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/*
* File: KolmogorovDistribution.java
* Authors: Kevin R. Dixon
* Company: Sandia National Laboratories
* Project: Cognitive Foundry
*
* Copyright July 13, 2007, Sandia Corporation. Under the terms of Contract
* DE-AC04-94AL85000, there is a non-exclusive license for use of this work by
* or on behalf of the U.S. Government. Export of this program may require a
* license from the United States Government. See CopyrightHistory.txt for
* complete details.
*
*/
package gov.sandia.cognition.statistics.distribution;
import gov.sandia.cognition.annotation.PublicationReference;
import gov.sandia.cognition.annotation.PublicationType;
import gov.sandia.cognition.math.matrix.Vector;
import gov.sandia.cognition.math.matrix.VectorFactory;
import gov.sandia.cognition.statistics.AbstractClosedFormUnivariateDistribution;
import gov.sandia.cognition.statistics.ClosedFormCumulativeDistributionFunction;
import gov.sandia.cognition.statistics.method.InverseTransformSampling;
import java.util.ArrayList;
import java.util.Collection;
import java.util.Random;
/**
* Contains the Cumulative Distribution Function description for the "D"
* statistic used within the Kolmogorov-Smirnov test.
*
* @author Kevin R. Dixon
* @since 2.0
*
*/
@PublicationReference(
author="Wikipedia",
title="Kolmogorov-Smirnov test, Kolmogorov distribution",
type=PublicationType.WebPage,
year=2009,
url="http://en.wikipedia.org/wiki/Kolmogorov_distribution#Kolmogorov_distribution"
)
public class KolmogorovDistribution
extends AbstractClosedFormUnivariateDistribution
{
/**
* Value of the mean, found empirically, as I can't seem to find the
* answer in any reference I can get my hands on, {@value}.
*/
public static final double MEAN = 0.868481392844716;
/**
* Value of the variance, found empirically, as I can't seem to find the
* answer in any reference I can get my hands on, {@value}.
*/
public static final double VARIANCE = 0.06759934611527044;
/**
* Creates a new instance of CumulativeDistribution
*/
public KolmogorovDistribution()
{
}
@Override
public Double getMean()
{
return MEAN;
}
@Override
public double getMeanAsDouble()
{
return MEAN;
}
@Override
public void sampleInto(
final Random random,
final int sampleCount,
final Collection output)
{
InverseTransformSampling.sampleInto(
this.getCDF(), random, sampleCount, output);
}
@Override
public double getVariance()
{
return VARIANCE;
}
@Override
public KolmogorovDistribution.CDF getCDF()
{
return new KolmogorovDistribution.CDF();
}
@Override
public Vector convertToVector()
{
return VectorFactory.getDefault().createVector(0);
}
@Override
public void convertFromVector(
final Vector parameters)
{
parameters.assertDimensionalityEquals(0);
}
@Override
public Double getMinSupport()
{
return 0.0;
}
@Override
public Double getMaxSupport()
{
return Double.POSITIVE_INFINITY;
}
/**
* Contains the Cumulative Distribution Function description for the "D"
* statistic used within the Kolmogorov-Smirnov test.
* This is taken from the probks() method from Numerical Recipes in C,
* p. 626.
*/
public static class CDF
extends KolmogorovDistribution
implements ClosedFormCumulativeDistributionFunction
{
/**
* Creates a new instance of CDF
*/
public CDF()
{
super();
}
@Override
public Double evaluate(
final Double input )
{
return evaluate( input.doubleValue() );
}
/**
* This is the probks() function from Numerical Recipes in C, pp. 626
* The NR probks() function actually computes the complement to the CDF,
* so all the return values in this method will be 1.0-NR, when
* comparing the code to the NR code.
* @param input
* Value at which to evaluate the CDF
* @return
* CDF value at the input
*/
@PublicationReference(
author={
"William H. Press",
"Saul A. Teukolsky",
"Willim T. Vetterling",
"Brian P. Flannery"
},
title="Numerical Recipes in C, Second Edition",
type=PublicationType.Book,
year=1992,
pages=626,
notes={
"Loosely based on the NRC probks() method.",
"Returns complement (1.0-value) of the NRC probks() method."
},
url="http://www.nrbook.com/a/bookcpdf.php"
)
public static double evaluate(
final double input )
{
if (input < 0.0)
{
return 0.0;
}
double fac = 2.0;
double sum = 0.0;
double term;
double termbf = 0.0;
double a2 = -2.0 * input * input;
final double EPS1 = 1e-3;
final double EPS2 = 1e-8;
final int MAX_ITERATIONS = 100;
for (int j = 1; j <= MAX_ITERATIONS; j++)
{
term = fac * Math.exp( a2 * j * j );
sum += term;
if ((Math.abs( term ) < EPS1 * termbf) ||
(Math.abs( term ) <= EPS2 * sum))
{
// Note: we're returning the complement of the NR function
// Sometimes the NR code will return a very small (~-1e-10)
// negative value. This just checks for that and floors it
double cdf = 1.0 - sum;
if (cdf < 0.0)
{
cdf = 0.0;
}
return cdf;
}
// Alternating signs in sum
fac = -fac;
termbf = Math.abs( term );
}
// We only reach here if we fail to converge
// Note: we're returning the complement of the NR function
return 0.0;
}
@Override
public KolmogorovDistribution.CDF getCDF()
{
return this;
}
}
}