NAG CL Interface
g08ebc (randtest_​pairs)

1 Purpose

2 Specification

3 Description

4 References

5 Arguments

1: $\mathbf{n}$ – Integer Input

On entry: $n$, the number of observations.

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

2: $\mathbf{x}\left[\mathbf{n}\right]$ – const double Input

On entry: the sequence of observations.

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

3: $\mathbf{max\_count}$ – Integer Input

On entry: $m$, the size of the matrix of counts.

Constraint: $\mathbf{max\_count}\ge 2$.

4: $\mathbf{lag}$ – Integer Input

On entry: $l$, the lag to be used in choosing pairs.

If $\mathbf{lag}=1$, then we consider the pairs $\left(\mathbf{x}\left[\mathit{i}-1\right],\mathbf{x}\left[\mathit{i}\right]\right)$, for $\mathit{i}=1,3,\dots ,n-1$, where $n$ is the number of observations.

If $\mathbf{lag}>1$, then we consider the pairs $\left(\mathbf{x}\left[i-1\right],\mathbf{x}\left[i+l-1\right]\right)$, for $i=1,2,\dots ,l,2l+1,2l+2,\dots ,3l,4l+1,\dots ,n-l$, where $n$ is the number of observations.

Constraint: $1\le \mathbf{lag}<\mathbf{n}$.

5: $\mathbf{chi}$ – double * Output

On exit: contains the ${\chi }^2$ test statistic, $X^2$, for testing the null hypothesis of randomness.

6: $\mathbf{df}$ – double * Output

On exit: contains the degrees of freedom for the ${\chi }^2$ statistic.

7: $\mathbf{prob}$ – double * Output

On exit: contains the upper tail probability associated with the ${\chi }^2$ test statistic, i.e., the significance level.

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

The NAG error argument (see Section 7 in the Introduction to the NAG Library CL Interface).

6 Error Indicators and Warnings

NE_ALLOC_FAIL

Dynamic memory allocation failed.
See Section 3.1.2 in the Introduction to the NAG Library CL Interface for further information.

NE_BAD_PARAM

On entry, argument $〈\mathit{\text{value}}〉$ had an illegal value.

NE_G08EB_CELL

max_count is too large relative to the number of pairs, therefore the expected value for at least one cell is less than or equal to $5.0$.
This implies that the ${\chi }^2$ distribution may not be a very good approximation to the distribution of test statistic.
$\mathbf{max\_count}=〈\mathit{\text{value}}〉$, number of pairs $=〈\mathit{\text{value}}〉$ and expected value $=〈\mathit{\text{value}}〉$.
All statistics are returned and may still be of use.

NE_G08EB_PAIRS

No pairs were found. This will occur if the value of lag is greater than or equal to the total number of observations.

NE_INT_2

On entry, $\mathbf{lag}=〈\mathit{\text{value}}〉$ and $\mathbf{n}=〈\mathit{\text{value}}〉$.
Constraint: $1\le \mathbf{lag}<\mathbf{n}$.

NE_INT_ARG_LE

On entry, $\mathbf{max\_count}=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{max\_count}\ge 2$.

NE_INT_ARG_LT

On entry, $\mathbf{n}=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{n}\ge 2$

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 7.5 in the Introduction to the NAG Library CL Interface for further information.

NE_NO_LICENCE

Your licence key may have expired or may not have been installed correctly.
See Section 8 in the Introduction to the NAG Library CL Interface for further information.

NE_REAL_ARRAY_CONS

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

7 Accuracy

8 Parallelism and Performance

9 Further Comments

10 Example

10.1 Program Text

10.2 Program Data

10.3 Program Results