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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 2.7 in How to Use the NAG Library and its Documentation).

6 Error Indicators and Warnings

NE_ALLOC_FAIL: Dynamic memory allocation failed.
See Section 2.3.1.2 in How to Use the NAG Library and its Documentation for further information.
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.

An unexpected error has been triggered by this function. Please contact NAG.
See Section 2.7.6 in How to Use the NAG Library and its Documentation for further information.
NE_NO_LICENCE: Your licence key may have expired or may not have been installed correctly.
See Section 2.7.5 in How to Use the NAG Library and its Documentation for further information.
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

nag_anderson_darling_exp_prob (g08clc) is not threaded in any implementation.

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)