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/*
* File: BetaDistribution.java
* Authors: Kevin R. Dixon
* Company: Sandia National Laboratories
* Project: Cognitive Foundry
*
* Copyright October 2, 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.MathUtil;
import gov.sandia.cognition.math.UnivariateStatisticsUtil;
import gov.sandia.cognition.math.matrix.VectorFactory;
import gov.sandia.cognition.math.matrix.Vector;
import gov.sandia.cognition.statistics.AbstractClosedFormSmoothUnivariateDistribution;
import gov.sandia.cognition.statistics.DistributionEstimator;
import gov.sandia.cognition.statistics.DistributionWeightedEstimator;
import gov.sandia.cognition.statistics.EstimableDistribution;
import gov.sandia.cognition.statistics.UnivariateProbabilityDensityFunction;
import gov.sandia.cognition.statistics.SmoothCumulativeDistributionFunction;
import gov.sandia.cognition.util.AbstractCloneableSerializable;
import gov.sandia.cognition.util.Pair;
import gov.sandia.cognition.util.WeightedValue;
import java.util.ArrayList;
import java.util.Collection;
import java.util.Random;
/**
* Computes the Beta-family of probability distributions.
*
* @author Kevin R. Dixon
* @since 2.0
*
*/
@PublicationReference(
author="Wikipedia",
title="Beta distribution",
type=PublicationType.WebPage,
year=2009,
url="http://en.wikipedia.org/wiki/Beta_distribution"
)
public class BetaDistribution
extends AbstractClosedFormSmoothUnivariateDistribution
implements EstimableDistribution
{
/**
* Default alpha, {@value}.
*/
public static final double DEFAULT_ALPHA = 2.0;
/**
* Default beta, {@value}.
*/
public static final double DEFAULT_BETA = 2.0;
/**
* Alpha shape parameter, must be greater than 0 (typically greater than 1)
*/
private double alpha;
/**
* Alpha shape parameter, must be greater than 0 (typically greater than 1)
*/
private double beta;
/**
* Default constructor.
*/
public BetaDistribution()
{
this( DEFAULT_ALPHA, DEFAULT_BETA );
}
/**
* Creates a new instance of BetaDistribution
* @param alpha
* Alpha shape parameter, must be greater than 0 (typically greater than 1)
* @param beta
* Beta shape parameter, must be greater than 0 (typically greater than 1)
*/
public BetaDistribution(
final double alpha,
final double beta )
{
this.setAlpha( alpha );
this.setBeta( beta );
}
/**
* Copy Constructor
* @param other
* BetaDistribution to copy
*/
public BetaDistribution(
final BetaDistribution other )
{
this( other.getAlpha(), other.getBeta() );
}
@Override
public BetaDistribution clone()
{
return (BetaDistribution) super.clone();
}
@Override
public double getMeanAsDouble()
{
return this.getAlpha() / (this.getAlpha() + this.getBeta());
}
@Override
public double getVariance()
{
double numerator = this.getAlpha() * this.getBeta();
double apb = this.getAlpha() + this.getBeta();
double denominator = apb * apb * (apb + 1);
return numerator / denominator;
}
@Override
public double sampleAsDouble(
final Random random)
{
final double x = GammaDistribution.sampleStandard(this.alpha, random);
final double y = GammaDistribution.sampleStandard(this.beta, random);
return x / (x + y);
}
@Override
public void sampleInto(
final Random random,
final double[] output,
final int start,
final int length)
{
final int end = start + length;
for (int i = start; i < end; i++)
{
output[i] = this.sampleAsDouble(random);
}
}
/**
* Gets the parameters of the distribution
* @return
* 2-dimensional Vector with [alpha beta]
*/
@Override
public Vector convertToVector()
{
return VectorFactory.getDefault().copyValues(
this.getAlpha(), this.getBeta() );
}
/**
* Sets the parameters of the distribution
* @param parameters
* 2-dimensional Vector with [alpha beta]
*/
@Override
public void convertFromVector(
