NAG Library Routine Document
G08CJF calculates the Anderson–Darling goodness-of-fit test statistic and its probability for the case of standard uniformly distributed data.
||Y(N), A2, P
Calculates the Anderson–Darling test statistic
) and its upper tail probability by using the approximation method of Marsaglia and Marsaglia (2004)
for the case of uniformly distributed data.
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)
- 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/Output
On entry: , for , the observations.
On exit: if , the data sorted in ascending order; otherwise the array is unchanged.
if , the values must be sorted in ascending order. Each must lie in the interval .
- 4: A2 – REAL (KIND=nag_wp)Output
On exit: , the Anderson–Darling test statistic.
- 5: P – REAL (KIND=nag_wp)Output
On exit: , the upper tail probability for .
- 6: 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.
The data in Y
must lie in the interval
Probabilities greater than approximately are accurate to five decimal places; lower value probabilities are accurate to six decimal places.
This example calculates the statistic and its -value for uniform data obtained by transforming exponential variates.
9.1 Program Text
Program Text (g08cjfe.f90)
9.2 Program Data
Program Data (g08cjfe.d)
9.3 Program Results
Program Results (g08cjfe.r)