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/*
* File: ExponentialDistribution.java
* Authors: Kevin R. Dixon
* Company: Sandia National Laboratories
* Project: Cognitive Foundry
*
* Copyright Dec 29, 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.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.DistributionWeightedEstimator;
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.ArgumentChecker;
import gov.sandia.cognition.util.WeightedValue;
import java.util.Collection;
import java.util.Random;
/**
* An Exponential distribution describes the time between events in a poisson
* process, resulting in a memoryless distribution.
* @author Kevin R. Dixon
* @since 3.0
*/
@PublicationReference(
author="Wikipedia",
title="Exponential distribution",
type=PublicationType.WebPage,
year=2009,
url="http://en.wikipedia.org/wiki/Exponential_distribution"
)
public class ExponentialDistribution
extends AbstractClosedFormSmoothUnivariateDistribution
implements EstimableDistribution
{
/**
* Default rate, {@value}.
*/
public static final double DEFAULT_RATE = 1.0;
/**
* Rate, or inverse scale, of the distribution, must be greater than zero.
*/
protected double rate;
/**
* Creates a new instance of ExponentialDistribution
*/
public ExponentialDistribution()
{
this( DEFAULT_RATE );
}
/**
* Creates a new instance of ExponentialDistribution
* @param rate
* Rate, or inverse scale, of the distribution, must be greater than zero.
*/
public ExponentialDistribution(
final double rate )
{
this.setRate(rate);
}
/**
* Creates a new instance of ExponentialDistribution
* @param other
* ExponentialDistribution to copy.
*/
public ExponentialDistribution(
final ExponentialDistribution other )
{
this( other.getRate() );
}
@Override
public ExponentialDistribution clone()
{
return (ExponentialDistribution) super.clone();
}
/**
* Getter for rate.
* @return
* Rate, or inverse scale, of the distribution, must be greater than zero.
*/
public double getRate()
{
return this.rate;
}
/**
* Setter for rate.
* @param rate
* Rate, or inverse scale, of the distribution, must be greater than zero.
*/
public void setRate(
final double rate)
{
ArgumentChecker.assertIsPositive("rate", rate);
this.rate = rate;
}
@Override
public double getMeanAsDouble()
{
return 1.0 / this.getRate();
}
@PublicationReference(
author={
"Christian P. Robert",
"George Casella"
},
title="Monte Carlo Statistical Methods, Second Edition",
type=PublicationType.Book,
year=2004,
pages=39,
notes="Example 2.5"
)
@Override
public double sampleAsDouble(
final Random random)
{
final double u = random.nextDouble();
return Math.log(u) / -this.rate;
}
@Override
public void sampleInto(
final Random random,
final double[] output,
final int start,
final int length)
{
final double negativeInverseScale = -1.0 / this.rate;
final int end = start + length;
for (int i = start; i < end; i++)
{
final double u = random.nextDouble();
output[i] = Math.log(u) * negativeInverseScale;
}
}
@Override
public ExponentialDistribution.CDF getCDF()
{
return new ExponentialDistribution.CDF( this );
}
@Override
public Vector convertToVector()
{
return VectorFactory.getDefault().copyValues( this.getRate() );
}
@Override
public void convertFromVector(
final Vector parameters)
{
parameters.assertDimensionalityEquals(1);
this.setRate( parameters.getElement(0) );
}
@Override
public double getVariance()
{
double d2 = this.rate * this.rate;
return 1.0/d2;
}
@Override
public ExponentialDistribution.PDF getProbabilityFunction()
{
return new ExponentialDistribution.PDF( this );
}
@Override
public Double getMinSupport()
{
return 0.0;
}
@Override
public Double getMaxSupport()
{
return Double.POSITIVE_INFINITY;
}
@Override
public ExponentialDistribution.MaximumLikelihoodEstimator getEstimator()
{
return new ExponentialDistribution.MaximumLikelihoodEstimator();
}
@Override
public String toString()
{
return "Rate: " + this.getRate();
}
/**
* PDF of the ExponentialDistribution.
*/
public static class PDF
extends ExponentialDistribution
implements UnivariateProbabilityDensityFunction
{
/**
* Default constructor.
*/
public PDF()
{
super();
}
/**
* Creates a new instance of PDF
* @param rate
* Rate, or inverse scale, of the distribution, must be greater than zero.
*/
public PDF(
final double rate )
{
super( rate );
}
/**
* Copy constructor
* @param other
* ExponentialDistribution to copy.
*/
public PDF(
final ExponentialDistribution other )
{
super( other );
}
@Override
public Double evaluate(
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)
{
if( input < 0.0 )
{
return 0.0;
}
else
{
return this.rate * Math.exp( -input * this.rate );
}
}
@Override
public double logEvaluate(
final Double input)
{
return this.logEvaluate((double) input);
}
@Override
public double logEvaluate(
final double input)
{
if( input < 0.0 )
{
return Math.log(0.0);
}
else
{
final double n1 = Math.log( this.rate );
final double n2 = -input * this.rate;
return n1 + n2;
}
}
@Override
public ExponentialDistribution.PDF getProbabilityFunction()
{
return this;
}
}
/**
* CDF of the ExponentialDistribution.
*/
public static class CDF
extends ExponentialDistribution
implements SmoothCumulativeDistributionFunction,
InvertibleCumulativeDistributionFunction
{
/**
* Default constructor.
*/
public CDF()
{
super();
}
/**
* Creates a new instance of CDF
* @param rate
* Rate, or inverse scale, of the distribution, must be greater than zero.
*/
public CDF(
final double rate )
{
super( rate );
}
/**
* Copy constructor
* @param other
* ExponentialDistribution to copy.
*/
public CDF(
final ExponentialDistribution 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)
{
if( input <= 0.0 )
{
return 0.0;
}
else
{
return 1.0 - Math.exp( -input * this.rate );
}
}
@Override
public ExponentialDistribution.CDF getCDF()
{
return this;
}
@Override
public ExponentialDistribution.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 -Math.log(1-probability) / this.rate;
}
}
}
/**
* Creates a ExponentialDistribution from data
*/
public static class MaximumLikelihoodEstimator
extends AbstractCloneableSerializable
implements DistributionEstimator
{
/**
* Default estimator.
*/
public MaximumLikelihoodEstimator()
{
}
@Override
public ExponentialDistribution learn(
final Collection data)
{
double mean = UnivariateStatisticsUtil.computeMean(data);
return new ExponentialDistribution( 1.0/mean );
}
}
/**
* Creates a ExponentialDistribution from weighted data
*/
public static class WeightedMaximumLikelihoodEstimator
extends AbstractCloneableSerializable
implements DistributionWeightedEstimator
{
/**
* Default constructor.
*/
public WeightedMaximumLikelihoodEstimator()
{
}
@Override
public ExponentialDistribution learn(
final Collection> data)
{
double mean = UnivariateStatisticsUtil.computeWeightedMean(data);
return new ExponentialDistribution(1.0/mean);
}
}
}
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