final Vector parameters )
{
if (parameters.getDimensionality() != 2)
{
throw new IllegalArgumentException(
"Expecting 2-dimensional parameter Vector!" );
}
this.setAlpha( parameters.getElement( 0 ) );
this.setBeta( parameters.getElement( 1 ) );
}
/**
* Getter for alpha
* @return
* Alpha shape parameter, must be greater than 0 (typically greater than 1)
*/
public double getAlpha()
{
return this.alpha;
}
/**
* Setter for alpha
* @param alpha
* Alpha shape parameter, must be greater than 0 (typically greater than 1)
*/
public void setAlpha(
final double alpha )
{
if (alpha <= 0.0)
{
throw new IllegalArgumentException( "Alpha must be > 0.0" );
}
this.alpha = alpha;
}
/**
* Getter for beta
* @return
* Beta shape parameter, must be greater than 0 (typically greater than 1)
*/
public double getBeta()
{
return this.beta;
}
/**
* Setter for beta
* @param beta
* Beta shape parameter, must be greater than 0 (typically greater than 1)
*/
public void setBeta(
final double beta )
{
if (beta <= 0.0)
{
throw new IllegalArgumentException( "Beta must be > 0.0" );
}
this.beta = beta;
}
@Override
public BetaDistribution.CDF getCDF()
{
return new BetaDistribution.CDF( this );
}
@Override
public BetaDistribution.PDF getProbabilityFunction()
{
return new BetaDistribution.PDF( this );
}
@Override
public Double getMinSupport()
{
return 0.0;
}
@Override
public Double getMaxSupport()
{
return 1.0;
}
@Override
public BetaDistribution.MomentMatchingEstimator getEstimator()
{
return new BetaDistribution.MomentMatchingEstimator();
}
/**
* Estimates the parameters of a Beta distribution using the matching
* of moments, not maximum likelihood.
*/
@PublicationReference(
author={
"Andrew Gelman",
"John B. Carlin",
"Hal S. Stern",
"Donald B. Rubin"
},
title="Bayesian Data Analysis, Second Edition",
type=PublicationType.Book,
year=2004,
pages=582,
notes="Equation A.3"
)
public static class MomentMatchingEstimator
extends AbstractCloneableSerializable
implements DistributionEstimator
{
/**
* Default constructor
*/
public MomentMatchingEstimator()
{
}
@Override
public BetaDistribution learn(
final Collection data)
{
Pair pair =
UnivariateStatisticsUtil.computeMeanAndVariance(data);
return learn( pair.getFirst(), pair.getSecond() );
}
/**
* Computes the Beta distribution describes by the given moments
* @param mean
* Mean of the distribution
* @param variance
* Variance of the distribution
* @return
* Beta distribution that has the same mean/variance as the
* given parameters.
*/
public static BetaDistribution learn(
final double mean,
final double variance )
{
double apb = mean*(1.0-mean) / variance - 1.0;
double alpha = Math.abs(apb * mean);
double beta = Math.abs(apb * (1.0-mean));
return new BetaDistribution( alpha, beta );
}
}
/**
* Estimates the parameters of a Beta distribution using the matching
* of moments, not maximum likelihood.
*/
@PublicationReference(
author={
"Andrew Gelman",
"John B. Carlin",
"Hal S. Stern",
"Donald B. Rubin"
},
title="Bayesian Data Analysis, Second Edition",
type=PublicationType.Book,
year=2004,
pages=582,
notes="Equation A.3"
)
public static class WeightedMomentMatchingEstimator
extends AbstractCloneableSerializable
implements DistributionWeightedEstimator
{
/**
* Default constructor
*/
public WeightedMomentMatchingEstimator()
{
}
@Override
public BetaDistribution learn(
final Collection> data)
{
Pair pair =
UnivariateStatisticsUtil.computeWeightedMeanAndVariance(data);
return MomentMatchingEstimator.learn(
pair.getFirst(), pair.getSecond() );
}
}
/**
* Beta distribution probability density function
*/
public static class PDF
extends BetaDistribution
implements UnivariateProbabilityDensityFunction
{
/**
* Default constructor.
