nag_anderson_darling_uniform_prob (g08cjc) (PDF version)
g08 Chapter Contents
g08 Chapter Introduction
NAG C Library Manual

NAG Library Function Document

nag_anderson_darling_uniform_prob (g08cjc)

+ Contents

    1  Purpose
    7  Accuracy

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 A2 (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:     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]doubleInput/Output
On entry: yi, for i=1,2,,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 yi must lie in the interval 0,1.
4:     a2double *Output
On exit: A2, the Anderson–Darling test statistic.
5:     pdouble *Output
On exit: p, the upper tail probability for A2.
6:     failNagError *Input/Output
The NAG error argument (see Section 3.6 in the Essential Introduction).

6  Error Indicators and Warnings

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.
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  Further Comments

None.

9  Example

This example calculates the A2 statistic and its p-value for uniform data obtained by transforming exponential variates.

9.1  Program Text

Program Text (g08cjce.c)

9.2  Program Data

Program Data (g08cjce.d)

9.3  Program Results

Program Results (g08cjce.r)


nag_anderson_darling_uniform_prob (g08cjc) (PDF version)
g08 Chapter Contents
g08 Chapter Introduction
NAG C Library Manual

© The Numerical Algorithms Group Ltd, Oxford, UK. 2012