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/*
* File: UnivariateRandomVariable.java
* Authors: Kevin R. Dixon
* Company: Sandia National Laboratories
* Project: Cognitive Foundry
*
* Copyright Jan 27, 2009, 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;
import gov.sandia.cognition.annotation.PublicationReference;
import gov.sandia.cognition.annotation.PublicationType;
import gov.sandia.cognition.statistics.distribution.ScalarDataDistribution;
import gov.sandia.cognition.statistics.method.ConfidenceInterval;
import gov.sandia.cognition.statistics.method.GaussianConfidence;
import gov.sandia.cognition.statistics.method.KolmogorovSmirnovConfidence;
import java.util.ArrayList;
import java.util.Collection;
import java.util.Random;
/**
* This is an implementation of a RandomVariable for scalar distributions. The
* primary method by which random-variable algebra is conducted is by
* empirically sampling the distributions, performing the algebra on the
* samples, and then fitting an empirical distribution to the resulting
* samples.
* @author Kevin R. Dixon
* @since 3.0
*/
@PublicationReference(
author="Wikipedia",
title="Algebra of random variables",
type=PublicationType.WebPage,
year=2009,
url="http://en.wikipedia.org/wiki/Algebra_of_random_variables"
)
public class UnivariateRandomVariable
extends AbstractRandomVariable
implements UnivariateDistribution
{
/**
* Default number of samples to draw from a distribution to perform the
* empirical algebra approximation, {@value}.
*/
public static final int DEFAULT_NUM_SAMPLES = 10000;
/**
* Number of samples to draw from the distribution to perform the
* empirical algebra approximation.
*/
private int numSamples;
/**
* Random number generator used for sampling the distribution.
*/
private Random random;
/**
* Scalar distribution that backs the random variable, from which samples
* will be drawn to approximate the distribution during algebra.
*/
private UnivariateDistribution distribution;
/**
* Creates a new instance of UnivariateRandomVariable
* @param distribution
* Scalar distribution that backs the random variable, from which samples
* will be drawn to approximate the distribution during algebra.
* @param random
* Random number generator used to sample the distribution
*/
public UnivariateRandomVariable(
final UnivariateDistribution distribution,
final Random random )
{
this( distribution, random, DEFAULT_NUM_SAMPLES );
}
/**
* Creates a new instance of UnivariateRandomVariable
* @param distribution
* Scalar distribution that backs the random variable, from which samples
* will be drawn to approximate the distribution during algebra.
* @param random
* Random number generator used to sample the distribution
* @param numSamples
*/
public UnivariateRandomVariable(
final UnivariateDistribution distribution,
final Random random,
final int numSamples )
{
this.setDistribution( distribution );
this.setRandom( random );
this.setNumSamples( numSamples );
}
@Override
public UnivariateRandomVariable clone()
{
return (UnivariateRandomVariable) super.clone();
}
@Override
@SuppressWarnings("unchecked")
public boolean equals(
final Object obj )
{
if( obj == null )
{
return false;
}
else if( obj == this )
{
return true;
}
else if( obj instanceof RandomVariable )
{
return this.equals( (RandomVariable) obj, 0.95 );
}
else
{
return false;
}
}
@Override
public boolean equals(
final RandomVariable other,
final double effectiveZero )
{
// effectiveZero=0.0 -> null hypothesis probability = 1.0
// effectiveZero=1.0 -> null hypothesis probability >= 0.0
// effectiveZero=0.95 -> null hypothesis probability >= 0.05
double pValue = 1.0-effectiveZero;
ArrayList data1 = this.sample( this.random, this.numSamples );
ArrayList data2 =
other.sample( this.random, this.numSamples );
KolmogorovSmirnovConfidence kstest = new KolmogorovSmirnovConfidence();
KolmogorovSmirnovConfidence.Statistic stat =
kstest.evaluateNullHypothesis( data1, data2 );
return stat.getNullHypothesisProbability() >= pValue;
}
/**
* Warning: The hashCode of this class is just the default hashCode,
* but equality uses a statistical test to see if two random variables
* are equal.
