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PR: http://nagoya.apache.org/bugzilla/show_bug.cgi?id=20488 

Submitted by:	Brent Worden

Initial submission of the distribution library


git-svn-id: https://svn.apache.org/repos/asf/jakarta/commons/proper/math/trunk@140892 13f79535-47bb-0310-9956-ffa450edef68
This commit is contained in:
Mark R. Diggory 2003-06-05 14:03:53 +00:00
parent b0bafaff5a
commit 2dec2474f9
12 changed files with 1408 additions and 211 deletions
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56
src/java/org/apache/commons/math/distribution/AbstractContinuousDistribution.java
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@ -74,7 +74,7 @@ public abstract class AbstractContinuousDistribution
}
/**
* For this disbution, X, this method returns P(x0 < X < x1). This
* For this distribution, X, this method returns P(x0 < X < x1). This
* is accomplished by using the equality P(x0 < X < x1) =
* P(X < x1) - P(X < x0).
*
@ -87,27 +87,67 @@ public abstract class AbstractContinuousDistribution
}
/**
* For this distribution, X, this method returns the critical point x, such
* that P(X &lt; x) = <code>p</code>.
*
* @param p the desired probability
* @return x, such that P(X &lt; x) = <code>p</code>
*/
public double inverseCummulativeProbability(final double p){
if(p < 0.0 || p > 1.0){
throw new IllegalArgumentException("p must be between 0.0 and 1.0 inclusive.");
throw new IllegalArgumentException(
"p must be between 0.0 and 1.0, inclusive.");
}
// by default, do simple root finding using bracketing and bisection.
// subclasses can overide if there is a better method.
UnivariateFunction rootFindingFunction = new UnivariateFunction() {
public double evaluate(double x) {
return cummulativeProbability(x) - p;
}
};
public double evaluate(double x) {
return cummulativeProbability(x) - p;
}
};
// bracket root
double[] bracket = RootFinding.bracket(rootFindingFunction, getMean(), getDomainLowerBound(), getDomainUpperBound());
double[] bracket = RootFinding.bracket(rootFindingFunction,
getInitialDomain(p), getDomainLowerBound(p),
getDomainUpperBound(p));
// find root
double root = RootFinding.bisection(rootFindingFunction, bracket[0], bracket[1]);
double root = RootFinding.bisection(rootFindingFunction, bracket[0],
bracket[1]);
return root;
}
/**
* Access the initial domain value, based on <code>p</code>, used to
* bracket a CDF root. This method is used by
* {@link #inverseCummulativeProbability(double)} to find critical values.
*
* @param p the desired probability for the critical value
* @return initial domain value
*/
protected abstract double getInitialDomain(double p);
/**
* Access the domain value lower bound, based on <code>p</code>, used to
* bracket a CDF root. This method is used by
* {@link #inverseCummulativeProbability(double)} to find critical values.
*
* @param p the desired probability for the critical value
* @return domain value lower bound, i.e.
* P(X &lt; <i>lower bound</i>) &lt; <code>p</code>
*/
protected abstract double getDomainLowerBound(double p);
/**
* Access the domain value upper bound, based on <code>p</code>, used to
* bracket a CDF root. This method is used by
* {@link #inverseCummulativeProbability(double)} to find critical values.
*
* @param p the desired probability for the critical value
* @return domain value upper bound, i.e.
* P(X &lt; <i>upper bound</i>) &gt; <code>p</code>
*/
protected abstract double getDomainUpperBound(double p);
}

87
src/java/org/apache/commons/math/distribution/ChiSquaredDistribution.java Normal file
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@ -0,0 +1,87 @@
/* ====================================================================
* The Apache Software License, Version 1.1
*
* Copyright (c) 2003 The Apache Software Foundation. All rights
* reserved.
*
* Redistribution and use in source and binary forms, with or without
* modification, are permitted provided that the following conditions
* are met:
*
* 1. Redistributions of source code must retain the above copyright
* notice, this list of conditions and the following disclaimer.
*
* 2. Redistributions in binary form must reproduce the above copyright
* notice, this list of conditions and the following disclaimer in
* the documentation and/or other materials provided with the
* distribution.
*
* 3. The end-user documentation included with the redistribution, if
* any, must include the following acknowlegement:
* "This product includes software developed by the
* Apache Software Foundation (http://www.apache.org/)."
* Alternately, this acknowlegement may appear in the software itself,
* if and wherever such third-party acknowlegements normally appear.
*
* 4. The names "The Jakarta Project", "Commons", and "Apache Software
* Foundation" must not be used to endorse or promote products derived
* from this software without prior written permission. For written
* permission, please contact apache@apache.org.
