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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. * <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)); } }