NAG Library Routine Document

G08CJF

(see G08CHF) and its upper tail probability by using the approximation method of Marsaglia and Marsaglia (2004) for the case of uniformly distributed data.

4 References

Anderson T W and Darling D A (1952) Asymptotic theory of certain ‘goodness-of-fit’ criteria based on stochastic processes Annals of Mathematical Statistics 23 193–212

Marsaglia G and Marsaglia J (2004) Evaluating the Anderson–Darling distribution J. Statist. Software 9(2)

5 Parameters

1: N – INTEGERInput: On entry: $n$ , the number of observations.
Constraint: $N > 1$ .
2: ISSORT – LOGICALInput: On entry: set $ISSORT = .TRUE.$ if the observations are sorted in ascending order; otherwise the routine will sort the observations.
3: Y(N) – REAL (KIND=nag_wp) arrayInput/Output: On entry: $y_{i}$ , for $i = 1, 2, \dots, n$ , the $n$ observations.

On exit: if $ISSORT = .FALSE.$ , the data sorted in ascending order; otherwise the array is unchanged.
Constraint: if $ISSORT = .TRUE.$ , the values must be sorted in ascending order. Each $y_{i}$ must lie in the interval $(0, 1)$ .
4: A2 – REAL (KIND=nag_wp)Output: On exit: $A^{2}$ , the Anderson–Darling test statistic.
5: P – REAL (KIND=nag_wp)Output: On exit: $p$ , the upper tail probability for $A^{2}$ .
6: IFAIL – INTEGERInput/Output: On entry: IFAIL must be set to $0$ , $- 1 or 1$ . If you are unfamiliar with this parameter you should refer to Section 3.3 in the Essential Introduction for details.
For environments where it might be inappropriate to halt program execution when an error is detected, the value $- 1 or 1$ is recommended. If the output of error messages is undesirable, then the value $1$ is recommended. Otherwise, if you are not familiar with this parameter, the recommended value is $0$ . When the value $- 1 or 1$ is used it is essential to test the value of IFAIL on exit.

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

6 Error Indicators and Warnings

If on entry

IFAIL = 0

- 1

, explanatory error messages are output on the current error message unit (as defined by X04AAF).

Errors or warnings detected by the routine:

$IFAIL = 1$

On entry,

N < 2

$IFAIL = 3$: The data in Y is not sorted in ascending order.

$IFAIL = 9$: The data in Y must lie in the interval $(0, 1)$ .

7 Accuracy

Probabilities greater than approximately

0.09

are accurate to five decimal places; lower value probabilities are accurate to six decimal places.

8 Further Comments

None.

9 Example

This example calculates the

A^{2}

statistic and its

p

-value for uniform data obtained by transforming exponential variates.

NAG Library Routine DocumentG08CJF

+− Contents

1 Purpose

2 Specification

3 Description