The function may be called by the names: g08cjc, nag_nonpar_gofstat_anddar_unif or nag_anderson_darling_uniform_prob.
3Description
Calculates the Anderson–Darling test statistic (see g08chc) and its upper tail probability by using the approximation method of Marsaglia and Marsaglia (2004) for the case of uniformly distributed data.
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
Marsaglia G and Marsaglia J (2004) Evaluating the Anderson–Darling distribution J. Statist. Software9(2)
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: – doubleInput/Output
On entry: , for , the observations.
On exit: if , the data sorted in ascending order; otherwise the array is unchanged.
Constraint:
if , the values must be sorted in ascending order. Each must lie in the interval .
4: – double *Output
On exit: , the Anderson–Darling test statistic.
5: – double *Output
On exit: , the upper tail probability for .
6: – 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.
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 greater than approximately are accurate to five decimal places; lower value probabilities are accurate to six decimal places.
8Parallelism and Performance
Background information to multithreading can be found in the Multithreading documentation.
g08cjc 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 statistic and its -value for uniform data obtained by transforming exponential variates.