*
* 5. Products derived from this software may not be called "Apache"
* nor may "Apache" appear in their names without prior written
* permission of the Apache Software Foundation.
*
* THIS SOFTWARE IS PROVIDED ``AS IS'' AND ANY EXPRESSED OR IMPLIED
* WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES
* OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE
* DISCLAIMED. IN NO EVENT SHALL THE APACHE SOFTWARE FOUNDATION OR
* ITS CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
* SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT
* LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF
* USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND
* ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY,
* OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT
* OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
* SUCH DAMAGE.
* ====================================================================
*
* This software consists of voluntary contributions made by many
* individuals on behalf of the Apache Software Foundation. For more
* information on the Apache Software Foundation, please see
* <http://www.apache.org/>.
*/
package org.apache.commons.math.stat.distribution;
/**
* <p>
* The Chi-Squared Distribution
* </p>
*
* <p>
* Instances of ChiSquaredDistribution objects should be created using
* {@link DistributionFactory#createChiSquareDistribution(double)}
* </p>
*
* <p>
* References:
* <ul>
* <li><a href="http://mathworld.wolfram.com/Chi-SquaredDistribution.html">
* Chi-Squared Distribution</a></li>
* </p>
*
* @author Brent Worden
*/
public interface ChiSquaredDistribution extends ContinuousDistribution {
/**
* Modify the degrees of freedom.
* @param degreesOfFreedom the new degrees of freedom.
*/
void setDegreesOfFreedom(double degreesOfFreedom);
/**
* Access the degrees of freedom.
* @return the degrees of freedom.
*/
double getDegreesOfFreedom();
}

129
src/java/org/apache/commons/math/distribution/ChiSquaredDistributionImpl.java Normal file
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@ -0,0 +1,129 @@
package org.apache.commons.math.stat.distribution;
/**
* The default implementation of {@link ChiSquaredDistribution}
*
* @author Brent Worden
*/
public class ChiSquaredDistributionImpl
extends AbstractContinuousDistribution
implements ChiSquaredDistribution {
/** Internal Gamma distribution. */
private GammaDistribution gamma;
/**
* Create a Chi-Squared distribution with the given degrees of freedom.
* @param degreesOfFreedom degrees of freedom.
*/
public ChiSquaredDistributionImpl(double degreesOfFreedom){
super();
setGamma(DistributionFactory.newInstance().createGammaDistribution(
degreesOfFreedom / 2.0, 2.0));
}
/**
* Modify the degrees of freedom.
* @param degreesOfFreedom the new degrees of freedom.
*/
public void setDegreesOfFreedom(double degreesOfFreedom) {
getGamma().setAlpha(degreesOfFreedom / 2.0);
}
/**
* Access the degrees of freedom.
* @return the degrees of freedom.
*/
public double getDegreesOfFreedom() {
return getGamma().getAlpha() * 2.0;
}
/**
* For this disbution, X, this method returns P(X &lt; x).
* @param x the value at which the CDF is evaluated.
* @return CDF for this distribution.
*/
public double cummulativeProbability(double x) {
return getGamma().cummulativeProbability(x);
}
/**
* Access the domain value lower bound, based on <code>p</code>, used to
* bracket a CDF root. This method is used by
* {@link #inverseCummulativeProbability(double)} to find critical values.
*
* @param p the desired probability for the critical value
* @return domain value lower bound, i.e.
* P(X &lt; <i>lower bound</i>) &lt; <code>p</code>
*/
protected double getDomainLowerBound(double p){
return Double.MIN_VALUE * getGamma().getBeta();
}
/**
* Access the domain value upper bound, based on <code>p</code>, used to
* bracket a CDF root. This method is used by
* {@link #inverseCummulativeProbability(double)} to find critical values.
*
* @param p the desired probability for the critical value
* @return domain value upper bound, i.e.
* P(X &lt; <i>upper bound</i>) &gt; <code>p</code>
*/
protected double getDomainUpperBound(double p){
// NOTE: chi squared is skewed to the left
// NOTE: therefore, P(X < &mu;) > .5
double ret;
if(p < .5){
// use mean
ret = getDegreesOfFreedom();
} else {
// use max
ret = Double.MAX_VALUE;
}
return ret;
}
/**
* Access the initial domain value, based on <code>p</code>, used to
* bracket a CDF root. This method is used by
* {@link #inverseCummulativeProbability(double)} to find critical values.
