de.lmu.ifi.dbs.elki.math.statistics.tests

Class StandardizedTwoSampleAndersonDarlingTest

java.lang.Object

de.lmu.ifi.dbs.elki.math.statistics.tests.StandardizedTwoSampleAndersonDarlingTest

All Implemented Interfaces:

GoodnessOfFitTest

@Reference(authors="F. W. Scholz, M. A. Stephens",title="K-sample Anderson\u2013Darling tests",booktitle="Journal of the American Statistical Association, 82(399)",url="https://doi.org/10.1080/01621459.1987.10478517",bibkey="doi:10.1080/01621459.1987.10478517") @Reference(authors="D. A. Darling",title="The Kolmogorov-Smirnov, Cramer-von Mises tests",booktitle="Annals of mathematical statistics 28(4)",url="https://doi.org/10.1214/aoms/1177706788",bibkey="doi:10.1214/aoms/1177706788") @Reference(authors="A. N. Pettitt",title="A two-sample Anderson-Darling rank statistic",booktitle="Biometrika 63 (1)",url="https://doi.org/10.1093/biomet/63.1.161",bibkey="doi:10.1093/biomet/63.1.161")
public class StandardizedTwoSampleAndersonDarlingTest
extends java.lang.Object
implements GoodnessOfFitTest

Perform a two-sample Anderson-Darling rank test, and standardize the statistic according to Scholz and Stephens. Ties are handled as discussed in Equation 7 of Scholz and Stephens.

To access the non-standardized A2 scores, use the function unstandardized(double[][]).

Compared to the Cramer-van Mises test, the Anderson-Darling test puts more weight on the tail of the distribution. This variant only uses the ranks.

References:

Darling's note on this equation

D. A. Darling
The Kolmogorov-Smirnov, Cramer-von Mises tests.
Annals of Mathematical Statistics 28(4)

More detailed discussion by Pettitt

A. N. Pettitt
A two-sample Anderson-Darling rank statistic
Biometrika 63 (1)

F. W. Scholz, M. A. Stephens
K-sample Anderson–Darling tests
Journal of the American Statistical Association, 82(399)

Since:

0.7.0

Author:

Erich Schubert

Field Summary

Fields

Modifier and Type	Field and Description
static StandardizedTwoSampleAndersonDarlingTest	STATIC Static instance.

Constructor Summary

Constructors

Constructor and Description
StandardizedTwoSampleAndersonDarlingTest()

Method Summary

Modifier and Type	Method and Description
double	deviation(double[][] samples) K-samples version of the Anderson-Darling test.
double	deviation(double[] sample1, double[] sample2) Measure the deviation of a full sample from a conditional sample.
private int	totalLength(double[][] samples) Total length of a set of Samples.
double	unstandardized(double[][] samples) Compute the non-standardized A2 test statistic for the k-samples test.
private double	unstandardized(double[][] samples, int N) Compute the non-standardized A2 test statistic for the k-samples test.
double	unstandardized(double[] sample1, double[] sample2) Compute the non-standardized A2 test statistic for the k-samples test.

Methods inherited from class java.lang.Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Field Detail

STATIC

public static final StandardizedTwoSampleAndersonDarlingTest STATIC

Static instance.

Constructor Detail

StandardizedTwoSampleAndersonDarlingTest

public StandardizedTwoSampleAndersonDarlingTest()

Method Detail

deviation

public double deviation(double[] sample1,
                        double[] sample2)

Description copied from interface: GoodnessOfFitTest

Measure the deviation of a full sample from a conditional sample. Sample arrays may be modified, e.g. sorted, by the test.

Specified by:

deviation in interface GoodnessOfFitTest

Parameters:

sample1 - Full sample

sample2 - Conditional sample

Returns:

Deviation

deviation

public double deviation(double[][] samples)

K-samples version of the Anderson-Darling test.

Parameters:

samples - Samples

Returns:

A2 score

unstandardized

public double unstandardized(double[][] samples)

Compute the non-standardized A2 test statistic for the k-samples test.

Parameters:

samples - Samples

Returns:

Test statistic

unstandardized

private double unstandardized(double[][] samples,
                              int N)

Compute the non-standardized A2 test statistic for the k-samples test.

This is based on Scholz and Stephens, Equation 7.

Parameters:

samples - Samples

N - total length

Returns:

Test statistic

unstandardized

public double unstandardized(double[] sample1,
                             double[] sample2)

Compute the non-standardized A2 test statistic for the k-samples test.

This is based on Scholz and Stephens, Equation 7.

Parameters:

sample1 - First sample

sample2 - Second sample

Returns:

Test statistic

totalLength

private int totalLength(double[][] samples)

Total length of a set of Samples.

Parameters:

samples - Samples

Returns:

Sum of the lengths.