/*
* Licensed to the Apache Software Foundation (ASF) under one or more
* contributor license agreements. See the NOTICE file distributed with
* this work for additional information regarding copyright ownership.
* The ASF licenses this file to You under the Apache License, Version 2.0
* (the "License"); you may not use this file except in compliance with
* the License. You may obtain a copy of the License at
*
* http://www.apache.org/licenses/LICENSE-2.0
*
* Unless required by applicable law or agreed to in writing, software
* distributed under the License is distributed on an "AS IS" BASIS,
* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
* See the License for the specific language governing permissions and
* limitations under the License.
*/
package org.apache.commons.math.distribution;
import java.io.Serializable;
import org.apache.commons.math.MathException;
import org.apache.commons.math.MathRuntimeException;
import org.apache.commons.math.exception.util.LocalizedFormats;
import org.apache.commons.math.special.Gamma;
import org.apache.commons.math.util.FastMath;
/**
* The default implementation of {@link GammaDistribution}.
*
* @version $Revision: 1054524 $ $Date: 2011-01-03 05:59:18 +0100 (lun. 03 janv. 2011) $
*/
public class GammaDistributionImpl extends AbstractContinuousDistribution
implements GammaDistribution, Serializable {
/**
* Default inverse cumulative probability accuracy
* @since 2.1
*/
public static final double DEFAULT_INVERSE_ABSOLUTE_ACCURACY = 1e-9;
/** Serializable version identifier */
private static final long serialVersionUID = -3239549463135430361L;
/** The shape parameter. */
private double alpha;
/** The scale parameter. */
private double beta;
/** Inverse cumulative probability accuracy */
private final double solverAbsoluteAccuracy;
/**
* 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) {
this(alpha, beta, DEFAULT_INVERSE_ABSOLUTE_ACCURACY);
}
/**
* Create a new gamma distribution with the given alpha and beta values.
* @param alpha the shape parameter.
* @param beta the scale parameter.
* @param inverseCumAccuracy the maximum absolute error in inverse cumulative probability estimates
* (defaults to {@link #DEFAULT_INVERSE_ABSOLUTE_ACCURACY})
* @since 2.1
*/
public GammaDistributionImpl(double alpha, double beta, double inverseCumAccuracy) {
super();
setAlphaInternal(alpha);
setBetaInternal(beta);
solverAbsoluteAccuracy = inverseCumAccuracy;
}
/**
* For this distribution, X, this method returns P(X < x).
*
* 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>
*
* @param x the value at which the CDF is evaluated.
* @return CDF for this distribution.
* @throws MathException if the cumulative probability can not be
* computed due to convergence or other numerical errors.
*/
public double cumulativeProbability(double x) throws MathException{
double ret;
if (x <= 0.0) {
ret = 0.0;
} else {
ret = Gamma.regularizedGammaP(alpha, x / beta);
}
return ret;
}
/**
* For this distribution, X, this method returns the critical point x, such
* that P(X < x) = <code>p</code>.
* <p>
* Returns 0 for p=0 and <code>Double.POSITIVE_INFINITY</code> for p=1.</p>
*
* @param p the desired probability
* @return x, such that P(X < x) = <code>p</code>
* @throws MathException if the inverse cumulative probability can not be
* computed due to convergence or other numerical errors.
* @throws IllegalArgumentException if <code>p</code> is not a valid
* probability.
*/
@Override
public double inverseCumulativeProbability(final double p)
throws MathException {
if (p == 0) {
return 0d;
}
if (p == 1) {
return Double.POSITIVE_INFINITY;
}
return super.inverseCumulativeProbability(p);
}
/**
* Modify the shape parameter, alpha.
* @param alpha the new shape parameter.
* @throws IllegalArgumentException if <code>alpha</code> is not positive.
* @deprecated as of 2.1 (class will become immutable in 3.0)
*/
@Deprecated
public void setAlpha(double alpha) {
setAlphaInternal(alpha);
}
/**
* Modify the shape parameter, alpha.
* @param newAlpha the new shape parameter.
* @throws IllegalArgumentException if <code>newAlpha</code> is not positive.
*/
private void setAlphaInternal(double newAlpha) {
if (newAlpha <= 0.0) {
throw MathRuntimeException.createIllegalArgumentException(
LocalizedFormats.NOT_POSITIVE_ALPHA,
newAlpha);
}
this.alpha = newAlpha;
}
/**
* Access the shape parameter, alpha
* @return alpha.
