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/*
* File: BinomialDistribution.java
* Authors: Kevin R. Dixon
* Company: Sandia National Laboratories
* Project: Cognitive Foundry
*
* Copyright August 19, 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.collection.IntegerCollection;
import gov.sandia.cognition.math.MathUtil;
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.AbstractClosedFormUnivariateDistribution;
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.ArrayList;
import java.util.Collection;
import java.util.Random;
/**
* Binomial distribution, which is a collection of Bernoulli trials
*
* @author Kevin R. Dixon
* @since 2.0
*
*/
@PublicationReference(
author="Wikipedia",
title="Binomial distribution",
type=PublicationType.WebPage,
year=2009,
url="http://en.wikipedia.org/wiki/Binomial_distribution"
)
public class BinomialDistribution
extends AbstractClosedFormUnivariateDistribution
implements ClosedFormDiscreteUnivariateDistribution,
EstimableDistribution
{
/**
* Default p, {@value}.
*/
public static final double DEFAULT_P = 0.5;
/**
* Default N, {@value}.
*/
public static final int DEFAULT_N = 1;
/**
* Total number of experiments, must be greater than zero
*/
private int N;
/**
* Probability of a positive outcome (Bernoulli probability), [0,1]
*/
private double p;
/**
* Default constructor.
*/
public BinomialDistribution()
{
this( DEFAULT_N, DEFAULT_P );
}
/**
* Creates a new instance of BinomialDistribution
* @param N
* Total number of experiments, must be greater than zero
* @param p
* Probability of a positive outcome (Bernoulli probability), [0,1]
*/
public BinomialDistribution(
final int N,
final double p )
{
this.setN( N );
this.setP( p );
}
/**
* Copy constructor
* @param other BinomialDistribution to copy
*/
public BinomialDistribution(
final BinomialDistribution other )
{
this( other.getN(), other.getP() );
}
@Override
public BinomialDistribution clone()
{
return (BinomialDistribution) super.clone();
}
@Override
public Double getMean()
{
return this.N * this.p;
}
/**
* Gets the variance of the distribution. This is sometimes called
* the second central moment by more pedantic people, which is equivalent
* to the square of the standard deviation.
* @return
* Variance of the distribution.
*/
@Override
public double getVariance()
{
return this.N*this.p*(1.0-this.p);
}
@Override
public ArrayList sample(
final Random random,
final int numSamples )
{
return ProbabilityMassFunctionUtil.sample(
this.getProbabilityFunction(), random, numSamples);
}
@Override
public Vector convertToVector()
{
return VectorFactory.getDefault().copyValues( this.getN(), this.getP() );
}
@Override
public void convertFromVector(
final Vector parameters )
{
if( parameters.getDimensionality() != 2 )
{
throw new IllegalArgumentException(
"Parameters must have dimension 2" );
}
this.setN( (int) parameters.getElement(0) );
this.setP( parameters.getElement(1) );
}
/**
* Getter for N
* @return
* Total number of experiments, must be greater than zero
*/
public int getN()
{
return this.N;
}
/**
* Setter for N
* @param N
* Total number of experiments, must be greater than zero
*/
public void setN(
final int N )
{
if (N < 1)
{
throw new IllegalArgumentException( "N >= 1" );
}
this.N = N;
}
/**
* 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 Collection getDomain()
{
return new IntegerCollection( 0, this.getN() );
}
@Override
public int getDomainSize()
{
return this.getN() + 1;
}
@Override
public BinomialDistribution.CDF getCDF()
{
return new BinomialDistribution.CDF( this );
}
@Override
public BinomialDistribution.PMF getProbabilityFunction()
{
return new BinomialDistribution.PMF( this );
}
@Override
public Integer getMinSupport()
{
return 0;
}
@Override
public Integer getMaxSupport()
{
return this.getN();
}
@Override
public BinomialDistribution.MaximumLikelihoodEstimator getEstimator()
{
return new BinomialDistribution.MaximumLikelihoodEstimator();
}
/**
* The Probability Mass Function of a binomial distribution.
*/
public static class PMF
extends BinomialDistribution
implements ProbabilityMassFunction
{
/**
* Default constructor.
