(see g08chc) and its upper tail probability by using the approximation method of Marsaglia and Marsaglia (2004) for the case of uniformly distributed data.

4 References

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)

5 Arguments

1: $n$ – Integer Input: On entry: $n$ , the number of observations.

Constraint: $n > 1$ .
2: $issort$ – Nag_Boolean Input: On entry: set $issort = Nag_TRUE$ if the observations are sorted in ascending order; otherwise the function will sort the observations.
3: $y [n]$ – double Input/Output: On entry: $y_{i}$ , for $i = 1, 2, \dots, n$ , the $n$ observations.

On exit: if $issort = Nag_FALSE$ , the data sorted in ascending order; otherwise the array is unchanged.

Constraint: if $issort = Nag_TRUE$ , the values must be sorted in ascending order. Each $y_{i}$ must lie in the interval $(0, 1)$ .
4: $a2$ – double * Output: On exit: $A^{2}$ , the Anderson–Darling test statistic.
5: $p$ – double * Output: On exit: $p$ , the upper tail probability for $A^{2}$ .
6: $fail$ – NagError * Input/Output: The NAG error argument (see Section 7 in the Introduction to the NAG Library CL Interface).

6 Error 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 $⟨ value ⟩$ had an illegal value.
NE_BOUND: The data in y must lie in the interval $(0, 1)$ .
NE_INT: On entry, $n = ⟨ value ⟩$ .
Constraint: $n > 1$ .
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: $issort = Nag_TRUE$ and the data in y is not sorted in ascending order.

7 Accuracy

Probabilities greater than approximately

0.09

are accurate to five decimal places; lower value probabilities are accurate to six decimal places.

8 Parallelism and Performance

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.

9 Further Comments

None.

10 Example

This example calculates the

A^{2}

statistic and its

p

-value for uniform data obtained by transforming exponential variates.

g08cj: FL CL CPP AD

NAG CL Interfaceg08cjc (gofstat_​anddar_​unif)

▸▿ Contents

1 Purpose

2 Specification

3 Description

4 References

5 Arguments

6 Error Indicators and Warnings

7 Accuracy

8 Parallelism and Performance

9 Further Comments

10 Example

10.1 Program Text

10.2 Program Data

10.3 Program Results

NAG CL Interface
g08cjc (gofstat_anddar_unif)