*
* @return @inheritDoc
*/
@Override
public int hashCode()
{
return super.hashCode();
}
@Override
public void plusEquals(
final RandomVariable other )
{
ArrayList X = this.sample( this.getRandom(), this.getNumSamples() );
ArrayList Y =
other.sample( this.getRandom(), this.getNumSamples() );
ArrayList Z = new ArrayList( this.getNumSamples() );
for( int n = 0; n < this.getNumSamples(); n++ )
{
Z.add( X.get(n).doubleValue() + Y.get(n).doubleValue() );
}
this.setDistribution( new ScalarDataDistribution.PMF( Z ) );
}
@Override
public void minusEquals(
final RandomVariable other )
{
ArrayList X = this.sample( this.getRandom(), this.getNumSamples() );
ArrayList Y =
other.sample( this.getRandom(), this.getNumSamples() );
ArrayList Z = new ArrayList( this.getNumSamples() );
for( int n = 0; n < this.getNumSamples(); n++ )
{
Z.add( X.get(n).doubleValue() - Y.get(n).doubleValue() );
}
this.setDistribution( new ScalarDataDistribution.PMF( Z ) );
}
@Override
public void dotTimesEquals(
final RandomVariable other )
{
ArrayList X = this.sample( this.getRandom(), this.getNumSamples() );
ArrayList Y =
other.sample( this.getRandom(), this.getNumSamples() );
ArrayList Z = new ArrayList( this.getNumSamples() );
for( int n = 0; n < this.getNumSamples(); n++ )
{
Z.add( X.get(n).doubleValue() * Y.get(n).doubleValue() );
}
this.setDistribution( new ScalarDataDistribution.PMF( Z ) );
}
@Override
public void scaleEquals(
final double scaleFactor )
{
ArrayList X = this.sample( this.getRandom(), this.getNumSamples() );
ArrayList Z = new ArrayList( this.getNumSamples() );
for( int n = 0; n < this.getNumSamples(); n++ )
{
Z.add( X.get(n).doubleValue() * scaleFactor );
}
this.setDistribution( new ScalarDataDistribution.PMF( Z ) );
}
@Override
public void scaledPlusEquals(
final double scaleFactor,
final RandomVariable other)
{
this.plusEquals(other.scale(scaleFactor));
}
@Override
public boolean isZero(
final double effectiveZero)
{
// TODO: Optimize this method to work faster.
final UnivariateRandomVariable zero = this.clone();
zero.zero();
return this.equals(zero, effectiveZero);
}
@Override
public Number sample(
final Random random)
{
return this.getDistribution().sample(random);
}
@Override
public ArrayList sample(
final Random random,
final int numSamples)
{
return new ArrayList(this.getDistribution().sample(random, numSamples));
}
@Override
public void sampleInto(
final Random random,
final int sampleCount,
final Collection output)
{
this.getDistribution().sampleInto(random, sampleCount, output);
}
/**
* Getter for numSamples
* @return
* Number of samples to draw from the distribution to perform the
* empirical algebra approximation.
*/
public int getNumSamples()
{
return this.numSamples;
}
/**
* Setter for numSamples
* @param numSamples
* Number of samples to draw from the distribution to perform the
* empirical algebra approximation.
*/
public void setNumSamples(
final int numSamples )
{
if( numSamples <= 0 )
{
throw new IllegalArgumentException(
"numSamples must be >= 1" );
}
this.numSamples = numSamples;
}
@Override
public Random getRandom()
{
return this.random;
}
@Override
public void setRandom(
final Random random )
{
this.random = random;
}
/**
* Getter for distribution
* @return
* Scalar distribution that backs the random variable, from which samples
* will be drawn to approximate the distribution during algebra.
*/
public UnivariateDistribution getDistribution()
{
return this.distribution;
}
/**
* Setter for distribution
* @param distribution
* Scalar distribution that backs the random variable, from which samples
* will be drawn to approximate the distribution during algebra.
*/
public void setDistribution(
final UnivariateDistribution distribution )
{
this.distribution = distribution;
}
@Override
public Number getMean()
{
return this.getDistribution().getMean();
}
@Override
public double getMeanAsDouble()
{
return this.getDistribution().getMeanAsDouble();
}
@Override
public double getVariance()
{
return this.getDistribution().getVariance();
}
@Override
public Double getMinSupport()
{
return Double.NEGATIVE_INFINITY;
}
@Override
public Double getMaxSupport()
{
return Double.POSITIVE_INFINITY;
}
/**
* Gets the 95% confidence interval estimated sampling error associated
* with this empirical random variable.
* @param confidence
* Confidence required. If you want 95% confidence, which is the standard
* in social science, then use 0.95.
* @return
* Estimated sampling error associated with this empirical random variable.
*/
@PublicationReference(
author="Wikipedia",
title="Standard error (statistics)",
type=PublicationType.WebPage,
year=2009,
url="http://en.wikipedia.org/wiki/Standard_error_(statistics)"
)
public ConfidenceInterval getSamplingError(
final double confidence )
{
return GaussianConfidence.computeConfidenceInterval( this, numSamples, confidence );
}
@SuppressWarnings("unchecked")
@Override
public CumulativeDistributionFunction getCDF()
{
return (CumulativeDistributionFunction) this.getDistribution().getCDF();
}
}