Package smile.stat.hypothesis

Record Class KSTest

java.lang.Object
java.lang.Record
smile.stat.hypothesis.KSTest
Record Components:
method - the type of test.
d - the Kolmogorov-Smirnov statistic.
pvalue - the p-value.
public record KSTest(String method, double d, double pvalue) extends Record
The Kolmogorov-Smirnov test (K-S test) is a form of minimum distance estimation used as a non-parametric test of equality of one-dimensional probability distributions. K-S test is used to compare a sample with a reference probability distribution (one-sample K-S test), or to compare two samples (two-sample K-S 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, or between the empirical distribution functions of two samples. The null distribution of this statistic is calculated under the null hypothesis that the samples are drawn from the same distribution (in the two-sample case) or that the sample is drawn from the reference distribution (in the one-sample case). In each case, the distributions considered under the null hypothesis are continuous distributions but are otherwise unrestricted.

The two-sample KS test is one of the most useful and general non-parametric methods for comparing two samples, as it is sensitive to differences in both location and shape of the empirical cumulative distribution functions of the two samples.

The Kolmogorov-Smirnov test can be modified to serve goodness of fit test. In the special case of testing for normality of the distribution, samples are standardized and compared with a standard normal distribution. This is equivalent to setting the mean and variance of the reference distribution equal to the sample estimates, and it is known that using the sample to modify the null hypothesis reduces the power of a test. Correcting for this bias leads to the Lilliefors test. However, even Lilliefors' modification is less powerful than the Shapiro-Wilk test or Anderson-Darling test for testing normality.

  • Constructor Summary

    Constructors
    Constructor
    Description
    KSTest(String method, double d, double pvalue)
    Creates an instance of a KSTest record class.

  • Method Summary

    Modifier and Type
    Method
    Description
    double
    d()
    Returns the value of the d record component.
    final boolean
    equals(Object o)
    Indicates whether some other object is "equal to" this one.
    final int
    hashCode()
    Returns a hash code value for this object.
    String
    method()
    Returns the value of the method record component.
    double
    pvalue()
    Returns the value of the pvalue record component.
    static KSTest
    test(double[] x, double[] y)
    The two-sample KS test for the null hypothesis that the data sets are drawn from the same distribution.
    static KSTest
    test(double[] x, Distribution dist)
    The one-sample KS test for the null hypothesis that the data set x is drawn from the given distribution.
    String
    toString()
    Returns a string representation of this record class.

    Methods inherited from class java.lang.Object

    clone, finalize, getClass, notify, notifyAll, wait, wait, wait

  • Constructor Details

    • KSTest

      public KSTest(String method, double d, double pvalue)
      Creates an instance of a KSTest record class.
      Parameters:
      method - the value for the method record component
      d - the value for the d record component
      pvalue - the value for the pvalue record component

  • Method Details

    • toString

      public String toString()
      Returns a string representation of this record class. The representation contains the name of the class, followed by the name and value of each of the record components.
      Specified by:
      toString in class Record
      Returns:
      a string representation of this object

    • test

      public static KSTest test(double[] x, Distribution dist)
      The one-sample KS test for the null hypothesis that the data set x is drawn from the given distribution. Small values of p-value show that the cumulative distribution function of x is significantly different from the given distribution. The array x is modified by being sorted into ascending order.
      Parameters:
      x - the sample values.
      dist - the distribution.
      Returns:
      the test results.

    • test

      public static KSTest test(double[] x, double[] y)
      The two-sample KS test for the null hypothesis that the data sets are drawn from the same distribution. Small values of p-value show that the cumulative distribution function of x is significantly different from that of y. The arrays x and y are modified by being sorted into ascending order.
      Parameters:
      x - the sample values.
      y - the sample values.
      Returns:
      the test results.

    • hashCode

      public final int hashCode()
      Returns a hash code value for this object. The value is derived from the hash code of each of the record components.
      Specified by:
      hashCode in class Record
      Returns:
      a hash code value for this object

    • equals

      public final boolean equals(Object o)
      Indicates whether some other object is "equal to" this one. The objects are equal if the other object is of the same class and if all the record components are equal. Reference components are compared with Objects::equals(Object,Object); primitive components are compared with '=='.
      Specified by:
      equals in class Record
      Parameters:
      o - the object with which to compare
      Returns:
      true if this object is the same as the o argument; false otherwise.

    • method

      public String method()
      Returns the value of the method record component.
      Returns:
      the value of the method record component

    • d

      public double d()
      Returns the value of the d record component.
      Returns:
      the value of the d record component

    • pvalue

      public double pvalue()
      Returns the value of the pvalue record component.
      Returns:
      the value of the pvalue record component