/*
* 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.exception.NotStrictlyPositiveException;
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 $Id: GammaDistributionImpl.java 1131229 2011-06-03 20:49:25Z luc $
*/
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 final double alpha;
/** The scale parameter. */
private final 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 Shape parameter.
* @param beta Scale parameter.
* @param inverseCumAccuracy Maximum absolute error in inverse
* cumulative probability estimates (defaults to
* {@link #DEFAULT_INVERSE_ABSOLUTE_ACCURACY}).
* @throws NotStrictlyPositiveException if {@code alpha <= 0} or
* {@code beta <= 0}.
* @since 2.1
*/
public GammaDistributionImpl(double alpha, double beta, double inverseCumAccuracy) {
if (alpha <= 0) {
throw new NotStrictlyPositiveException(LocalizedFormats.ALPHA, alpha);
}
if (beta <= 0) {
throw new NotStrictlyPositiveException(LocalizedFormats.BETA, beta);
}
this.alpha = alpha;
this.beta = beta;
solverAbsoluteAccuracy = inverseCumAccuracy;
}
/**
* For this distribution, {@code X}, this method returns {@code 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 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) {
ret = 0;
} else {
ret = Gamma.regularizedGammaP(alpha, x / beta);
}
return ret;
}
/**
* For this distribution, {@code X}, this method returns the critical
* point {@code x}, such that {@code P(X < x) = p}.
* It will return 0 when p = 0 and {@code Double.POSITIVE_INFINITY}
* when p = 1.
*
* @param p Desired probability.
* @return {@code x}, such that {@code P(X < x) = p}.
* @throws MathException if the inverse cumulative probability cannot be
* computed due to convergence or other numerical errors.
* @throws org.apache.commons.math.exception.OutOfRangeException if
* {@code p} is not a valid probability.
*/
@Override
public double inverseCumulativeProbability(final double p)
throws MathException {
if (p == 0) {
return 0;
}
if (p == 1) {
return Double.POSITIVE_INFINITY;
}
return super.inverseCumulativeProbability(p);
}
/**
* {@inheritDoc}
*/
public double getAlpha() {
return alpha;
}
/**
* {@inheritDoc}
*/
public double getBeta() {
return beta;
}
/**
* {@inheritDoc}
*/
@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));
}
/**
* Access the domain value lower bound, based on {@code p}, used to
* bracket a CDF root. This method is used by
* {@link #inverseCumulativeProbability(double)} to find critical values.
*
* @param p Desired probability for the critical value.
* @return the domain value lower bound, i.e. {@code P(X < 'lower bound') < p}.
*/
@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}, used to
* bracket a CDF root. This method is used by
* {@link #inverseCumulativeProbability(double)} to find critical values.
*
* @param p Desired probability for the critical value.
* @return the domain value upper bound, i.e. {@code P(X < 'upper bound') > p}.
*/
@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 < 0.5) {
// use mean
ret = alpha * beta;
} else {
// use max value
ret = Double.MAX_VALUE;
}
return ret;
}
/**
* Access the initial domain value, based on {@code p}, used to
* bracket a CDF root. This method is used by
* {@link #inverseCumulativeProbability(double)} to find critical values.
*
* @param p Desired probability for the critical value.
* @return the 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 < 0.5) {
// use 1/2 mean
ret = alpha * beta * 0.5;
} 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;
}
/**
* {@inheritDoc}
*
* The lower bound of the support is always 0 no matter the parameters.
*
* @return lower bound of the support (always 0)
*/
@Override
public double getSupportLowerBound() {
return 0;
}
/**
* {@inheritDoc}
*
* The upper bound of the support is always positive infinity
* no matter the parameters.
*
* @return upper bound of the support (always Double.POSITIVE_INFINITY)
*/
@Override
public double getSupportUpperBound() {
return Double.POSITIVE_INFINITY;
}
/**
* {@inheritDoc}
*
* For shape parameter <code>alpha</code> and scale
* parameter <code>beta</code>, the mean is
* <code>alpha * beta</code>
*
* @return {@inheritDoc}
*/
@Override
protected double calculateNumericalMean() {
return getAlpha() * getBeta();
}
/**
* {@inheritDoc}
*
* For shape parameter <code>alpha</code> and scale
* parameter <code>beta</code>, the variance is
* <code>alpha * beta^2</code>
*
* @return {@inheritDoc}
*/
@Override
protected double calculateNumericalVariance() {
final double b = getBeta();
return getAlpha() * b * b;
}
/**
* {@inheritDoc}
*/
@Override
public boolean isSupportLowerBoundInclusive() {
return true;
}
/**
* {@inheritDoc}
*/
@Override
public boolean isSupportUpperBoundInclusive() {
return false;
}
}