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, and M. A. Stephens",
           title="K-sample Anderson\u2013Darling tests",
           booktitle="Journal of the American Statistical Association, 82(399)",
           url="http://dx.doi.org/10.1080/01621459.1987.10478517")
public class StandardizedTwoSampleAndersonDarlingTest
extends 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:

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

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

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

Author:

Erich Schubert

Field Summary

Fields

Modifier and Type	Field and Description
static Void	ADDITIONAL_REFERENCE_1 Additional reference -- Darling's note on this equation
static Void	ADDITIONAL_REFERENCE_2 More detailed discussion by Pettitt
static StandardizedTwoSampleAndersonDarlingTest	STATIC Static instance.

Constructor Summary

Constructors

Constructor and Description
StandardizedTwoSampleAndersonDarlingTest()

Method Summary

Methods

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.

ADDITIONAL_REFERENCE_1

@Reference(authors="D. A. Darling",
           title="The Kolmogorov-Smirnov, Cramer-von Mises tests",
           booktitle="Annals of mathematical statistics 28(4)",
           url="http://dx.doi.org/10.1214/aoms/1177706788")
public static final Void ADDITIONAL_REFERENCE_1

Additional reference -- Darling's note on this equation

ADDITIONAL_REFERENCE_2

@Reference(authors="A. N. Pettitt",
           title="A two-sample Anderson-Darling rank statistic",
           booktitle="Biometrika 63 (1)",
           url="http://dx.doi.org/10.1093/biomet/63.1.161")
public static final Void ADDITIONAL_REFERENCE_2

More detailed discussion by Pettitt

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.