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/*
* File: UniformDistribution.java
* Authors: Kevin R. Dixon
* Company: Sandia National Laboratories
* Project: Cognitive Foundry
*
* Copyright August 16, 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.UnivariateStatisticsUtil;
import gov.sandia.cognition.math.matrix.Vector;
import gov.sandia.cognition.math.matrix.VectorFactory;
import gov.sandia.cognition.statistics.AbstractClosedFormSmoothUnivariateDistribution;
import gov.sandia.cognition.statistics.DistributionEstimator;
import gov.sandia.cognition.statistics.EstimableDistribution;
import gov.sandia.cognition.statistics.InvertibleCumulativeDistributionFunction;
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 java.util.Collection;
import java.util.Random;
/**
* Contains the (very simple) definition of a continuous Uniform distribution,
* parameterized between the minimum and maximum bounds.
*
* @author Kevin R. Dixon
* @since 3.0
*/
@PublicationReference(
author="Wikipedia",
title="Uniform distribution (continuous)",
type=PublicationType.WebPage,
year=2009,
url="http://en.wikipedia.org/wiki/Uniform_distribution_(continuous)"
)
public class UniformDistribution
extends AbstractClosedFormSmoothUnivariateDistribution
implements EstimableDistribution
{
/**
* Default min, {@value}.
*/
public static final double DEFAULT_MIN = 0.0;
/**
* Default max, {@value}.
*/
public static final double DEFAULT_MAX = 1.0;
/**
* Minimum x bound on the distribution
*/
private double minSupport;
/**
* Maximum bound on the distribution
*/
private double maxSupport;
/**
* Creates a new instance of UniformDistribution
*/
public UniformDistribution()
{
this( DEFAULT_MIN, DEFAULT_MAX );
}
/**
* Creates a new instance of UniformDistribution
* @param minSupport
* Minimum x bound on the distribution
* @param maxSupport
* Maximum bound on the distribution
*/
public UniformDistribution(
final double minSupport,
final double maxSupport )
{
this.setMinSupport( minSupport );
this.setMaxSupport( maxSupport );
}
/**
* Copy constructor
* @param other
* UniformDistribution to copy
*/
public UniformDistribution(
final UniformDistribution other )
{
this( other.getMinSupport(), other.getMaxSupport() );
}
@Override
public UniformDistribution clone()
{
return (UniformDistribution) super.clone();
}
@Override
public double getMeanAsDouble()
{
return (this.getMaxSupport() + this.getMinSupport()) / 2.0;
}
@Override
public double getVariance()
{
double d = this.getMaxSupport() - this.getMinSupport();
return d * d / 12.0;
}
@Override
public Double sample(
final Random random)
{
final double a = this.getMinSupport();
final double delta = this.getMaxSupport() - a;
double x = random.nextDouble();
return (x * delta) + a;
}
@Override
public void sampleInto(
final Random random,
final double[] output,
final int start,
final int length)
{
final double a = this.getMinSupport();
final double delta = this.getMaxSupport() - a;
final int end = start + length;
for (int i = start; i < end; i++)
{
double x = random.nextDouble();
output[i] = (x * delta) + a;
}
}
@Override
public Double getMinSupport()
{
return this.minSupport;
}
/**
* Setter for minSupport
* @param minSupport
* Minimum x bound on the distribution
*/
public void setMinSupport(
final double minSupport )
{
this.minSupport = minSupport;
}
@Override
public Double getMaxSupport()
{
return this.maxSupport;
}
/**
* Setter for maxSupport
* @param maxSupport
* Maximum x bound on the distribution
*/
public void setMaxSupport(
final double maxSupport )
{
this.maxSupport = maxSupport;
}
@Override
public Vector convertToVector()
{
return VectorFactory.getDefault().copyValues(
this.getMinSupport(), this.getMaxSupport() );
}
@Override
public void convertFromVector(
final Vector parameters )
{
parameters.assertDimensionalityEquals(2);
double a = parameters.getElement(0);
double b = parameters.getElement(1);
this.setMinSupport( Math.min(a,b) );
this.setMaxSupport( Math.max(a, b) );
}
@Override
public UniformDistribution.CDF getCDF()
{
return new UniformDistribution.CDF( this );
}
@Override
public UniformDistribution.PDF getProbabilityFunction()
{
return new UniformDistribution.PDF( this );
}
@Override
public UniformDistribution.MaximumLikelihoodEstimator getEstimator()
{
return new UniformDistribution.MaximumLikelihoodEstimator();
}
/**
* Cumulative Distribution Function of a uniform
*/
public static class CDF
extends UniformDistribution
implements SmoothCumulativeDistributionFunction,
InvertibleCumulativeDistributionFunction
{
/**
* Creates a new instance of CDF
*/
