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:     nIntegerInput
On entry: n, the number of observations.
Constraint: n>1.
2:     issortNag_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:     ybardouble *Output
On exit: the maximum likelihood estimate of mean.
5:     yvardouble *Output
On exit: the maximum likelihood estimate of variance.
6:     a2double *Output
On exit: A2, the Anderson–Darling test statistic.
7:     aa2double *Output
On exit: the adjusted A2.
8:     pdouble *Output
On exit: p, the upper tail probability for the adjusted A2.
9:     failNagError *Input/Output
The NAG error argument (see Section 3.6 in the Essential Introduction).

6  Error Indicators and Warnings

Dynamic memory allocation failed.
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.
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


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. 2014