org.apache.commons.math.distribution
Class KolmogorovSmirnovDistributionImpl

java.lang.Object
  org.apache.commons.math.distribution.KolmogorovSmirnovDistributionImpl

All Implemented Interfaces:

java.io.Serializable, KolmogorovSmirnovDistribution

public class KolmogorovSmirnovDistributionImpl
extends java.lang.Object
implements KolmogorovSmirnovDistribution, java.io.Serializable

The default implementation of KolmogorovSmirnovDistribution.

Treats the distribution of the two-sided P(Dn< d) where Dn= sup_x | G(x) - Gn (x) | for the theoretical cdf G and the emperical cdf Gn.

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

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

See also Kolmogorov-Smirnov test on Wikipedia for details.

References:

• [1] Evaluating Kolmogorov's Distribution by George Marsaglia, Wai Wan Tsang, and Jingbo Wang
• [2] Computing the Two-Sided Kolmogorov-Smirnov Distribution by Richard Simard and Pierre L'Ecuyer

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

Version:

$Id: KolmogorovSmirnovDistributionImpl.java 1178235 2011-10-02 19:43:17Z luc $

See Also:

Serialized Form

Constructor Summary

KolmogorovSmirnovDistributionImpl(int n)

Method Summary

double	cdf(double d) Calculates P(Dn < 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(Dn < d) using method described in [1] with quick decisions for extreme values given in [2] (see above).
double	cdfExact(double d) Calculates P(Dn < 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

KolmogorovSmirnovDistributionImpl

public KolmogorovSmirnovDistributionImpl(int n)

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.

Specified by:

cdf in interface KolmogorovSmirnovDistribution

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.