1  2
 1  23 24
 2  24 13


Expected value =    20.75
Chisq          =     6.1446
DF             =     7.0
Probability    =     0.5230