NAG Library Routine Document
G08CKF calculates the Anderson–Darling goodness-of-fit test statistic and its probability for the case of a fully-unspecified Normal distribution.
||Y(N), YBAR, YVAR, A2, AA2, P
Calculates the Anderson–Darling test statistic
) and its upper tail probability for the small sample correction:
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
- 1: N – INTEGERInput
On entry: , the number of observations.
- 2: ISSORT – LOGICALInput
On entry: set if the observations are sorted in ascending order; otherwise the routine will sort the observations.
- 3: Y(N) – REAL (KIND=nag_wp) arrayInput
On entry: , for , the observations.
if , 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: , the Anderson–Darling test statistic.
- 7: AA2 – REAL (KIND=nag_wp)Output
On exit: the adjusted .
- 8: P – REAL (KIND=nag_wp)Output
On exit: , the upper tail probability for the adjusted .
- 9: IFAIL – INTEGERInput/Output
must be set to
. If you are unfamiliar with this parameter you should refer to Section 3.3
in the Essential Introduction for details.
For environments where it might be inappropriate to halt program execution when an error is detected, the value
is recommended. If the output of error messages is undesirable, then the value
is recommended. Otherwise, if you are not familiar with this parameter, the recommended value is
. When the value is used it is essential to test the value of IFAIL on exit.
unless the routine detects an error or a warning has been flagged (see Section 6
6 Error Indicators and Warnings
If on entry
, explanatory error messages are output on the current error message unit (as defined by X04AAF
Errors or warnings detected by the routine:
The data in Y
is not sorted in ascending order.
Probabilities are calculated using piecewise polynomial approximations to values estimated by simulation.
This example calculates the statistics for data assumed to arise from a fully-unspecified Normal distribution and the -value.
9.1 Program Text
Program Text (g08ckfe.f90)
9.2 Program Data
Program Data (g08ckfe.d)
9.3 Program Results
Program Results (g08ckfe.r)