g08clf calculates the Anderson–Darling goodness-of-fit test statistic and its probability for the case of an unspecified exponential distribution.

2 Specification

Fortran Interface

Subroutine g08clf (

n, issort, y, ybar, a2, aa2, p, ifail)

Integer, Intent (In)	::	n
Integer, Intent (Inout)	::	ifail
Real (Kind=nag_wp), Intent (In)	::	y(n)
Real (Kind=nag_wp), Intent (Out)	::	ybar, a2, aa2, p
Logical, Intent (In)	::	issort

C Header Interface

#include <nag.h>

void	g08clf_ (const Integer n, const logical issort, const double y[], double ybar, double a2, double aa2, double p, Integer *ifail)

The routine may be called by the names g08clf or nagf_nonpar_gofstat_anddar_exp.

3 Description

Calculates the Anderson–Darling test statistic

A^{2}

(see g08chf) and its upper tail probability for the small sample correction:

Adjusted ​ A^{2} = A^{2} (1 + 0.6 / n),

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: $issort$ – Logical Input: On entry: set $issort = .TRUE.$ if the observations are sorted in ascending order; otherwise the routine will sort the observations.
3: $y (n)$ – Real (Kind=nag_wp) array Input: On entry: $y_{i}$ , for $i = 1, 2, \dots, n$ , the $n$ observations.

Constraint: if $issort = .TRUE.$ , values must be sorted in ascending order. Each $y_{i}$ must be greater than zero.
4: $ybar$ – Real (Kind=nag_wp) Output: On exit: the maximum likelihood estimate of mean.
5: $a2$ – Real (Kind=nag_wp) Output: On exit: $A^{2}$ , the Anderson–Darling test statistic.
6: $aa2$ – Real (Kind=nag_wp) Output: On exit: the adjusted $A^{2}$ .
7: $p$ – Real (Kind=nag_wp) Output: On exit: $p$ , the upper tail probability for the adjusted $A^{2}$ .
8: $ifail$ – Integer Input/Output: On entry: ifail must be set to $0$ , $−1$ or $1$ to set behaviour on detection of an error; these values have no effect when no error is detected.
A value of $0$ causes the printing of an error message and program execution will be halted; otherwise program execution continues. A value of $−1$ means that an error message is printed while a value of $1$ means that it is not.

If halting is not appropriate, the value $−1$ or $1$ is recommended. If message printing is undesirable, then the value $1$ is recommended. Otherwise, the value $0$ is recommended. When the value $- 1$ or $1$ is used it is essential to test the value of ifail on exit.

On exit: $ifail = 0$ unless the routine detects an error or a warning has been flagged (see Section 6).

6 Error Indicators and Warnings

If on entry

ifail = 0

−1

, explanatory error messages are output on the current error message unit (as defined by x04aaf).

Errors or warnings detected by the routine:

$ifail = 1$: On entry, $n = ⟨ value ⟩$ .
Constraint: $n > 1$ .

$ifail = 3$: $issort = .TRUE.$ and the data in y is not sorted in ascending order.

$ifail = 9$: The data in y must be greater than zero.

$ifail = - 99$: An unexpected error has been triggered by this routine. Please contact NAG.
See Section 7 in the Introduction to the NAG Library FL Interface for further information.

$ifail = - 399$: Your licence key may have expired or may not have been installed correctly.
See Section 8 in the Introduction to the NAG Library FL Interface for further information.

$ifail = - 999$: Dynamic memory allocation failed.
See Section 9 in the Introduction to the NAG Library FL Interface for further information.

7 Accuracy

Probabilities are calculated using piecewise polynomial approximations to values estimated by simulation.

8 Parallelism and Performance

g08clf 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 routine. Please also consult the Users' Note for your implementation for any additional implementation-specific information.

9 Further Comments

None.

10 Example

This example calculates the

A^{2}

statistics for data assumed to arise from an unspecified exponential distribution and calculates the

p

-value.

g08cl: FL CL CPP AD

NAG FL Interfaceg08clf (gofstat_​anddar_​exp)

▸▿ Contents

1 Purpose

2 Specification

3 Description

4 References

5 Arguments

6 Error Indicators and Warnings

7 Accuracy

8 Parallelism and Performance

9 Further Comments

10 Example

10.1 Program Text

10.2 Program Data

10.3 Program Results

NAG FL Interface
g08clf (gofstat_anddar_exp)