*
* @param p the desired probability for the critical value
* @return initial domain value
*/
protected double getInitialDomain(double p){
// NOTE: chi squared is skewed to the left
// NOTE: therefore, P(X < &mu;) > .5
double ret;
if(p < .5){
// use 1/2 mean
ret = getDegreesOfFreedom() * .5;
} else {
// use mean
ret = getDegreesOfFreedom();
}
return ret;
}
/**
* Modify the Gamma distribution.
* @param gamma the new distribution.
*/
private void setGamma(GammaDistribution gamma) {
this.gamma = gamma;
}
/**
* Access the Gamma distribution.
* @return the internal Gamma distribution.
*/
private GammaDistribution getGamma() {
return gamma;
}
}

15
src/java/org/apache/commons/math/distribution/ContinuousDistribution.java
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@ -80,19 +80,4 @@ public interface ContinuousDistribution {
* @return x.
*/
double inverseCummulativeProbability(double p);
/**
*
*/
double getMean();
/**
*
*/
double getDomainLowerBound();
/**
*
*/
double getDomainUpperBound();
}

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src/java/org/apache/commons/math/distribution/DistributionFactory.java Normal file
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@ -0,0 +1,113 @@
/* ====================================================================
* The Apache Software License, Version 1.1
*
* Copyright (c) 2003 The Apache Software Foundation. All rights
* reserved.
*
* Redistribution and use in source and binary forms, with or without
* modification, are permitted provided that the following conditions
* are met:
*
* 1. Redistributions of source code must retain the above copyright
* notice, this list of conditions and the following disclaimer.
*
* 2. Redistributions in binary form must reproduce the above copyright
* notice, this list of conditions and the following disclaimer in
* the documentation and/or other materials provided with the
* distribution.
*
* 3. The end-user documentation included with the redistribution, if
* any, must include the following acknowlegement:
* "This product includes software developed by the
* Apache Software Foundation (http://www.apache.org/)."
* Alternately, this acknowlegement may appear in the software itself,
* if and wherever such third-party acknowlegements normally appear.
*
* 4. The names "The Jakarta Project", "Commons", and "Apache Software
* Foundation" must not be used to endorse or promote products derived
* from this software without prior written permission. For written
* permission, please contact apache@apache.org.
*
* 5. Products derived from this software may not be called "Apache"
* nor may "Apache" appear in their names without prior written
* permission of the Apache Software Foundation.
*
* THIS SOFTWARE IS PROVIDED ``AS IS'' AND ANY EXPRESSED OR IMPLIED
* WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES
* OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE
* DISCLAIMED. IN NO EVENT SHALL THE APACHE SOFTWARE FOUNDATION OR
* ITS CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
* SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT
* LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF
* USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND
* ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY,
* OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT
* OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
* SUCH DAMAGE.
* ====================================================================
*
* This software consists of voluntary contributions made by many
* individuals on behalf of the Apache Software Foundation. For more
* information on the Apache Software Foundation, please see
* <http://www.apache.org/>.
*/
package org.apache.commons.math.stat.distribution;
/**
* <p>
* This factory provids the means to create common statistical distributions.
* The following distributions are supported:
* <ul>
* <li>Chi-Squared</li>
* <li>Gamma</li>
* </ul>
* </p>
*
* <p>
* Common usage:<pre>
* DistributionFactory factory = DistributionFactory.newInstance();
*
* // create a Chi-Square distribution with 5 degrees of freedom.
* ChiSquaredDistribution chi = factory.createChiSquareDistribution(5.0);
* </pre>
* </p>
*
* @author Brent Worden
*/
public abstract class DistributionFactory {
/**
* Default constructor.
*/
protected DistributionFactory() {
super();
}
/**
* Create an instance of a <code>DistributionFactory</code>
* @return a new factory.
*/
public static DistributionFactory newInstance() {
// for now, return the only concrete factory.
// later, allow for a plugable implementation, possible using SPI and
// commons-discovery.
return new DistributionFactoryImpl();
}
/**
* Create a new chi-square distribution with the given degrees of freedom.
* @param degreesOfFreedom degrees of freedom.
* @return a new chi-square distribution.
*/
public abstract ChiSquaredDistribution createChiSquareDistribution(
double degreesOfFreedom
);
/**
* Create a new gamma distribution with the given alpha and beta values.
* @param alpha the shape parameter.
* @param beta the scale parameter.
* @return a new gamma distribution.
*/
public abstract GammaDistribution createGammaDistribution(
double alpha, double beta);
}

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src/java/org/apache/commons/math/distribution/DistributionFactoryImpl.java Normal file
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@ -0,0 +1,93 @@
/* ====================================================================
* The Apache Software License, Version 1.1
*
* Copyright (c) 2003 The Apache Software Foundation. All rights
* reserved.