*/
public double getAlpha() {
return alpha;
}
/**
* Modify the scale parameter, beta.
* @param newBeta the new scale parameter.
* @throws IllegalArgumentException if <code>newBeta</code> is not positive.
* @deprecated as of 2.1 (class will become immutable in 3.0)
*/
@Deprecated
public void setBeta(double newBeta) {
setBetaInternal(newBeta);
}
/**
* Modify the scale parameter, beta.
* @param newBeta the new scale parameter.
* @throws IllegalArgumentException if <code>newBeta</code> is not positive.
*/
private void setBetaInternal(double newBeta) {
if (newBeta <= 0.0) {
throw MathRuntimeException.createIllegalArgumentException(
LocalizedFormats.NOT_POSITIVE_BETA,
newBeta);
}
this.beta = newBeta;
}
/**
* Access the scale parameter, beta
* @return beta.
*/
public double getBeta() {
return beta;
}
/**
* Returns the probability density for a particular point.
*
* @param x The point at which the density should be computed.
* @return The pdf at point x.
*/
@Override
public double density(double x) {
if (x < 0) return 0;
return FastMath.pow(x / beta, alpha - 1) / beta * FastMath.exp(-x / beta) / FastMath.exp(Gamma.logGamma(alpha));
}
/**
* Return the probability density for a particular point.
*
* @param x The point at which the density should be computed.
* @return The pdf at point x.
* @deprecated
*/
@Deprecated
public double density(Double x) {
return density(x.doubleValue());
}
/**
* Access the domain value lower bound, based on <code>p</code>, used to
* bracket a CDF root. This method is used by
* {@link #inverseCumulativeProbability(double)} to find critical values.
*
* @param p the desired probability for the critical value
* @return domain value lower bound, i.e.
* P(X < <i>lower bound</i>) < <code>p</code>
*/
@Override
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 #inverseCumulativeProbability(double)} to find critical values.
*
* @param p the desired probability for the critical value
* @return domain value upper bound, i.e.
* P(X < <i>upper bound</i>) > <code>p</code>
*/
@Override
protected double getDomainUpperBound(double p) {
// TODO: try to improve on this estimate
// NOTE: gamma is skewed to the left
// NOTE: therefore, P(X < μ) > .5
double ret;
if (p < .5) {
// use mean
ret = alpha * beta;
} 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 #inverseCumulativeProbability(double)} to find critical values.
*
* @param p the desired probability for the critical value
* @return initial domain value
*/
@Override
protected double getInitialDomain(double p) {
// TODO: try to improve on this estimate
// Gamma is skewed to the left, therefore, P(X < μ) > .5
double ret;
if (p < .5) {
// use 1/2 mean
ret = alpha * beta * .5;
} else {
// use mean
ret = alpha * beta;
}
return ret;
}
/**
* Return the absolute accuracy setting of the solver used to estimate
* inverse cumulative probabilities.
*
* @return the solver absolute accuracy
* @since 2.1
*/
@Override
protected double getSolverAbsoluteAccuracy() {
return solverAbsoluteAccuracy;
}
/**
* Returns the upper bound of the support for the distribution.
*
* The lower bound of the support is always 0, regardless of the parameters.
*
* @return lower bound of the support (always 0)
* @since 2.2
*/
public double getSupportLowerBound() {
return 0;
}
/**
* Returns the upper bound of the support for the distribution.
*
* The upper bound of the support is always positive infinity,
* regardless of the parameters.
*
* @return upper bound of the support (always Double.POSITIVE_INFINITY)
* @since 2.2
*/
public double getSupportUpperBound() {
return Double.POSITIVE_INFINITY;
}
/**
* Returns the mean.
*
* For shape parameter <code>alpha</code> and scale
* parameter <code>beta</code>, the mean is
* <code>alpha * beta</code>
*
* @return the mean
* @since 2.2
*/
public double getNumericalMean() {
return getAlpha() * getBeta();
}
/**
* Returns the variance.
*
* For shape parameter <code>alpha</code> and scale
* parameter <code>beta</code>, the variance is
* <code>alpha * beta^2</code>
*
* @return the variance
* @since 2.2
*/
public double getNumericalVariance() {
final double b = getBeta();
return getAlpha() * b * b;
}
}