/*
* File: WeibullDistribution.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.math.MathUtil;
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.UnivariateProbabilityDensityFunction;
import gov.sandia.cognition.statistics.SmoothCumulativeDistributionFunction;
import java.util.ArrayList;
import java.util.Random;
/**
* Describes a Weibull distribution, which is often used to describe the
* mortality, lifespan, or size distribution of objects.
* @author Kevin R. Dixon
* @since 3.0
*/
@PublicationReference(
author="Wikipedia",
title="Weibull Distribution",
type=PublicationType.WebPage,
year=2010,
url="http://en.wikipedia.org/wiki/Weibull_distribution"
)
public class WeibullDistribution
extends AbstractClosedFormSmoothUnivariateDistribution
{
/**
* Default shape, {@value}.
*/
public static final double DEFAULT_SHAPE = 1.0;
/**
* Default scale, {@value}
*/
public static final double DEFAULT_SCALE = 1.0;
/**
* Shape parameter, must be greater than 0.0
*/
protected double shape;
/**
* Scale parameter, must be greater than 0.0
*/
protected double scale;
/**
* Creates a new instance of WeibullDistribution
*/
public WeibullDistribution()
{
this( DEFAULT_SHAPE, DEFAULT_SCALE );
}
/**
* Creates a new instance of WeibullDistribution
* @param shape
* Shape parameter, must be greater than 0.0
* @param scale
* Scale parameter, must be greater than 0.0
*/
public WeibullDistribution(
final double shape,
final double scale)
{
this.shape = shape;
this.scale = scale;
}
/**
* Copy constructor
* @param other
* WeibullDistribution to copy
*/
public WeibullDistribution(
final WeibullDistribution other )
{
this( other.getShape(), other.getScale() );
}
@Override
public WeibullDistribution clone()
{
return (WeibullDistribution) super.clone();
}
/**
* Getter for shape
* @return
* Shape parameter, must be greater than 0.0
*/
public double getShape()
{
return this.shape;
}
/**
* Setter for shape
* @param shape
* Shape parameter, must be greater than 0.0
*/
public void setShape(
final double shape)
{
if( shape <= 0.0 )
{
throw new IllegalArgumentException(
"Shape must be > 0.0" );
}
this.shape = shape;
}
/**
* Getter for scale
* @return
* Scale parameter, must be greater than 0.0
*/
public double getScale()
{
return this.scale;
}
/**
* Setter for scale
* @param scale
* Scale parameter, must be greater than 0.0
*/
public void setScale(
final double scale)
{
if( scale <= 0.0 )
{
throw new IllegalArgumentException(
"Scale must be > 0.0" );
}
this.scale = scale;
}
@Override
public double getMeanAsDouble()
{
return this.scale * Math.exp( MathUtil.logGammaFunction(
1.0 + 1.0/this.shape ) );
}
@Override
public double getVariance()
{
final double mean = this.getMean();
return this.scale*this.scale * Math.exp( MathUtil.logGammaFunction(
1.0 + 2.0/this.shape ) ) - mean*mean;
}
@Override
public double sampleAsDouble(Random random)
{
final double exp = 1.0 / this.shape;
final double u = random.nextDouble();
return this.scale * Math.pow(-Math.log(u), exp);
}
@Override
public void sampleInto(
final Random random,
final double[] output,
final int start,
final int length)
{
final double exp = 1.0/this.shape;
final int end = start + length;
for (int n = start; n < end; n++)
{
final double u = random.nextDouble();
output[n] = this.scale * Math.pow(-Math.log(u), exp);
}
}
@Override
public Vector convertToVector()
{
return VectorFactory.getDefault().copyValues(
this.getShape(), this.getScale() );
}
@Override
public void convertFromVector(
final Vector parameters)
{
parameters.assertDimensionalityEquals(2);
this.setShape( parameters.getElement(0) );
this.setScale( parameters.getElement(1) );
}
@Override
public Double getMinSupport()
{
return 0.0;
}
@Override
public Double getMaxSupport()
{
return Double.POSITIVE_INFINITY;
}
@Override
public WeibullDistribution.PDF getProbabilityFunction()
{
return new WeibullDistribution.PDF( this );
}
@Override
public WeibullDistribution.CDF getCDF()
{
return new WeibullDistribution.CDF( this );
}
/**
* PDF of the Weibull distribution
*/
public static class PDF
extends WeibullDistribution
implements UnivariateProbabilityDensityFunction
{
/**
* Creates a new instance of WeibullDistribution
*/
public PDF()
{
super();
}
/**
* Creates a new instance of WeibullDistribution
* @param shape
* Shape parameter, must be greater than 0.0
* @param scale
* Scale parameter, must be greater than 0.0
*/
public PDF(
final double shape,
final double scale)
{
super( shape, scale );
}
/**
* Copy constructor
* @param other
* WeibullDistribution to copy
*/
public PDF(
final WeibullDistribution other )
{
super( other );
}
@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);
}
double logSum = 0.0;
logSum += Math.log(this.shape/this.scale);
logSum += (this.shape-1.0) * Math.log(input/this.scale);
logSum -= Math.pow( input/this.scale, this.shape );
return logSum;
}
@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(
double input)
{
return Math.exp( this.logEvaluate(input) );
}
@Override
public WeibullDistribution.PDF getProbabilityFunction()
{
return this;
}
}
/**
* CDF of the Weibull distribution
*/
public static class CDF
extends WeibullDistribution
implements SmoothCumulativeDistributionFunction
{
/**
* Creates a new instance of WeibullDistribution
*/
public CDF()
{
super();
}
/**
* Creates a new instance of WeibullDistribution
* @param shape
* Shape parameter, must be greater than 0.0
* @param scale
* Scale parameter, must be greater than 0.0
*/
public CDF(
final double shape,
final double scale)
{
super( shape, scale );
}
/**
* Copy constructor
* @param other
* WeibullDistribution to copy
*/
public CDF(
final WeibullDistribution other )
{
super( other );
}
@Override
public WeibullDistribution.PDF getDerivative()
{
return this.getProbabilityFunction();
}
@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( -Math.pow( input/this.scale, this.shape ) );
}
}
@Override
public Double differentiate(
final Double input)
{
return this.getDerivative().evaluate( input );
}
@Override
public WeibullDistribution.CDF getCDF()
{
return this;
}
}
}