*
* Redistribution and use in source and binary forms, with or without
* modification, are permitted provided that the following conditions
* are met:
*
* 1. Redistributions of source code must retain the above copyright
* notice, this list of conditions and the following disclaimer.
*
* 2. Redistributions in binary form must reproduce the above copyright
* notice, this list of conditions and the following disclaimer in
* the documentation and/or other materials provided with the
* distribution.
*
* 3. The end-user documentation included with the redistribution, if
* any, must include the following acknowlegement:
* "This product includes software developed by the
* Apache Software Foundation (http://www.apache.org/)."
* Alternately, this acknowlegement may appear in the software itself,
* if and wherever such third-party acknowlegements normally appear.
*
* 4. The names "The Jakarta Project", "Commons", and "Apache Software
* Foundation" must not be used to endorse or promote products derived
* from this software without prior written permission. For written
* permission, please contact apache@apache.org.
*
* 5. Products derived from this software may not be called "Apache"
* nor may "Apache" appear in their names without prior written
* permission of the Apache Software Foundation.
*
* THIS SOFTWARE IS PROVIDED ``AS IS'' AND ANY EXPRESSED OR IMPLIED
* WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES
* OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE
* DISCLAIMED. IN NO EVENT SHALL THE APACHE SOFTWARE FOUNDATION OR
* ITS CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
* SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT
* LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF
* USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND
* ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY,
* OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT
* OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
* SUCH DAMAGE.
* ====================================================================
*
* This software consists of voluntary contributions made by many
* individuals on behalf of the Apache Software Foundation. For more
* information on the Apache Software Foundation, please see
* <http://www.apache.org/>.
*/
package org.apache.commons.math.stat.distribution;
/**
* A concrete distribution factory. This is the default factory used by
* Commons-Math.
*
* @author Brent Worden
*/
public class DistributionFactoryImpl extends DistributionFactory {
/**
* Default constructor. Package scope to prevent unwanted instantiation.
*/
DistributionFactoryImpl() {
super();
}
/**
* Create a new chi-square distribution with the given degrees of freedom.
* @param degreesOfFreedom degrees of freedom.
* @return a new chi-square distribution.
*/
public ChiSquaredDistribution createChiSquareDistribution(
final double degreesOfFreedom) {
return new ChiSquaredDistributionImpl(degreesOfFreedom);
}
/**
* Create a new gamma distribution the given alpha and beta values.
* @param alpha the shape parameter.
* @param beta the scale parameter.
* @return a new gamma distribution.
*/
public GammaDistribution createGammaDistribution(
double alpha, double beta) {
return new GammaDistributionImpl(alpha, beta);
}
}

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src/java/org/apache/commons/math/distribution/GammaDistribution.java Normal file
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@ -0,0 +1,99 @@
/* ====================================================================
* The Apache Software License, Version 1.1
*
* Copyright (c) 2003 The Apache Software Foundation. All rights
* reserved.
*
* Redistribution and use in source and binary forms, with or without
* modification, are permitted provided that the following conditions
* are met:
*
* 1. Redistributions of source code must retain the above copyright
* notice, this list of conditions and the following disclaimer.
*
* 2. Redistributions in binary form must reproduce the above copyright
* notice, this list of conditions and the following disclaimer in
* the documentation and/or other materials provided with the
* distribution.
*
* 3. The end-user documentation included with the redistribution, if
* any, must include the following acknowlegement:
* "This product includes software developed by the
* Apache Software Foundation (http://www.apache.org/)."
* Alternately, this acknowlegement may appear in the software itself,
* if and wherever such third-party acknowlegements normally appear.
*
* 4. The names "The Jakarta Project", "Commons", and "Apache Software
* Foundation" must not be used to endorse or promote products derived
* from this software without prior written permission. For written
* permission, please contact apache@apache.org.
*
* 5. Products derived from this software may not be called "Apache"
* nor may "Apache" appear in their names without prior written
* permission of the Apache Software Foundation.
*
* THIS SOFTWARE IS PROVIDED ``AS IS'' AND ANY EXPRESSED OR IMPLIED
* WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES
* OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE
* DISCLAIMED. IN NO EVENT SHALL THE APACHE SOFTWARE FOUNDATION OR
* ITS CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
* SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT
* LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF
* USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND
* ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY,
* OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT
* OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
* SUCH DAMAGE.
* ====================================================================
*
* This software consists of voluntary contributions made by many
* individuals on behalf of the Apache Software Foundation. For more
* information on the Apache Software Foundation, please see
* <http://www.apache.org/>.
