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/*
* File: GeometricDistribution.java
* Authors: Kevin R. Dixon
* Company: Sandia National Laboratories
* Project: Cognitive Foundry
*
* Copyright May 30, 2010, 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.collection.IntegerSpan;
import gov.sandia.cognition.math.ProbabilityUtil;
import gov.sandia.cognition.math.UnivariateStatisticsUtil;
import gov.sandia.cognition.math.matrix.Vector;
import gov.sandia.cognition.math.matrix.VectorFactory;
import gov.sandia.cognition.statistics.AbstractClosedFormIntegerDistribution;
import gov.sandia.cognition.statistics.ClosedFormDiscreteUnivariateDistribution;
import gov.sandia.cognition.statistics.ClosedFormCumulativeDistributionFunction;
import gov.sandia.cognition.statistics.DistributionEstimator;
import gov.sandia.cognition.statistics.EstimableDistribution;
import gov.sandia.cognition.statistics.ProbabilityMassFunction;
import gov.sandia.cognition.statistics.ProbabilityMassFunctionUtil;
import gov.sandia.cognition.util.AbstractCloneableSerializable;
import java.util.Collection;
import java.util.Random;
/**
* The geometric distribution models the number of successes before the first
* failure occurs under an independent succession of Bernoulli tests.
* @author Kevin R. Dixon
* @since 3.0
*/
@PublicationReference(
author="Mathworks",
title="Geometric Distribution",
type=PublicationType.WebPage,
year=2010,
url="http://www.mathworks.com/access/helpdesk/help/toolbox/stats/brn2ivz-58.html"
)
public class GeometricDistribution
extends AbstractClosedFormIntegerDistribution
implements ClosedFormDiscreteUnivariateDistribution,
EstimableDistribution
{
/**
* Default p, {@value}.
*/
public static final double DEFAULT_P = 0.5;
/**
* Probability of a positive outcome (Bernoulli probability), [0,1]
*/
protected double p;
/**
* Creates a new instance of GeometricDistribution
*/
public GeometricDistribution()
{
this( DEFAULT_P );
}
/**
* Creates a new instance of GeometricDistribution
* @param p
* Probability of a positive outcome (Bernoulli probability), [0,1]
*/
public GeometricDistribution(
final double p)
{
this.setP(p);
}
/**
* Copy constructor
* @param other
* GeometricDistribution to copy
*/
public GeometricDistribution(
final GeometricDistribution other )
{
this( other.getP() );
}
@Override
public GeometricDistribution clone()
{
return (GeometricDistribution) super.clone();
}
/**
* Getter for p
* @return
* Probability of a positive outcome (Bernoulli probability), [0,1]
*/
public double getP()
{
return this.p;
}
/**
* Setter for p
* @param p
* Probability of a positive outcome (Bernoulli probability), [0,1]
*/
public void setP(
final double p )
{
ProbabilityUtil.assertIsProbability(p);
this.p = p;
}
@Override
public Double getMean()
{
return this.getMeanAsDouble();
}
@Override
public double getMeanAsDouble()
{
return (1.0-this.p)/this.p;
}
@Override
public double getVariance()
{
return (1.0-this.p) / (this.p*this.p);
}
@Override
public int sampleAsInt(
final Random random)
{
final double denom = Math.log(1.0 - this.p);
final double lnu = Math.log(random.nextDouble());
return (int) Math.floor(lnu / denom);
}
@Override
public void sampleInto(
final Random random,
final int sampleCount,
final Collection output)
{
final double denom = Math.log(1.0 - this.p);
for (int n = 0; n < sampleCount; n++)
{
final double lnu = Math.log(random.nextDouble());
output.add((int) Math.floor(lnu / denom));
}
}
@Override
public Vector convertToVector()
{
return VectorFactory.getDefault().copyValues(this.getP());
}
@Override
public void convertFromVector(
Vector parameters)
{
parameters.assertDimensionalityEquals(1);
this.setP( parameters.getElement(0) );
}
@Override
public Integer getMinSupport()
{
return 0;
}
@Override
public Integer getMaxSupport()
{
return Integer.MAX_VALUE;
}
@Override
public IntegerSpan getDomain()
{
final double std = Math.sqrt( this.getVariance() );
final int max = (int) Math.ceil( std*10.0 + 10.0 );
return new IntegerSpan( this.getMinSupport(), max);
}
@Override
public int getDomainSize()
{
return getDomain().size();
}
@Override
public GeometricDistribution.CDF getCDF()
{
return new GeometricDistribution.CDF( this );
}
@Override
public GeometricDistribution.PMF getProbabilityFunction()
{
return new GeometricDistribution.PMF( this );
}
@Override
public GeometricDistribution.MaximumLikelihoodEstimator getEstimator()
{
return new GeometricDistribution.MaximumLikelihoodEstimator();
}
/**
* PMF of the Geometric distribution
*/
public static class PMF
extends GeometricDistribution
implements ProbabilityMassFunction
{
/**
* Creates a new instance of GeometricDistribution
*/
public PMF()
{
super();
}
/**
* Creates a new instance of GeometricDistribution
* @param p
* Probability of a positive outcome (Bernoulli probability), [0,1]
*/
public PMF(
final double p)
{
super( p );
}
/**
* Copy constructor
* @param other
* GeometricDistribution to copy
*/
public PMF(
final GeometricDistribution other )
{
super( other );
}
@Override
public double getEntropy()
{
return ProbabilityMassFunctionUtil.getEntropy(this);
}
@Override
public double logEvaluate(
final Number input)
{
final int k = input.intValue();
if( k < 0 )
{
return Math.log(0.0);
}
return k * Math.log( 1.0-this.p ) + Math.log( this.p );
}
@Override
public Double evaluate(
final Number input)
{
return Math.exp( this.logEvaluate(input) );
}
@Override
public GeometricDistribution.PMF getProbabilityFunction()
{
return this;
}
}
/**
* CDF of the Geometric distribution
*/
public static class CDF
extends GeometricDistribution
implements ClosedFormCumulativeDistributionFunction
{
/**
* Creates a new instance of GeometricDistribution
*/
public CDF()
{
super();
}
/**
* Creates a new instance of GeometricDistribution
* @param p
* Probability of a positive outcome (Bernoulli probability), [0,1]
*/
public CDF(
final double p)
{
super( p );
}
/**
* Copy constructor
* @param other
* GeometricDistribution to copy
*/
public CDF(
final GeometricDistribution other )
{
super( other );
}
@Override
public Double evaluate(
final Number input)
{
final int k = input.intValue();
if( k < 0 )
{
return 0.0;
}
else
{
return 1.0 - Math.pow(1.0-this.p, k+1);
}
}
@Override
public GeometricDistribution.CDF getCDF()
{
return this;
}
}
/**
* Maximum likelihood estimator of the distribution
*/
public static class MaximumLikelihoodEstimator
extends AbstractCloneableSerializable
implements DistributionEstimator
{
/**
* Default constructor
*/
public MaximumLikelihoodEstimator()
{
}
@Override
public GeometricDistribution.PMF learn(
final Collection data )
{
double mean = UnivariateStatisticsUtil.computeMean(data);
double p = 1.0/(1+mean);
return new GeometricDistribution.PMF( p );
}
}
}