NAG Library Function Document

nag_anderson_darling_exp_prob (g08clc)

+− 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

1 Purpose

nag_anderson_darling_exp_prob (g08clc) calculates the Anderson–Darling goodness-of-fit test statistic and its probability for the case of an unspecified exponential distribution.

2 Specification

#include <nag.h>

#include <nagg08.h>

void	nag_anderson_darling_exp_prob (Integer n, Nag_Boolean issort, const double y[], double ybar, double a2, double aa2, double p, NagError *fail)

3 Description

Calculates the Anderson–Darling test statistic

A^{2}

(see nag_anderson_darling_stat (g08chc)) and its upper tail probability for the small sample correction:

Adjusted ​ A^{2} = A^{2} (1 + 0.6 / n),

for

n

observations.

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

Stephens M A and D'Agostino R B (1986) Goodness-of-Fit Techniques Marcel Dekker, New York

5 Arguments

1: n – IntegerInput: On entry: $n$ , the number of observations.
Constraint: $n > 1$ .
2: issort – Nag_BooleanInput: On entry: set $issort = Nag_TRUE$ if the observations are sorted in ascending order; otherwise the function will sort the observations.
3: y[n] – const doubleInput: On entry: $y_{i}$ , for $i = 1, 2, \dots, n$ , the $n$ observations.
Constraint: if $issort = Nag_TRUE$ , values must be sorted in ascending order. Each $y_{i}$ must be greater than zero.
4: ybar – double *Output: On exit: the maximum likelihood estimate of mean.
5: a2 – double *Output: On exit: $A^{2}$ , the Anderson–Darling test statistic.
6: aa2 – double *Output: On exit: the adjusted $A^{2}$ .
7: p – double *Output: On exit: $p$ , the upper tail probability for the adjusted $A^{2}$ .
8: fail – NagError *Input/Output: The NAG error argument (see Section 3.6 in the Essential Introduction).

6 Error Indicators and Warnings

NE_ALLOC_FAIL: Dynamic memory allocation failed.
NE_BAD_PARAM: On entry, argument $⟨value⟩$ had an illegal value.
NE_BOUND: The data in y must be greater than zero.
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.
NE_NOT_INCREASING: $issort = Nag_TRUE$ and the data in y is not sorted in ascending order.

7 Accuracy

Probabilities are calculated using piecewise polynomial approximations to values estimated by simulation.

8 Parallelism and Performance

Not applicable.

9 Further Comments

None.

10 Example

This example calculates the

A^{2}

statistics for data assumed to arise from an unspecified exponential distribution and calculates the

p

-value.

NAG Library Function Documentnag_anderson_darling_exp_prob (g08clc)