*/
package org.apache.commons.math.stat.distribution;
/**
* <p>
* The Gamma Distribution
* </p>
*
* <p>
* Instances of GammaDistribution objects should be created using
* {@link DistributionFactory#createGammaDistribution(double)}
* </p>
*
* <p>
* References:
* <ul>
* <li><a href="http://mathworld.wolfram.com/GammaDistribution.html">
* Gamma Distribution</a></li>
* </p>
*
* @author Brent Worden
*/
public interface GammaDistribution extends ContinuousDistribution {
/**
* Modify the shape parameter, alpha.
* @param alpha the new shape parameter.
*/
void setAlpha(double alpha);
/**
* Access the shape parameter, alpha
* @return alpha.
*/
double getAlpha();
/**
* Modify the scale parameter, beta.
* @param beta the new scale parameter.
*/
void setBeta(double beta);
/**
* Access the scale parameter, beta
* @return beta.
*/
double getBeta();
}

218
src/java/org/apache/commons/math/distribution/GammaDistributionImpl.java Normal file
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@ -0,0 +1,218 @@
/* ====================================================================
* The Apache Software License, Version 1.1
*
* Copyright (c) 2003 The Apache Software Foundation. All rights
* reserved.
*
* Redistribution and use in source and binary forms, with or without
* modification, are permitted provided that the following conditions
* are met:
*
* 1. Redistributions of source code must retain the above copyright
* notice, this list of conditions and the following disclaimer.
*
* 2. Redistributions in binary form must reproduce the above copyright
* notice, this list of conditions and the following disclaimer in
* the documentation and/or other materials provided with the
* distribution.
*
* 3. The end-user documentation included with the redistribution, if
* any, must include the following acknowlegement:
* "This product includes software developed by the
* Apache Software Foundation (http://www.apache.org/)."
* Alternately, this acknowlegement may appear in the software itself,
* if and wherever such third-party acknowlegements normally appear.
*
* 4. The names "The Jakarta Project", "Commons", and "Apache Software
* Foundation" must not be used to endorse or promote products derived
* from this software without prior written permission. For written
* permission, please contact apache@apache.org.
*
* 5. Products derived from this software may not be called "Apache"
* nor may "Apache" appear in their names without prior written
* permission of the Apache Software Foundation.
*
* THIS SOFTWARE IS PROVIDED ``AS IS'' AND ANY EXPRESSED OR IMPLIED
* WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES
* OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE
* DISCLAIMED. IN NO EVENT SHALL THE APACHE SOFTWARE FOUNDATION OR
* ITS CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
* SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT
* LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF
* USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND
* ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY,
* OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT
* OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
* SUCH DAMAGE.
* ====================================================================
*
* This software consists of voluntary contributions made by many
* individuals on behalf of the Apache Software Foundation. For more
* information on the Apache Software Foundation, please see
* <http://www.apache.org/>.
*/
package org.apache.commons.math.stat.distribution;
import org.apache.commons.math.special.Gamma;
/**
* The default implementation of {@link GammaDistribution}
*
* @author Brent Worden
*/
public class GammaDistributionImpl extends AbstractContinuousDistribution
implements GammaDistribution {
/** The shape parameter. */
private double alpha;
/** The scale parameter. */
private double beta;
/**
* Create a new gamma distribution with the given alpha and beta values.
* @param alpha the shape parameter.
* @param beta the scale parameter.
*/
public GammaDistributionImpl(double alpha, double beta) {
super();
setAlpha(alpha);
setBeta(beta);
}
/**
* <p>
* For this disbution, X, this method returns P(X &lt; x).
* </p>
*
* <p>
* The implementation of this method is based on:
* <ul>
* <li>
* <a href="http://mathworld.wolfram.com/Chi-SquaredDistribution.html">
* Chi-Squared Distribution</a>, equation (9).</li>
* <li>Casella, G., & Berger, R. (1990). <i>Statistical Inference</i>.
* Belmont, CA: Duxbury Press.</li>
* </ul>
* </p>
*
* @param x the value at which the CDF is evaluated.
* @return CDF for this distribution.
*/
public double cummulativeProbability(double x) {
double ret;
if (x <= 0.0) {
ret = 0.0;
} else {
ret = Gamma.regularizedGammaP(getAlpha(), x / getBeta());
}
return ret;
}
/**
* Modify the shape parameter, alpha.
* @param alpha the new shape parameter.
*/
public void setAlpha(double alpha) {
if (alpha <= 0.0) {
throw new IllegalArgumentException("alpha must be positive");
}
this.alpha = alpha;
}
/**
* Access the shape parameter, alpha
* @return alpha.
*/
public double getAlpha() {
return alpha;
}
/**
* Modify the scale parameter, beta.
