com.numericalmethod.suanshu.stats.test.distribution.kolmogorov
Class KolmogorovSmirnov

java.lang.Object
  com.numericalmethod.suanshu.stats.test.HypothesisTest
      com.numericalmethod.suanshu.stats.test.distribution.kolmogorov.KolmogorovSmirnov

Direct Known Subclasses:

KolmogorovSmirnov1Sample, KolmogorovSmirnov2Samples

public class KolmogorovSmirnov
extends HypothesisTest

The Kolmogorov–Smirnov test (KS test) is used to compare a sample with a reference probability distribution (one-sample KS test), or to compare two samples (two-sample KS test).

The Kolmogorov–Smirnov statistic quantifies a distance between the empirical distribution function of the sample and the cumulative distribution function of the reference distribution (one-sample KS test), or between the empirical distribution functions of two samples (two-sample KS test).

The null distribution of this statistic is calculated under the null hypothesis that the sample is drawn from the reference distribution (in the one-sample case), or that the samples are drawn from the same distribution (in the two-sample case)

In each case, the distributions considered under the null hypothesis are continuous distributions but are otherwise unrestricted.

The test-statistics is either D_n, D_n⁺, or D_n^-, depending on the side to compute

By R convention, when exact p-values are not available, we use limiting distribution. Exact p-values are not available in the case of ties for one-sample case.

The R equivalent function is ks.test.

See Also:

• Nonparametric Statistical Inference. 4th edition. Jean Dickinson Gibbons, Subhabrata Chakraborti. CRC.
• Wikipedia: Kolmogorov–Smirnov test

Nested Class Summary

static class	KolmogorovSmirnov.Side the type of Kolmogorov-Smirnov statistic available
static class	KolmogorovSmirnov.Type the types of Kolmogorov-Smirnov tests available

Field Summary

KolmogorovSmirnov.Side	side the type of Kolmogorov-Smirnov statistic to be computed
KolmogorovSmirnov.Type	type the type of Kolmogorov-Smirnov test to be performed

Fields inherited from class com.numericalmethod.suanshu.stats.test.HypothesisTest

k, N, pValue, testStatistics

Method Summary

java.lang.String	alternativeHypothesis() Get a description of the alternative hypothesis.
java.lang.String	nullHypothesis() Get a description of the null hypothesis.

Methods inherited from class com.numericalmethod.suanshu.stats.test.HypothesisTest

oneSidedPvalue, pValue, rejectNull, testStatistics

Methods inherited from class java.lang.Object

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

Field Detail

type

public final KolmogorovSmirnov.Type type

the type of Kolmogorov-Smirnov test to be performed

side

public final KolmogorovSmirnov.Side side

the type of Kolmogorov-Smirnov statistic to be computed

Method Detail

nullHypothesis

public java.lang.String nullHypothesis()

Description copied from class: HypothesisTest

Get a description of the null hypothesis.

Specified by:

nullHypothesis in class HypothesisTest

Returns:

the null hypothesis description

See Also:

Wikipedia: Null hypothesis

alternativeHypothesis

public java.lang.String alternativeHypothesis()

Description copied from class: HypothesisTest

Get a description of the alternative hypothesis.

Specified by:

alternativeHypothesis in class HypothesisTest

Returns:

the alternative hypothesis description

See Also:

Wikipedia: Alternative hypothesis