Class StandardizedTwoSampleAndersonDarlingTest
- java.lang.Object
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- elki.math.statistics.tests.StandardizedTwoSampleAndersonDarlingTest
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- 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
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Field Summary
Fields Modifier and Type Field Description static StandardizedTwoSampleAndersonDarlingTest
STATIC
Static instance.
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Constructor Summary
Constructors Constructor Description StandardizedTwoSampleAndersonDarlingTest()
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Method Summary
All Methods Instance Methods Concrete Methods Modifier and Type Method 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.
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Field Detail
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STATIC
public static final StandardizedTwoSampleAndersonDarlingTest STATIC
Static instance.
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Method Detail
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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 interfaceGoodnessOfFitTest
- Parameters:
sample1
- Full samplesample2
- Conditional sample- Returns:
- Deviation
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deviation
public double deviation(double[][] samples)
K-samples version of the Anderson-Darling test.- Parameters:
samples
- Samples- Returns:
- A2 score
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unstandardized
public double unstandardized(double[][] samples)
Compute the non-standardized A2 test statistic for the k-samples test.- Parameters:
samples
- Samples- Returns:
- Test statistic
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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
- SamplesN
- total length- Returns:
- Test statistic
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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 samplesample2
- Second sample- Returns:
- Test statistic
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totalLength
private int totalLength(double[][] samples)
Total length of a set of Samples.- Parameters:
samples
- Samples- Returns:
- Sum of the lengths.
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