NAG FL Interface
g08ckf (gofstat_​anddar_​normal)

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1 Purpose

g08ckf calculates the Anderson–Darling goodness-of-fit test statistic and its probability for the case of a fully-unspecified Normal distribution.

2 Specification

Fortran Interface
Subroutine g08ckf ( n, issort, y, ybar, yvar, 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, yvar, a2, aa2, p
Logical, Intent (In) :: issort
C Header Interface
#include <nag.h>
void  g08ckf_ (const Integer *n, const logical *issort, const double y[], double *ybar, double *yvar, double *a2, double *aa2, double *p, Integer *ifail)
The routine may be called by the names g08ckf or nagf_nonpar_gofstat_anddar_normal.

3 Description

Calculates the Anderson–Darling test statistic A2 (see g08chf) 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 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: yi, for i=1,2,,n, the n observations.
Constraint: if issort=.TRUE., the values must be sorted in ascending order.
4: ybar Real (Kind=nag_wp) Output
On exit: the maximum likelihood estimate of mean.
5: yvar Real (Kind=nag_wp) Output
On exit: the maximum likelihood estimate of variance.
6: a2 Real (Kind=nag_wp) Output
On exit: A2, the Anderson–Darling test statistic.
7: aa2 Real (Kind=nag_wp) Output
On exit: the adjusted A2.
8: p Real (Kind=nag_wp) Output
On exit: p, the upper tail probability for the adjusted A2.
9: 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 or −1, explanatory error messages are output on the current error message unit (as defined by x04aaf).
Errors or warnings detected by the routine:
On entry, n=value.
Constraint: n>1.
issort=.TRUE. and the data in y is not sorted in ascending order.
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.
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.
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

Background information to multithreading can be found in the Multithreading documentation.
g08ckf 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


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 (g08ckfe.f90)

10.2 Program Data

Program Data (g08ckfe.d)

10.3 Program Results

Program Results (g08ckfe.r)