NAG CL Interface
g08cjc (gofstat_​anddar_​unif)

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1 Purpose

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>
void  g08cjc (Integer n, Nag_Boolean issort, double y[], double *a2, double *p, NagError *fail)
The function may be called by the names: g08cjc, nag_nonpar_gofstat_anddar_unif or nag_anderson_darling_uniform_prob.

3 Description

Calculates the Anderson–Darling test statistic A2 (see 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: 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] double Input/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: a2 double * Output
On exit: A2, the Anderson–Darling test statistic.
5: p double * Output
On exit: p, the upper tail probability for A2.
6: 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.
The data in y must lie in the interval (0,1).
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 greater than approximately 0.09 are accurate to five decimal places; lower value probabilities are accurate to six decimal places.

8 Parallelism and Performance

Background information to multithreading can be found in the Multithreading documentation.
g08cjc 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 statistic and its p-value for uniform data obtained by transforming exponential variates.

10.1 Program Text

Program Text (g08cjce.c)

10.2 Program Data

Program Data (g08cjce.d)

10.3 Program Results

Program Results (g08cjce.r)