The function may be called by the names: g08ckc, nag_nonpar_gofstat_anddar_normal or nag_anderson_darling_normal_prob.
3Description
Calculates the Anderson–Darling test statistic (see g08chc) and its upper tail probability for the small sample correction:
for observations.
4References
Anderson T W and Darling D A (1952) Asymptotic theory of certain ‘goodness-of-fit’ criteria based on stochastic processes Annals of Mathematical Statistics23 193–212
Stephens M A and D'Agostino R B (1986) Goodness-of-Fit Techniques Marcel Dekker, New York
5Arguments
1: – IntegerInput
On entry: , the number of observations.
Constraint:
.
2: – Nag_BooleanInput
On entry: set if the observations are sorted in ascending order; otherwise the function will sort the observations.
3: – const doubleInput
On entry: , for , the observations.
Constraint:
if , the values must be sorted in ascending order.
4: – double *Output
On exit: the maximum likelihood estimate of mean.
5: – double *Output
On exit: the maximum likelihood estimate of variance.
6: – double *Output
On exit: , the Anderson–Darling test statistic.
7: – double *Output
On exit: the adjusted .
8: – double *Output
On exit: , the upper tail probability for the adjusted .
9: – NagError *Input/Output
The NAG error argument (see Section 7 in the Introduction to the NAG Library CL Interface).
6Error Indicators and Warnings
NE_ALLOC_FAIL
Dynamic memory allocation failed.
See Section 3.1.2 in the Introduction to the NAG Library CL Interface for further information.
NE_BAD_PARAM
On entry, argument had an illegal value.
NE_INT
On entry, .
Constraint: .
NE_INTERNAL_ERROR
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.
NE_NO_LICENCE
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.
NE_NOT_INCREASING
and the data in y is not sorted in ascending order.
7Accuracy
Probabilities are calculated using piecewise polynomial approximations to values estimated by simulation.
8Parallelism and Performance
g08ckc 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.
9Further Comments
None.
10Example
This example calculates the statistics for data assumed to arise from a fully-unspecified Normal distribution and the -value.