NAG Library Function Document

nag_anderson_darling_uniform_prob (g08cjc)

+− Contents

1 Purpose

2 Specification

3 Description

4 References

5 Arguments

6 Error Indicators and Warnings

7 Accuracy

8 Parallelism and Performance

9 Further Comments

+− 10 Example

10.1 Program Text

10.2 Program Data

10.3 Program Results

1 Purpose

nag_anderson_darling_uniform_prob (g08cjc) calculates the Anderson–Darling goodness-of-fit test statistic and its probability for the case of standard uniformly distributed data.

2 Specification

#include <nag.h>

#include <nagg08.h>

void	nag_anderson_darling_uniform_prob (Integer n, Nag_Boolean issort, double y[], double a2, double p, NagError *fail)

3 Description

Calculates the Anderson–Darling test statistic

A^{2}

(see nag_anderson_darling_stat (g08chc)) 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 Arguments

1: n – IntegerInput: On entry: $n$ , the number of observations.
Constraint: $n > 1$ .
2: issort – Nag_BooleanInput: On entry: set $issort = Nag_TRUE$ if the observations are sorted in ascending order; otherwise the function will sort the observations.
3: y[n] – doubleInput/Output: On entry: $y_{i}$ , for $i = 1, 2, \dots, n$ , the $n$ observations.

On exit: if $issort = Nag_FALSE$ , the data sorted in ascending order; otherwise the array is unchanged.
Constraint: if $issort = Nag_TRUE$ , the values must be sorted in ascending order. Each $y_{i}$ must lie in the interval $(0, 1)$ .
4: a2 – double *Output: On exit: $A^{2}$ , the Anderson–Darling test statistic.
5: p – double *Output: On exit: $p$ , the upper tail probability for $A^{2}$ .
6: fail – NagError *Input/Output: The NAG error argument (see Section 3.6 in the Essential Introduction).

6 Error Indicators and Warnings

NE_BAD_PARAM: On entry, argument $⟨value⟩$ had an illegal value.
NE_BOUND: The data in y must lie in the interval $(0, 1)$ .
NE_INT: On entry, $n = ⟨value⟩$ .
Constraint: $n > 1$ .
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.
NE_NOT_INCREASING: $issort = Nag_TRUE$ and the data in y is not sorted in ascending order.

7 Accuracy

Probabilities greater than approximately

0.09

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

8 Parallelism and Performance

Not applicable.

9 Further Comments

None.

10 Example

This example calculates the

A^{2}

statistic and its

p

-value for uniform data obtained by transforming exponential variates.

NAG Library Function Documentnag_anderson_darling_uniform_prob (g08cjc)