nag_anderson_darling_normal_prob (g08ckc) (PDF version)
g08 Chapter Contents
g08 Chapter Introduction
NAG Library Manual

NAG Library Function Document

nag_anderson_darling_normal_prob (g08ckc)

 Contents

    1  Purpose
    7  Accuracy

1  Purpose

nag_anderson_darling_normal_prob (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>
#include <nagg08.h>
void  nag_anderson_darling_normal_prob (Integer n, Nag_Boolean issort, const double y[], double *ybar, double *yvar, double *a2, double *aa2, double *p, NagError *fail)

3  Description

Calculates the Anderson–Darling test statistic A2 (see nag_anderson_darling_stat (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 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] const doubleInput
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 3.6 in the Essential Introduction).

6  Error Indicators and Warnings

NE_ALLOC_FAIL
Dynamic memory allocation failed.
See Section 3.2.1.2 in the Essential Introduction 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.
An unexpected error has been triggered by this function. Please contact NAG.
See Section 3.6.6 in the Essential Introduction for further information.
NE_NO_LICENCE
Your licence key may have expired or may not have been installed correctly.
See Section 3.6.5 in the Essential Introduction 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

Not applicable.

9  Further Comments

None.

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)


nag_anderson_darling_normal_prob (g08ckc) (PDF version)
g08 Chapter Contents
g08 Chapter Introduction
NAG Library Manual

© The Numerical Algorithms Group Ltd, Oxford, UK. 2015