* @param beta the new scale parameter.
*/
public void setBeta(double beta) {
if (beta <= 0.0) {
throw new IllegalArgumentException("beta must be positive");
}
this.beta = beta;
}
/**
* Access the scale parameter, beta
* @return beta.
*/
public double getBeta() {
return beta;
}
/**
* Access the domain value lower bound, based on <code>p</code>, used to
* bracket a CDF root. This method is used by
* {@link #inverseCummulativeProbability(double)} to find critical values.
*
* @param p the desired probability for the critical value
* @return domain value lower bound, i.e.
* P(X &lt; <i>lower bound</i>) &lt; <code>p</code>
*/
protected double getDomainLowerBound(double p) {
// TODO: try to improve on this estimate
return Double.MIN_VALUE;
}
/**
* Access the domain value upper bound, based on <code>p</code>, used to
* bracket a CDF root. This method is used by
* {@link #inverseCummulativeProbability(double)} to find critical values.
*
* @param p the desired probability for the critical value
* @return domain value upper bound, i.e.
* P(X &lt; <i>upper bound</i>) &gt; <code>p</code>
*/
protected double getDomainUpperBound(double p) {
// NOTE: gamma is skewed to the left
// NOTE: therefore, P(X < &mu;) > .5
// TODO: try to improve on this estimate
double ret;
if(p < .5){
// use mean
ret = getAlpha() * getBeta();
} else {
// use max value
ret = Double.MAX_VALUE;
}
return ret;
}
/**
* Access the initial domain value, based on <code>p</code>, used to
* bracket a CDF root. This method is used by
* {@link #inverseCummulativeProbability(double)} to find critical values.
*
* @param p the desired probability for the critical value
* @return initial domain value
*/
protected double getInitialDomain(double p) {
// NOTE: gamma is skewed to the left
// NOTE: therefore, P(X < &mu;) > .5
// TODO: try to improve on this estimate
double ret;
if(p < .5){
// use 1/2 mean
ret = getAlpha() * getBeta() * .5;
} else {
// use mean
ret = getAlpha() * getBeta();
}
return ret;
}
}

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/* ====================================================================
* The Apache Software License, Version 1.1
*
* Copyright (c) 2003 The Apache Software Foundation. All rights
* reserved.
*
* Redistribution and use in source and binary forms, with or without
* modification, are permitted provided that the following conditions
* are met:
*
* 1. Redistributions of source code must retain the above copyright
* notice, this list of conditions and the following disclaimer.
*
* 2. Redistributions in binary form must reproduce the above copyright
* notice, this list of conditions and the following disclaimer in
* the documentation and/or other materials provided with the
* distribution.
*
* 3. The end-user documentation included with the redistribution, if
* any, must include the following acknowlegement:
* "This product includes software developed by the
* Apache Software Foundation (http://www.apache.org/)."
* Alternately, this acknowlegement may appear in the software itself,
* if and wherever such third-party acknowlegements normally appear.
*
* 4. The names "The Jakarta Project", "Commons", and "Apache Software
* Foundation" must not be used to endorse or promote products derived
* from this software without prior written permission. For written
* permission, please contact apache@apache.org.
*
* 5. Products derived from this software may not be called "Apache"
* nor may "Apache" appear in their names without prior written
* permission of the Apache Software Foundation.
*
* THIS SOFTWARE IS PROVIDED ``AS IS'' AND ANY EXPRESSED OR IMPLIED
* WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES
* OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE
* DISCLAIMED. IN NO EVENT SHALL THE APACHE SOFTWARE FOUNDATION OR
* ITS CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
* SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT
* LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF
* USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND
* ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY,
* OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT
* OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
* SUCH DAMAGE.
* ====================================================================
*
* This software consists of voluntary contributions made by many
* individuals on behalf of the Apache Software Foundation. For more
* information on the Apache Software Foundation, please see
* <http://www.apache.org/>.
*/
package org.apache.commons.math.special;
import org.apache.commons.math.ConvergenceException;
/**
* This is a utility class that provides computation methods related to the
* Gamma family of functions.
*
* @author Brent Worden
*/
public class Gamma {
/** Maximum number of iteration allowed for iterative methods. */
// TODO: try to reduce this. regularizedGammaP doesn't converge very
// fast for large values of x.
private static final int MAXIMUM_ITERATIONS = 100;
/** Maximum allowed numerical error. */
private static final double EPSILON = 10e-9;
/**
* Default constructor. Prohibit instantiation.
*/
private Gamma() {
super();
}
/**
* <p>
* Returns the regularized gamma function P(a, x).
