The function may be called by the names: g08chc, nag_nonpar_gofstat_anddar or nag_anderson_darling_stat.
Denote by the Anderson–Darling test statistic for observations of a variable assumed to be standard uniform and sorted in ascending order, then:
When observations of a random variable are non-uniformly distributed, the probability integral transformation (PIT):
where is the cumulative distribution function of the distribution of interest, yields a uniformly distributed random variable . The PIT is true only if all parameters of a distribution are known as opposed to estimated; otherwise it is an approximation.
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
1: – IntegerInput
On entry: , the number of observations.
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.
if , the values must be sorted in ascending order. Each must lie in the interval .
4: – NagError *Input/Output
The NAG error argument (see Section 7 in the Introduction to the NAG Library CL Interface).
6Error Indicators and Warnings
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.
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.
and the data in y is not sorted in ascending order.
8Parallelism and Performance
g08chc 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.
This example calculates the statistic for data assumed to arise from an exponential distribution with a sample parameter estimate and simulates its -value using the NAG basic random number generator.