g08ckc calculates the Anderson–Darling goodness-of-fit test statistic and its probability for the case of a fully-unspecified Normal distribution.

2 Specification

#include <nag.h>

void	g08ckc (Integer n, Nag_Boolean issort, const double y[], double ybar, double yvar, double a2, double aa2, double p, NagError fail)

The function may be called by the names: g08ckc, nag_nonpar_gofstat_anddar_normal or nag_anderson_darling_normal_prob.

3 Description

Calculates the Anderson–Darling test statistic

A^{2}

(see g08chc) and its upper tail probability for the small sample correction:

Adjusted ​ A^{2} = A^{2} (1 + 0.75 / n + 2.25 / n^{2}),

for

n

observations.

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

Stephens M A and D'Agostino R B (1986) Goodness-of-Fit Techniques Marcel Dekker, New York

5 Arguments

1: $n$ – Integer Input: On entry: $n$ , the number of observations.

Constraint: $n > 1$ .
2: $issort$ – Nag_Boolean Input: On entry: set $issort = Nag_TRUE$ if the observations are sorted in ascending order; otherwise the function will sort the observations.
3: $y [n]$ – const double Input: On entry: $y_{i}$ , for $i = 1, 2, \dots, n$ , the $n$ observations.

Constraint: if $issort = Nag_TRUE$ , the values must be sorted in ascending order.
4: $ybar$ – double * Output: On exit: the maximum likelihood estimate of mean.
5: $yvar$ – double * Output: On exit: the maximum likelihood estimate of variance.
6: $a2$ – double * Output: On exit: $A^{2}$ , the Anderson–Darling test statistic.
7: $aa2$ – double * Output: On exit: the adjusted $A^{2}$ .
8: $p$ – double * Output: On exit: $p$ , the upper tail probability for the adjusted $A^{2}$ .
9: $fail$ – 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 $⟨ value ⟩$ had an illegal value.
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.
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_NOT_INCREASING: $issort = Nag_TRUE$ and the data in y is not sorted in ascending order.

7 Accuracy

Probabilities are calculated using piecewise polynomial approximations to values estimated by simulation.

8 Parallelism and Performance

Background information to multithreading can be found in the Multithreading documentation.

g08ckc is threaded by NAG for parallel execution in multithreaded implementations of the NAG Library.

Please consult the X06 Chapter Introduction for information on how to control and interrogate the OpenMP environment used within this function. Please also consult the Users' Note for your implementation for any additional implementation-specific information.

9 Further Comments

None.

10 Example

This example calculates the

A^{2}

statistics for data assumed to arise from a fully-unspecified Normal distribution and the

p

-value.

g08ck: FL CL CPP AD PY MB

NAG CL Interfaceg08ckc (gofstat_​anddar_​normal)

▸▿ 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

NAG CL Interface
g08ckc (gofstat_anddar_normal)