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/*
* 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 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.special.Beta;
import org.apache.commons.math.util.FastMath;
/**
* Implements the Beta distribution.
*
* References:
*
*
* @version $Revision: 1054524 $ $Date: 2011-01-03 05:59:18 +0100 (lun. 03 janv. 2011) $
* @since 2.0
*/
public class BetaDistributionImpl
extends AbstractContinuousDistribution implements BetaDistribution {
/**
* 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 = -1221965979403477668L;
/** First shape parameter. */
private double alpha;
/** Second shape parameter. */
private double beta;
/** Normalizing factor used in density computations.
* updated whenever alpha or beta are changed.
*/
private double z;
/** Inverse cumulative probability accuracy */
private final double solverAbsoluteAccuracy;
/**
* Build a new instance.
* @param alpha first shape parameter (must be positive)
* @param beta second shape parameter (must be positive)
* @param inverseCumAccuracy the maximum absolute error in inverse cumulative probability estimates
* (defaults to {@link #DEFAULT_INVERSE_ABSOLUTE_ACCURACY})
* @since 2.1
*/
public BetaDistributionImpl(double alpha, double beta, double inverseCumAccuracy) {
this.alpha = alpha;
this.beta = beta;
z = Double.NaN;
solverAbsoluteAccuracy = inverseCumAccuracy;
}
/**
* Build a new instance.
* @param alpha first shape parameter (must be positive)
* @param beta second shape parameter (must be positive)
*/
public BetaDistributionImpl(double alpha, double beta) {
this(alpha, beta, DEFAULT_INVERSE_ABSOLUTE_ACCURACY);
}
/** {@inheritDoc}
* @deprecated as of 2.1 (class will become immutable in 3.0)
*/
@Deprecated
public void setAlpha(double alpha) {
this.alpha = alpha;
z = Double.NaN;
}
/** {@inheritDoc} */
public double getAlpha() {
return alpha;
}
/** {@inheritDoc}
* @deprecated as of 2.1 (class will become immutable in 3.0)
*/
@Deprecated
public void setBeta(double beta) {
this.beta = beta;
z = Double.NaN;
}
/** {@inheritDoc} */
public double getBeta() {
return beta;
}
/**
* Recompute the normalization factor.
*/
private void recomputeZ() {
if (Double.isNaN(z)) {
z = Gamma.logGamma(alpha) + Gamma.logGamma(beta) - Gamma.logGamma(alpha + beta);
}
}
/**
* 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());
}
/**
* 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.
* @since 2.1
*/
@Override
public double density(double x) {
recomputeZ();
if (x < 0 || x > 1) {
return 0;
} else if (x == 0) {
if (alpha < 1) {
throw MathRuntimeException.createIllegalArgumentException(
LocalizedFormats.CANNOT_COMPUTE_BETA_DENSITY_AT_0_FOR_SOME_ALPHA, alpha);
}
return 0;
} else if (x == 1) {
if (beta < 1) {
throw MathRuntimeException.createIllegalArgumentException(
LocalizedFormats.CANNOT_COMPUTE_BETA_DENSITY_AT_1_FOR_SOME_BETA, beta);
}
return 0;
} else {
double logX = FastMath.log(x);
double log1mX = FastMath.log1p(-x);
return FastMath.exp((alpha - 1) * logX + (beta - 1) * log1mX - z);
}
}
/** {@inheritDoc} */
@Override
public double inverseCumulativeProbability(double p) throws MathException {
if (p == 0) {
return 0;
} else if (p == 1) {
return 1;
} else {
return super.inverseCumulativeProbability(p);
}
}
/** {@inheritDoc} */
@Override
protected double getInitialDomain(double p) {
return p;
}
/** {@inheritDoc} */
@Override
protected double getDomainLowerBound(double p) {
return 0;
}
/** {@inheritDoc} */
@Override
protected double getDomainUpperBound(double p) {
return 1;
}
/** {@inheritDoc} */
public double cumulativeProbability(double x) throws MathException {
if (x <= 0) {
return 0;
} else if (x >= 1) {
return 1;
} else {
return Beta.regularizedBeta(x, alpha, beta);
}
}
/** {@inheritDoc} */
@Override
public double cumulativeProbability(double x0, double x1) throws MathException {
return cumulativeProbability(x1) - cumulativeProbability(x0);
}
/**
* 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 lower bound of the support for this distribution.
* The support of the Beta distribution is always [0, 1], regardless
* of the parameters, so this method always returns 0.
*
* @return lower bound of the support (always 0)
* @since 2.2
*/
public double getSupportLowerBound() {
return 0;
}
/**
* Returns the upper bound of the support for this distribution.
* The support of the Beta distribution is always [0, 1], regardless
* of the parameters, so this method always returns 1.
*
* @return lower bound of the support (always 1)
* @since 2.2
*/
public double getSupportUpperBound() {
return 1;
}
/**
* Returns the mean.
*
* For first shape parameter s1 and
* second shape parameter s2, the mean is
* s1 / (s1 + s2)
*
* @return the mean
* @since 2.2
*/
public double getNumericalMean() {
final double a = getAlpha();
return a / (a + getBeta());
}
/**
* Returns the variance.
*
* For first shape parameter s1 and
* second shape parameter s2,
* the variance is
* [ s1 * s2 ] / [ (s1 + s2)^2 * (s1 + s2 + 1) ]
*
* @return the variance
* @since 2.2
*/
public double getNumericalVariance() {
final double a = getAlpha();
final double b = getBeta();
final double alphabetasum = a + b;
return (a * b) / ((alphabetasum * alphabetasum) * (alphabetasum + 1));
}
}
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