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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 2.7 in How to Use the NAG Library and its Documentation).

6 Error Indicators and Warnings

NE_ALLOC_FAIL: Dynamic memory allocation failed.
See Section 2.3.1.2 in How to Use the NAG Library and its Documentation for further information.
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.

An unexpected error has been triggered by this function. Please contact NAG.
See Section 2.7.6 in How to Use the NAG Library and its Documentation for further information.
NE_NO_LICENCE: Your licence key may have expired or may not have been installed correctly.
See Section 2.7.5 in How to Use the NAG Library and its Documentation for further information.
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

nag_anderson_darling_uniform_prob (g08cjc) is not threaded in any implementation.

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)