* </p>
*
* <p>
* The implementation of this method is based on:
* <ul>
* <li>
* <a href="http://mathworld.wolfram.com/RegularizedGammaFunction.html">
* Regularized Gamma Function</a>, equation (1).</li>
* <li>
* <a href="http://mathworld.wolfram.com/IncompleteGammaFunction.html">
* Incomplete Gamma Function</a>, equation (4).</li>
* <li>
* <a href="http://mathworld.wolfram.com/ConfluentHypergeometricFunctionoftheFirstKind.html">
* Confluent Hypergeometric Function of the First Kind</a>, equation (1).
* </li>
* </ul>
* </p>
*
* @param a ???
* @param x ???
* @return the regularized gamma function P(a, x)
*/
public static double regularizedGammaP(double a, double x) {
double ret;
if (a <= 0.0) {
throw new IllegalArgumentException("a must be positive");
} else if (x <= 0.0) {
throw new IllegalArgumentException("x must be non-negative");
} else {
// calculate series
double n = 0.0; // current element index
double an = 1.0 / a; // n-th element in the series
double sum = an; // partial sum
while (Math.abs(an) > EPSILON && n < MAXIMUM_ITERATIONS) {
// compute next element in the series
n = n + 1.0;
an = an * (x / (a + n));
// update partial sum
sum = sum + an;
}
if (n >= MAXIMUM_ITERATIONS) {
throw new ConvergenceException(
"maximum number of iterations reached");
} else {
ret = Math.exp(-x + (a * Math.log(x)) - logGamma(a)) * sum;
}
}
return ret;
}
/**
* <p>
* Returns the natural logarithm of the gamma function &#915;(x).
* </p>
*
* <p>
* The implementation of this method is based on:
* <ul>
* <li><a href="http://mathworld.wolfram.com/GammaFunction.html">
* Gamma Function</a>, equation (28).</li>
* <li><a href="http://mathworld.wolfram.com/LanczosApproximation.html">
* Lanczos Approximation</a>, equations (1) through (5).</li>
* <li><a href="http://my.fit.edu/~gabdo/gamma.txt">Paul Godfrey, A note on
* the computation of the convergent Lanczos complex Gamma approximation
* </a></li>
* </ul>
* </p>
*
* @param x ???
* @return log(&#915;(x))
*/
public static double logGamma(double x) {
double ret;
if (x <= 0.0) {
throw new IllegalArgumentException(
"x must be non-negative");
} else {
double g = 607.0 / 128.0;
// Lanczos coefficients
double[] c =
{
0.99999999999999709182,
57.156235665862923517,
-59.597960355475491248,
14.136097974741747174,
-0.49191381609762019978,
.33994649984811888699e-4,
.46523628927048575665e-4,
-.98374475304879564677e-4,
.15808870322491248884e-3,
-.21026444172410488319e-3,
.21743961811521264320e-3,
-.16431810653676389022e-3,
.84418223983852743293e-4,
-.26190838401581408670e-4,
.36899182659531622704e-5,
};
double sum = 0.0;
for (int i = 1; i < c.length; ++i) {
sum = sum + (c[i] / (x + i));
}
sum = sum + c[0];
double tmp = x + g + .5;
ret = ((x + .5) * Math.log(tmp)) - tmp
+ (.5 * Math.log(2.0 * Math.PI)) + Math.log(sum) - Math.log(x);
}
return ret;
}
}

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package org.apache.commons.math.stat.distribution;
import junit.framework.TestCase;
/**
* @author Brent Worden
*/
public class ChiSquareDistributionTest extends TestCase {
private ChiSquaredDistribution chiSquare;
/**
* Constructor for ChiSquareDistributionTest.
* @param name
*/
public ChiSquareDistributionTest(String name) {
super(name);
}
/*
* @see TestCase#setUp()
*/
protected void setUp() throws Exception {
super.setUp();
chiSquare = DistributionFactory.newInstance().createChiSquareDistribution(5.0);
}
/*
* @see TestCase#tearDown()
*/
protected void tearDown() throws Exception {
chiSquare = null;
super.tearDown();
}
public void testLowerTailProbability(){
testProbability( .210, .001);
testProbability( .554, .010);
testProbability( .831, .025);
testProbability(1.145, .050);
testProbability(1.610, .100);
}
public void testUpperTailProbability(){
testProbability(20.515, .999);
testProbability(15.086, .990);
testProbability(12.833, .975);
testProbability(11.070, .950);
testProbability( 9.236, .900);
}
public void testLowerTailValues(){
testValue(.001, .210);
testValue(.010, .554);
testValue(.025, .831);
testValue(.050, 1.145);
testValue(.100, 1.610);
}
public void testUpperTailValues(){
testValue(.999, 20.515);
testValue(.990, 15.086);
testValue(.975, 12.833);
testValue(.950, 11.070);
testValue(.900, 9.236);
}
private void testProbability(double x, double expected){
double actual = chiSquare.cummulativeProbability(x);
assertEquals("probability for " + x, expected, actual, 10e-4);
}
private void testValue(double p, double expected){
double actual = chiSquare.inverseCummulativeProbability(p);
assertEquals("value for " + p, expected, actual, 10e-4);
}
}

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package org.apache.commons.math.stat.distribution;
import junit.framework.TestCase;
/**
* @author Brent Worden
*/
public class DistributionFactoryImplTest extends TestCase {
/** */
private DistributionFactory factory;
/**
* Constructor for DistributionFactoryImplTest.
