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Chapter Contents
Chapter Introduction
NAG Toolbox

NAG Toolbox: nag_nonpar_gofstat_anddar_exp (g08cl)


    1  Purpose
    2  Syntax
    7  Accuracy
    9  Example


nag_nonpar_gofstat_anddar_exp (g08cl) calculates the Anderson–Darling goodness-of-fit test statistic and its probability for the case of an unspecified exponential distribution.


[ybar, a2, aa2, p, ifail] = g08cl(issort, y, 'n', n)
[ybar, a2, aa2, p, ifail] = nag_nonpar_gofstat_anddar_exp(issort, y, 'n', n)


Calculates the Anderson–Darling test statistic A2 (see nag_nonpar_gofstat_anddar (g08ch)) and its upper tail probability for the small sample correction:
Adjusted ​ A2 = A2 1+0.6/n ,  
for n observations.


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


Compulsory Input Parameters

1:     issort – logical scalar
Set issort=true if the observations are sorted in ascending order; otherwise the function will sort the observations.
2:     yn – double array
yi, for i=1,2,,n, the n observations.
Constraint: if issort=true, values must be sorted in ascending order. Each yi must be greater than zero.

Optional Input Parameters

1:     n int64int32nag_int scalar
Default: the dimension of the array y.
n, the number of observations.
Constraint: n>1.

Output Parameters

1:     ybar – double scalar
The maximum likelihood estimate of mean.
2:     a2 – double scalar
A2, the Anderson–Darling test statistic.
3:     aa2 – double scalar
The adjusted A2.
4:     p – double scalar
p, the upper tail probability for the adjusted A2.
5:     ifail int64int32nag_int scalar
ifail=0 unless the function detects an error (see Error Indicators and Warnings).

Error Indicators and Warnings

Errors or warnings detected by the function:
Constraint: n>1.
issort=true and the data in y is not sorted in ascending order.
The data in y must be greater than zero.
An unexpected error has been triggered by this routine. Please contact NAG.
Your licence key may have expired or may not have been installed correctly.
Dynamic memory allocation failed.


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

Further Comments



This example calculates the A2 statistics for data assumed to arise from an unspecified exponential distribution and calculates the p-value.
function g08cl_example

fprintf('g08cl example results\n\n');

y = [0.4782745, 1.2858962, 1.1163891, 2.0410619, 2.2648109, 0.0833660, ...
     1.2527554, 0.4031288, 0.7808981, 0.1977674, 3.2539440, 1.8113504, ...
     1.2279834, 3.9178773, 1.4494309, 0.1358438, 1.8061778, 6.0441929, ...
     0.9671624, 3.2035042, 0.8067364, 0.4179364, 3.5351774, 0.3975414, ...
     0.6120960, 0.1332589];
% Let g08cl sort the data
issort = false;

% Calculate a-squared and probability
[ybar, a2, aa2, p, ifail] = g08cl( ...
                                   issort, y);

% Results
fprintf('H0: data from exponential distribution with mean %10.4e\n', ybar);
fprintf('Test statistic, A-squared: %8.4f\n', a2);
fprintf('Adjusted A-squared:        %8.4f\n', aa2);
fprintf('Upper tail probability:    %8.4f\n', p);

g08cl example results

H0: data from exponential distribution with mean 1.5240e+00
Test statistic, A-squared:   0.1616
Adjusted A-squared:          0.1654
Upper tail probability:      0.9831

PDF version (NAG web site, 64-bit version, 64-bit version)
Chapter Contents
Chapter Introduction
NAG Toolbox

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