public CDF()
{
super();
}
/**
* Creates a new instance of CDF
* @param minSupport
* Minimum x bound on the distribution
* @param maxSupport
* Maximum bound on the distribution
*/
public CDF(
final double minSupport,
final double maxSupport )
{
super( minSupport, maxSupport );
}
/**
* Copy constructor
* @param other
* UniformDistribution to copy
*/
public CDF(
final UniformDistribution other )
{
super( other );
}
@Override
public UniformDistribution.CDF clone()
{
return (CDF) super.clone();
}
@Override
public double evaluate(
final double input )
{
return evaluate( input, this.getMinSupport(), this.getMaxSupport() );
}
@Override
public Double evaluate(
final Double input )
{
return this.evaluate( input.doubleValue() );
}
@Override
public double evaluateAsDouble(
final Double input)
{
return this.evaluate(input.doubleValue());
}
/**
* Evaluates the Uniform(minSupport,maxSupport) CDF for the given input
*
* @return Uniform(minSupport,maxSupport) CDF evaluated at input
* @param minSupport
* Minimum x bound on the distribution
* @param maxSupport
* Maximum x bound on the distribution
* @param input Input to evaluate the CDF at
*/
public static double evaluate(
final double input,
final double minSupport,
final double maxSupport )
{
double p;
if (input < minSupport)
{
p = 0.0;
}
else if (input > maxSupport)
{
p = 1.0;
}
else
{
p = (input - minSupport) / (maxSupport - minSupport);
}
return p;
}
@Override
public UniformDistribution.CDF getCDF()
{
return this;
}
@Override
public UniformDistribution.PDF getDerivative()
{
return this.getProbabilityFunction();
}
@Override
public Double differentiate(
final Double input)
{
return this.getDerivative().evaluate(input);
}
@Override
public Double inverse(
final double probability)
{
if( probability <= 0.0 )
{
return this.getMinSupport();
}
else if( probability >= 1.0 )
{
return this.getMaxSupport();
}
else
{
return probability*(this.getMaxSupport()-this.getMinSupport()) + this.getMinSupport();
}
}
}
/**
* Probability density function of a Uniform Distribution
*/
public static class PDF
extends UniformDistribution
implements UnivariateProbabilityDensityFunction
{
/**
* Creates a new instance of PDF
*/
public PDF()
{
super();
}
/**
* Creates a new instance of PDF
* @param minSupport
* Minimum x bound on the distribution
* @param maxSupport
* Maximum bound on the distribution
*/
public PDF(
final double minSupport,
final double maxSupport )
{
super( minSupport, maxSupport );
}
/**
* Copy constructor
* @param other
* UniformDistribution to copy
*/
public PDF(
final UniformDistribution other )
{
super( other );
}
@Override
public double evaluate(
final double input )
{
return evaluate( input, this.getMinSupport(), this.getMaxSupport() );
}
/**
* Evaluates the Uniform(minSupport,maxSupport) PDF for the given input
*
* @return Uniform(minSupport,maxSupport) PDF evaluated at input
* @param minSupport
* Minimum x bound on the distribution
* @param maxSupport
* Maximum x bound on the distribution
* @param input Input to evaluate the CDF at
*/
public static double evaluate(
final double input,
final double minSupport,
final double maxSupport )
{
if( (input < minSupport) ||
(input > maxSupport) )
{
return 0.0;
}
else
{
double d = maxSupport - minSupport;
if( d != 0.0 )
{
return 1.0/d;
}
else
{
return Double.POSITIVE_INFINITY;
}
}
}
@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 logEvaluate(
final Double input)
{
return this.logEvaluate((double) input);
}
@Override
public double logEvaluate(
final double input)
{
return Math.log( this.evaluate(input) );
}
@Override
public UniformDistribution.PDF getProbabilityFunction()
{
return this;
}
}
/**
* Maximum Likelihood Estimator of a uniform distribution.
*/
// TODO: This reference is for a discrete distribution sampled without replacement.
@PublicationReference(
author="Wikipedia",
title="German tank problem",
type=PublicationType.WebPage,
year=2010,
url="http://en.wikipedia.org/wiki/German_tank_problem"
)
public static class MaximumLikelihoodEstimator
extends AbstractCloneableSerializable
implements DistributionEstimator
{
/**
* Default constructor
*/
public MaximumLikelihoodEstimator()
{
}
@Override
public UniformDistribution.PDF learn(
final Collection data)
{
Pair result = UnivariateStatisticsUtil.computeMinAndMax(data);
final double min = result.getFirst();
final double max = result.getSecond();
final int k = data.size();
double a = min - Math.abs(min/k);
double b = max + Math.abs(max/k);
return new UniformDistribution.PDF( a, b );
}
}
}
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