*/
public PDF()
{
super();
}
/**
* Creates a new PDF
* @param alpha
* Alpha shape parameter, must be greater than 0 (typically greater than 1)
* @param beta
* Beta shape parameter, must be greater than 0 (typically greater than 1)
*/
public PDF(
final double alpha,
final double beta )
{
super( alpha, beta );
}
/**
* Copy constructor
* @param other
* Underlying Beta Distribution
*/
public PDF(
final BetaDistribution other )
{
super( other );
}
@Override
public Double evaluate(
final Double input )
{
return this.evaluate( input.doubleValue() );
}
@Override
public double evaluateAsDouble(
final Double input)
{
return this.evaluate(input.doubleValue());
}
@Override
public double evaluate(
final double input )
{
return evaluate( input, this.getAlpha(), this.getBeta() );
}
/**
* Evaluate the Beta-distribution PDF for beta(x;alpha,beta)
* @param x
* Input to the beta PDF, must be on the interval [0,1]
* @param alpha
* Alpha shape parameter, must be greater than 0 (typically greater than 1)
* @param beta
* Beta shape parameter, must be greater than 0 (typically greater than 1)
* @return
* beta(x;alpha,beta)
*/
public static double evaluate(
final double x,
final double alpha,
final double beta )
{
double p;
if (x < 0.0)
{
p = 0.0;
}
else if (x > 1.0)
{
p = 0.0;
}
else
{
p = Math.exp( logEvaluate(x, alpha, beta) );
}
return p;
}
@Override
public double logEvaluate(
final Double input)
{
return this.logEvaluate((double) input);
}
@Override
public double logEvaluate(
final double input)
{
return logEvaluate(input, this.getAlpha(), this.getBeta() );
}
/**
* Evaluate the Beta-distribution PDF for beta(x;alpha,beta)
* @param x
* Input to the beta PDF, must be on the interval [0,1]
* @param alpha
* Alpha shape parameter, must be greater than 0 (typically greater than 1)
* @param beta
* Beta shape parameter, must be greater than 0 (typically greater than 1)
* @return
* beta(x;alpha,beta)
*/
public static double logEvaluate(
final double x,
final double alpha,
final double beta )
{
double plog;
if (x < 0.0)
{
plog = Math.log(0.0);
}
else if (x > 1.0)
{
plog = Math.log(0.0);
}
else
{
final double n1 = (alpha-1) * Math.log(x);
final double n2 = (beta-1) * Math.log( 1.0-x );
final double d1 = MathUtil.logBetaFunction( alpha, beta );
plog = n1 + n2 - d1;
}
return plog;
}
@Override
public BetaDistribution.PDF getProbabilityFunction()
{
return this;
}
}
/**
* CDF of the Beta-family distribution
*/
public static class CDF
extends BetaDistribution
implements SmoothCumulativeDistributionFunction
{
/**
* Default constructor.
*/
public CDF()
{
super();
}
/**
* Creates a new CDF
* @param alpha
* Alpha shape parameter, must be greater than 0 (typically greater than 1)
* @param beta
* Beta shape parameter, must be greater than 0 (typically greater than 1)
*/
public CDF(
final double alpha,
final double beta )
{
super( alpha, beta );
}
/**
* Copy constructor
* @param other
* Underlying Beta Distribution
*/
public CDF(
final BetaDistribution other )
{
super( other );
}
@Override
public Double evaluate(
final Double input )
{
return this.evaluate( input.doubleValue() );
}
@Override
public double evaluateAsDouble(
final Double input)
{
return this.evaluate(input.doubleValue());
}
@Override
public double evaluate(
final double input )
{
return evaluate(
input, this.getAlpha(), this.getBeta() );
}
/**
* Evaluate the Beta-distribution CDF for Beta(x;alpha,beta)
* @param x
* Input to the beta CDF, must be on the interval [0,1]
* @param alpha
* Alpha shape parameter, must be greater than 0 (typically greater than 1)
* @param beta
* Beta shape parameter, must be greater than 0 (typically greater than 1)
* @return
* Beta(x;alpha,beta)
*/
public static double evaluate(
final double x,
final double alpha,
final double beta )
{
double p;
if (x <= 0.0)
{
p = 0.0;
}
else if (x >= 1.0)
{
p = 1.0;
}
else
{
p = MathUtil.regularizedIncompleteBetaFunction( alpha, beta, x );
}
return p;
}
@Override
public BetaDistribution.CDF getCDF()
{
return this;
}
@Override
public BetaDistribution.PDF getDerivative()
{
return this.getProbabilityFunction();
}
@Override
public Double differentiate(
final Double input)
{
return this.getDerivative().evaluate(input);
}
}
}
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