* @param name
*/
public DistributionFactoryImplTest(String name) {
super(name);
}
/**
* @throws java.lang.Exception
*/
protected void setUp() throws Exception {
super.setUp();
factory = new DistributionFactoryImpl();
}
/**
* @throws java.lang.Exception
*/
protected void tearDown() throws Exception {
factory = null;
super.tearDown();
}
public void testCreateChiSquareDistributionNegative(){
try {
factory.createChiSquareDistribution(-1.0);
fail("negative degrees of freedom. IllegalArgumentException expected");
} catch (IllegalArgumentException ex) {
;
}
}
public void testCreateChiSquareDistributionZero(){
try {
factory.createChiSquareDistribution(0.0);
fail("zero degrees of freedom. IllegalArgumentException expected");
} catch (IllegalArgumentException ex) {
;
}
}
public void testCreateChiSquareDistributionPositive(){
try {
factory.createChiSquareDistribution(1.0);
} catch (IllegalArgumentException ex) {
fail("positive degrees of freedom. IllegalArgumentException is not expected");
}
}
public void testCreateGammaDistributionNegativePositive(){
try {
factory.createGammaDistribution(-1.0, 1.0);
fail("negative alpha. IllegalArgumentException expected");
} catch (IllegalArgumentException ex) {
;
}
}
public void testCreateGammaDistributionZeroPositive(){
try {
factory.createGammaDistribution(0.0, 1.0);
fail("zero alpha. IllegalArgumentException expected");
} catch (IllegalArgumentException ex) {
;
}
}
public void testCreateGammaDistributionPositiveNegative(){
try {
factory.createGammaDistribution(1.0, -1.0);
fail("negative beta. IllegalArgumentException expected");
} catch (IllegalArgumentException ex) {
;
}
}
public void testCreateGammaDistributionPositiveZero(){
try {
factory.createGammaDistribution(1.0, 0.0);
fail("zero beta. IllegalArgumentException expected");
} catch (IllegalArgumentException ex) {
;
}
}
public void testCreateGammaDistributionPositivePositive(){
try {
factory.createGammaDistribution(1.0, 1.0);
} catch (IllegalArgumentException ex) {
fail("positive alpah and beta. IllegalArgumentException is not expected");
}
}
//
// public void testCreateTDistributionNegative(){
// try {
// factory.createTDistribution(-1.0);
// fail("negative degrees of freedom. IllegalArgumentException expected");
// } catch (IllegalArgumentException ex) {
// ;
// }
// }
//
// public void testCreateTDistributionZero(){
// try {
// factory.createTDistribution(0.0);
// fail("zero degrees of freedom. IllegalArgumentException expected");
// } catch (IllegalArgumentException ex) {
// ;
// }
// }
//
// public void testCreateTDistributionPositive(){
// try {
// factory.createTDistribution(1.0);
// } catch (IllegalArgumentException ex) {
// fail("positive degrees of freedom. IllegalArgumentException is not expected");
// }
// }
}

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package org.apache.commons.math.stat.distribution;
import junit.framework.TestCase;
/**
* @author Brent Worden
*/
public class GammaDistributionTest extends TestCase {
/**
* Constructor for ChiSquareDistributionTest.
* @param name
*/
public GammaDistributionTest(String name) {
super(name);
}
public void testProbabilities(){
testProbability(15.5, 4.0, 2.0, .9499);
testProbability( 0.5, 4.0, 1.0, .0018);
testProbability(10.0, 1.0, 2.0, .9933);
testProbability( 5.0, 2.0, 2.0, .7127);
}
private void testProbability(double x, double a, double b, double expected){
double actual = DistributionFactory.newInstance().createGammaDistribution(a, b).cummulativeProbability(x);
assertEquals("probability for " + x, expected, actual, 10e-4);
}
}