org.apache.commons.math3.distribution
Class KolmogorovSmirnovDistribution

java.lang.Object
  extended by org.apache.commons.math3.distribution.KolmogorovSmirnovDistribution
All Implemented Interfaces:
Serializable

public class KolmogorovSmirnovDistribution
extends Object
implements Serializable

Implementation of the Kolmogorov-Smirnov distribution.

Treats the distribution of the two-sided P(D_n < d) where D_n = sup_x |G(x) - G_n (x)| for the theoretical cdf G and the empirical cdf G_n.

This implementation is based on [1] with certain quick decisions for extreme values given in [2].

In short, when wanting to evaluate P(D_n < d), the method in [1] is to write d = (k - h) / n for positive integer k and 0 <= h < 1. Then P(D_n < d) = (n! / n^n) * t_kk, where t_kk is the (k, k)'th entry in the special matrix H^n, i.e. H to the n'th power.

References:

Note that [1] contains an error in computing h, refer to MATH-437 for details.

Version:
$Id: KolmogorovSmirnovDistribution.java 1416643 2012-12-03 19:37:14Z tn $
See Also:
Kolmogorov-Smirnov test (Wikipedia), Serialized Form

Constructor Summary
KolmogorovSmirnovDistribution(int n)
           
 
Method Summary
 double cdf(double d)
          Calculates P(D_n < d) using method described in [1] with quick decisions for extreme values given in [2] (see above).
 double cdf(double d, boolean exact)
          Calculates P(D_n < d) using method described in [1] with quick decisions for extreme values given in [2] (see above).
 double cdfExact(double d)
          Calculates P(D_n < d) using method described in [1] with quick decisions for extreme values given in [2] (see above).
 
Methods inherited from class java.lang.Object
clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait
 

Constructor Detail

KolmogorovSmirnovDistribution

public KolmogorovSmirnovDistribution(int n)
                              throws NotStrictlyPositiveException
Parameters:
n - Number of observations
Throws:
NotStrictlyPositiveException - if n <= 0
Method Detail

cdf

public double cdf(double d)
           throws MathArithmeticException
Calculates P(D_n < d) using method described in [1] with quick decisions for extreme values given in [2] (see above). The result is not exact as with cdfExact(double) because calculations are based on double rather than BigFraction.

Parameters:
d - statistic
Returns:
the two-sided probability of P(D_n < d)
Throws:
MathArithmeticException - if algorithm fails to convert h to a BigFraction in expressing d as (k - h) / m for integer k, m and 0 <= h < 1.

cdfExact

public double cdfExact(double d)
                throws MathArithmeticException
Calculates P(D_n < d) using method described in [1] with quick decisions for extreme values given in [2] (see above). The result is exact in the sense that BigFraction/BigReal is used everywhere at the expense of very slow execution time. Almost never choose this in real applications unless you are very sure; this is almost solely for verification purposes. Normally, you would choose cdf(double)

Parameters:
d - statistic
Returns:
the two-sided probability of P(D_n < d)
Throws:
MathArithmeticException - if algorithm fails to convert h to a BigFraction in expressing d as (k - h) / m for integer k, m and 0 <= h < 1.

cdf

public double cdf(double d,
                  boolean exact)
           throws MathArithmeticException
Calculates P(D_n < d) using method described in [1] with quick decisions for extreme values given in [2] (see above).

Parameters:
d - statistic
exact - whether the probability should be calculated exact using BigFraction everywhere at the expense of very slow execution time, or if double should be used convenient places to gain speed. Almost never choose true in real applications unless you are very sure; true is almost solely for verification purposes.
Returns:
the two-sided probability of P(D_n < d)
Throws:
MathArithmeticException - if algorithm fails to convert h to a BigFraction in expressing d as (k - h) / m for integer k, m and 0 <= h < 1.


Copyright © 2003-2013 The Apache Software Foundation. All Rights Reserved.