Java tutorial
/* * 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.math3.distribution; import org.apache.commons.math3.exception.NumberIsTooSmallException; import org.apache.commons.math3.exception.util.LocalizedFormats; import org.apache.commons.math3.special.Gamma; import org.apache.commons.math3.special.Beta; import org.apache.commons.math3.util.FastMath; import org.apache.commons.math3.random.RandomGenerator; import org.apache.commons.math3.random.Well19937c; /** * Implements the Beta distribution. * * @see <a href="http://en.wikipedia.org/wiki/Beta_distribution">Beta distribution</a> * @version $Id: BetaDistribution.java 1416643 2012-12-03 19:37:14Z tn $ * @since 2.0 (changed to concrete class in 3.0) */ public class BetaDistribution extends AbstractRealDistribution { /** * 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 final double alpha; /** Second shape parameter. */ private final 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). */ public BetaDistribution(double alpha, double beta) { this(alpha, beta, DEFAULT_INVERSE_ABSOLUTE_ACCURACY); } /** * Build a new instance. * * @param alpha First shape parameter (must be positive). * @param beta Second shape parameter (must be positive). * @param inverseCumAccuracy Maximum absolute error in inverse * cumulative probability estimates (defaults to * {@link #DEFAULT_INVERSE_ABSOLUTE_ACCURACY}). * @since 2.1 */ public BetaDistribution(double alpha, double beta, double inverseCumAccuracy) { this(new Well19937c(), alpha, beta, inverseCumAccuracy); } /** * Creates a β distribution. * * @param rng Random number generator. * @param alpha First shape parameter (must be positive). * @param beta Second shape parameter (must be positive). * @param inverseCumAccuracy Maximum absolute error in inverse * cumulative probability estimates (defaults to * {@link #DEFAULT_INVERSE_ABSOLUTE_ACCURACY}). * @since 3.1 */ public BetaDistribution(RandomGenerator rng, double alpha, double beta, double inverseCumAccuracy) { super(rng); this.alpha = alpha; this.beta = beta; z = Double.NaN; solverAbsoluteAccuracy = inverseCumAccuracy; } /** * Access the first shape parameter, {@code alpha}. * * @return the first shape parameter. */ public double getAlpha() { return alpha; } /** * Access the second shape parameter, {@code beta}. * * @return the second shape parameter. */ 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); } } /** {@inheritDoc} */ public double density(double x) { recomputeZ(); if (x < 0 || x > 1) { return 0; } else if (x == 0) { if (alpha < 1) { throw new NumberIsTooSmallException( LocalizedFormats.CANNOT_COMPUTE_BETA_DENSITY_AT_0_FOR_SOME_ALPHA, alpha, 1, false); } return 0; } else if (x == 1) { if (beta < 1) { throw new NumberIsTooSmallException(LocalizedFormats.CANNOT_COMPUTE_BETA_DENSITY_AT_1_FOR_SOME_BETA, beta, 1, false); } return 0; } else { double logX = FastMath.log(x); double log1mX = FastMath.log1p(-x); return FastMath.exp((alpha - 1) * logX + (beta - 1) * log1mX - z); } } /** {@inheritDoc} */ public double cumulativeProbability(double x) { if (x <= 0) { return 0; } else if (x >= 1) { return 1; } else { return Beta.regularizedBeta(x, alpha, beta); } } /** * 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} * * For first shape parameter {@code alpha} and second shape parameter * {@code beta}, the mean is {@code alpha / (alpha + beta)}. */ public double getNumericalMean() { final double a = getAlpha(); return a / (a + getBeta()); } /** * {@inheritDoc} * * For first shape parameter {@code alpha} and second shape parameter * {@code beta}, the variance is * {@code (alpha * beta) / [(alpha + beta)^2 * (alpha + beta + 1)]}. */ public double getNumericalVariance() { final double a = getAlpha(); final double b = getBeta(); final double alphabetasum = a + b; return (a * b) / ((alphabetasum * alphabetasum) * (alphabetasum + 1)); } /** * {@inheritDoc} * * The lower bound of the support is always 0 no matter the parameters. * * @return lower bound of the support (always 0) */ public double getSupportLowerBound() { return 0; } /** * {@inheritDoc} * * The upper bound of the support is always 1 no matter the parameters. * * @return upper bound of the support (always 1) */ public double getSupportUpperBound() { return 1; } /** {@inheritDoc} */ public boolean isSupportLowerBoundInclusive() { return false; } /** {@inheritDoc} */ public boolean isSupportUpperBoundInclusive() { return false; } /** * {@inheritDoc} * * The support of this distribution is connected. * * @return {@code true} */ public boolean isSupportConnected() { return true; } }