NAG CL Interface
g08ckc (gofstat_​anddar_​normal)

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1 Purpose

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 A2 (see g08chc) and its upper tail probability for the small sample correction:
Adjusted ​ A2 = A2 (1+0.75/n+2.25/n2) ,  
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: yi, for i=1,2,,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: A2, the Anderson–Darling test statistic.
7: aa2 double * Output
On exit: the adjusted A2.
8: p double * Output
On exit: p, the upper tail probability for the adjusted A2.
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

Dynamic memory allocation failed.
See Section 3.1.2 in the Introduction to the NAG Library CL Interface for further information.
On entry, argument value had an illegal value.
On entry, n=value.
Constraint: n>1.
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.
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.
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


10 Example

This example calculates the A2 statistics for data assumed to arise from a fully-unspecified Normal distribution and the p-value.

10.1 Program Text

Program Text (g08ckce.c)

10.2 Program Data

Program Data (g08ckce.d)

10.3 Program Results

Program Results (g08ckce.r)