| /* |
| * 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. |
| * <p> |
| * References: |
| * <ul> |
| * <li><a href="http://en.wikipedia.org/wiki/Beta_distribution"> |
| * Beta distribution</a></li> |
| * </ul> |
| * </p> |
| * @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 <code>s1</code> and |
| * second shape parameter <code>s2</code>, the mean is |
| * <code>s1 / (s1 + s2)</code> |
| * |
| * @return the mean |
| * @since 2.2 |
| */ |
| public double getNumericalMean() { |
| final double a = getAlpha(); |
| return a / (a + getBeta()); |
| } |
| |
| /** |
| * Returns the variance. |
| * |
| * For first shape parameter <code>s1</code> and |
| * second shape parameter <code>s2</code>, |
| * the variance is |
| * <code>[ s1 * s2 ] / [ (s1 + s2)^2 * (s1 + s2 + 1) ]</code> |
| * |
| * @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)); |
| } |
| |
| } |