*/
public PMF()
{
super();
}
/**
* Creates a new instance of PMF
* @param N
* Total number of experiments, must be greater than zero
* @param p
* Probability of a positive outcome (Bernoulli probability), [0,1]
*/
public PMF(
final int N,
final double p )
{
super( N, p );
}
/**
* Copy constructor
* @param other BinomialDistribution to copy
*/
public PMF(
final BinomialDistribution other )
{
super( other );
}
/**
* Returns the binomial PMF for the parameters N, k, p, which is the
* probability of exactly k successes in N experiments with expected
* per-trial success probability (Bernoulli) p
* @param input
* Number of successes
* @return
* Probability of exactly input successes in N experiments with expected
* per-trial success probability (Bernoulli) p
*/
@Override
public Double evaluate(
final Number input )
{
return evaluate( this.getN(), input.intValue(), this.getP() );
}
/**
* Returns the binomial CDF for the parameters N, k, p, which is the
* probability of exactly k successes in N experiments with expected
* per-trial success probability (Bernoulli) p
* @param N
* Total number of experiments
* @param k
* Total number of successes
* @param p
* Expected probability of success, Bernoulli parameter
* @return
* Probability of exactly k successes in N experiments with expected
* per-trial success probability (Bernoulli) p
*/
public static double evaluate(
final int N,
final int k,
final double p )
{
if (k < 0)
{
return 0.0;
}
else if (k > N)
{
return 0.0;
}
else
{
return Math.exp(logEvaluate(N, k, p));
}
}
@Override
public double logEvaluate(
final Number input)
{
return logEvaluate( this.getN(), input.intValue(), this.getP() );
}
/**
* Computes the natural logarithm of the PMF.
* @param N
* Total number of experiments
* @param k
* Total number of successes
* @param p
* Expected probability of success, Bernoulli parameter
* @return
* Computes the natural logarithm of the PMF.
*/
public static double logEvaluate(
final int N,
final int k,
final double p )
{
if (k < 0)
{
return Math.log(0.0);
}
else if (k > N)
{
return Math.log(0.0);
}
else
{
double n1 = MathUtil.logBinomialCoefficient(N, k);
double n2 = (k==0) ? 0.0 : (k * Math.log(p));
double n3 = ((N-k)==0) ? 0.0 : ((N-k) * Math.log(1.0-p));
return n1+n2+n3;
}
}
@Override
public double getEntropy()
{
return ProbabilityMassFunctionUtil.getEntropy( this );
}
@Override
public BinomialDistribution.PMF getProbabilityFunction()
{
return this;
}
}
/**
* CDF of the Binomial distribution, which is the probability of getting
* up to "x" successes in "N" trials with a Bernoulli probability of "p"
*/
public static class CDF
extends BinomialDistribution
implements ClosedFormCumulativeDistributionFunction
{
/**
* Default constructor.
*/
public CDF()
{
super();
}
/**
* Creates a new instance of BinomialDistribution
* @param N
* Total number of experiments, must be greater than zero
* @param p
* Probability of a positive outcome (Bernoulli probability), [0,1]
*/
public CDF(
final int N,
final double p )
{
super( N, p );
}
/**
* Creates a new instance of CDF
* @param other Underlying Binomial PMF to use
*/
public CDF(
final BinomialDistribution other )
{
super( other );
}
@Override
public Double evaluate(
final Number input )
{
int k = input.intValue();
return evaluate( this.getN(), k, this.getP() );
}
/**
* Evaluates the CDF for integer values of x, N, and double p
* @param k Number of successful trials
* @param N
* Total number of possibilities in the distribution
* @param p
* Bernoulli probability of a positive experiment outcome
* @return
* Value of the Binomial CDF(N,n,p)
*/
public static double evaluate(
final int N,
final int k,
final double p )
{
double retval;
if (k < 0)
{
retval = 0.0;
}
else if (k >= N)
{
retval = 1.0;
}
else
{
retval = 1.0 - MathUtil.regularizedIncompleteBetaFunction(
k + 1, N - k, p );
}
return retval;
}
@Override
public CDF getCDF()
{
return this;
}
}
/**
* Maximum likelihood estimator of the distribution
*/
public static class MaximumLikelihoodEstimator
extends AbstractCloneableSerializable
implements DistributionEstimator
{
/**
* Default constructor
*/
public MaximumLikelihoodEstimator()
{
}
@Override
public BinomialDistribution.PMF learn(
final Collection data )
{
double r = UnivariateStatisticsUtil.computeMaximum(data);
// int N = (int) Math.ceil( r );
int N = (int) Math.ceil( r + 1.0/data.size() );
double psum = 0.0;
for( Number value : data )
{
double p = value.doubleValue() / N;
psum += p;
}
double phat = psum/data.size();
return new BinomialDistribution.PMF( N, phat );
}
}
}
