# SuanShu, a Java numerical and statistical library

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

## Class KolmogorovSmirnov

• Direct Known Subclasses:
KolmogorovSmirnov1Sample, KolmogorovSmirnov2Samples

public abstract class KolmogorovSmirnov
extends HypothesisTest
The Kolmogorov-Smirnov test (KS test) compares 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 the 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 Dn, Dn+, or Dn-, depending on the side to compute.

By R convention, when the exact p-value is not available, we use the limiting distribution. The exact p-value is not available in the case of ties for the one-sample case.

The R equivalent function is ks.test.

• ### Nested Class Summary

Nested Classes
Modifier and Type Class and Description
static class  KolmogorovSmirnov.Side
the available types of the Kolmogorov-Smirnov statistic
static class  KolmogorovSmirnov.Type
the available types of the Kolmogorov-Smirnov tests
• ### Method Summary

All Methods
Modifier and Type Method and Description
String getAlternativeHypothesis()
Get the description of the alternative hypothesis.
String getNullHypothesis()
Get a description of the null hypothesis.
• ### Methods inherited from class com.numericalmethod.suanshu.stats.test.HypothesisTest

isNullRejected, nGroups, nObs, oneSidedPvalue, pValue, statistics
• ### Methods inherited from class java.lang.Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait
• ### Method Detail

• #### getNullHypothesis

public String getNullHypothesis()
Description copied from class: HypothesisTest
Get a description of the null hypothesis.
Specified by:
getNullHypothesis in class HypothesisTest
Returns:
the null hypothesis description
Wikipedia: Null hypothesis
• #### getAlternativeHypothesis

public String getAlternativeHypothesis()
Description copied from class: HypothesisTest
Get the description of the alternative hypothesis.
Specified by:
getAlternativeHypothesis in class HypothesisTest
Returns:
the alternative hypothesis description