org.apache.commons.math3.distribution
Class KolmogorovSmirnovDistribution

java.lang.Object
  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:

• [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: KolmogorovSmirnovDistribution.java 3720 2012-03-16 16:34:17Z CardosoP $

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.