001 /*
002 * Licensed to the Apache Software Foundation (ASF) under one or more
003 * contributor license agreements. See the NOTICE file distributed with
004 * this work for additional information regarding copyright ownership.
005 * The ASF licenses this file to You under the Apache License, Version 2.0
006 * (the "License"); you may not use this file except in compliance with
007 * the License. You may obtain a copy of the License at
008 *
009 * http://www.apache.org/licenses/LICENSE-2.0
010 *
011 * Unless required by applicable law or agreed to in writing, software
012 * distributed under the License is distributed on an "AS IS" BASIS,
013 * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
014 * See the License for the specific language governing permissions and
015 * limitations under the License.
016 */
017 package org.apache.commons.math3.distribution;
018
019 import org.apache.commons.math3.exception.NumberIsTooSmallException;
020 import org.apache.commons.math3.exception.util.LocalizedFormats;
021 import org.apache.commons.math3.special.Gamma;
022 import org.apache.commons.math3.special.Beta;
023 import org.apache.commons.math3.util.FastMath;
024 import org.apache.commons.math3.random.RandomGenerator;
025 import org.apache.commons.math3.random.Well19937c;
026
027 /**
028 * Implements the Beta distribution.
029 *
030 * @see <a href="http://en.wikipedia.org/wiki/Beta_distribution">Beta distribution</a>
031 * @version $Id: BetaDistribution.java 1416643 2012-12-03 19:37:14Z tn $
032 * @since 2.0 (changed to concrete class in 3.0)
033 */
034 public class BetaDistribution extends AbstractRealDistribution {
035 /**
036 * Default inverse cumulative probability accuracy.
037 * @since 2.1
038 */
039 public static final double DEFAULT_INVERSE_ABSOLUTE_ACCURACY = 1e-9;
040 /** Serializable version identifier. */
041 private static final long serialVersionUID = -1221965979403477668L;
042 /** First shape parameter. */
043 private final double alpha;
044 /** Second shape parameter. */
045 private final double beta;
046 /** Normalizing factor used in density computations.
047 * updated whenever alpha or beta are changed.
048 */
049 private double z;
050 /** Inverse cumulative probability accuracy. */
051 private final double solverAbsoluteAccuracy;
052
053 /**
054 * Build a new instance.
055 *
056 * @param alpha First shape parameter (must be positive).
057 * @param beta Second shape parameter (must be positive).
058 */
059 public BetaDistribution(double alpha, double beta) {
060 this(alpha, beta, DEFAULT_INVERSE_ABSOLUTE_ACCURACY);
061 }
062
063 /**
064 * Build a new instance.
065 *
066 * @param alpha First shape parameter (must be positive).
067 * @param beta Second shape parameter (must be positive).
068 * @param inverseCumAccuracy Maximum absolute error in inverse
069 * cumulative probability estimates (defaults to
070 * {@link #DEFAULT_INVERSE_ABSOLUTE_ACCURACY}).
071 * @since 2.1
072 */
073 public BetaDistribution(double alpha, double beta, double inverseCumAccuracy) {
074 this(new Well19937c(), alpha, beta, inverseCumAccuracy);
075 }
076
077 /**
078 * Creates a β distribution.
079 *
080 * @param rng Random number generator.
081 * @param alpha First shape parameter (must be positive).
082 * @param beta Second shape parameter (must be positive).
083 * @param inverseCumAccuracy Maximum absolute error in inverse
084 * cumulative probability estimates (defaults to
085 * {@link #DEFAULT_INVERSE_ABSOLUTE_ACCURACY}).
086 * @since 3.1
087 */
088 public BetaDistribution(RandomGenerator rng,
089 double alpha,
090 double beta,
091 double inverseCumAccuracy) {
092 super(rng);
093
094 this.alpha = alpha;
095 this.beta = beta;
096 z = Double.NaN;
097 solverAbsoluteAccuracy = inverseCumAccuracy;
098 }
099
100 /**
101 * Access the first shape parameter, {@code alpha}.
102 *
103 * @return the first shape parameter.
104 */
105 public double getAlpha() {
106 return alpha;
107 }
108
109 /**
110 * Access the second shape parameter, {@code beta}.
111 *
112 * @return the second shape parameter.
113 */
114 public double getBeta() {
115 return beta;
116 }
117
118 /** Recompute the normalization factor. */
119 private void recomputeZ() {
120 if (Double.isNaN(z)) {
121 z = Gamma.logGamma(alpha) + Gamma.logGamma(beta) - Gamma.logGamma(alpha + beta);
122 }
123 }
124
125 /** {@inheritDoc} */
126 public double density(double x) {
127 recomputeZ();
128 if (x < 0 || x > 1) {
129 return 0;
130 } else if (x == 0) {
131 if (alpha < 1) {
132 throw new NumberIsTooSmallException(LocalizedFormats.CANNOT_COMPUTE_BETA_DENSITY_AT_0_FOR_SOME_ALPHA, alpha, 1, false);
133 }
134 return 0;
135 } else if (x == 1) {
136 if (beta < 1) {
137 throw new NumberIsTooSmallException(LocalizedFormats.CANNOT_COMPUTE_BETA_DENSITY_AT_1_FOR_SOME_BETA, beta, 1, false);
138 }
139 return 0;
140 } else {
141 double logX = FastMath.log(x);
142 double log1mX = FastMath.log1p(-x);
143 return FastMath.exp((alpha - 1) * logX + (beta - 1) * log1mX - z);
144 }
145 }
146
147 /** {@inheritDoc} */
148 public double cumulativeProbability(double x) {
149 if (x <= 0) {
150 return 0;
151 } else if (x >= 1) {
152 return 1;
153 } else {
154 return Beta.regularizedBeta(x, alpha, beta);
155 }
156 }
157
158 /**
159 * Return the absolute accuracy setting of the solver used to estimate
160 * inverse cumulative probabilities.
161 *
162 * @return the solver absolute accuracy.
163 * @since 2.1
164 */
165 @Override
166 protected double getSolverAbsoluteAccuracy() {
167 return solverAbsoluteAccuracy;
168 }
169
170 /**
171 * {@inheritDoc}
172 *
173 * For first shape parameter {@code alpha} and second shape parameter
174 * {@code beta}, the mean is {@code alpha / (alpha + beta)}.
175 */
176 public double getNumericalMean() {
177 final double a = getAlpha();
178 return a / (a + getBeta());
179 }
180
181 /**
182 * {@inheritDoc}
183 *
184 * For first shape parameter {@code alpha} and second shape parameter
185 * {@code beta}, the variance is
186 * {@code (alpha * beta) / [(alpha + beta)^2 * (alpha + beta + 1)]}.
187 */
188 public double getNumericalVariance() {
189 final double a = getAlpha();
190 final double b = getBeta();
191 final double alphabetasum = a + b;
192 return (a * b) / ((alphabetasum * alphabetasum) * (alphabetasum + 1));
193 }
194
195 /**
196 * {@inheritDoc}
197 *
198 * The lower bound of the support is always 0 no matter the parameters.
199 *
200 * @return lower bound of the support (always 0)
201 */
202 public double getSupportLowerBound() {
203 return 0;
204 }
205
206 /**
207 * {@inheritDoc}
208 *
209 * The upper bound of the support is always 1 no matter the parameters.
210 *
211 * @return upper bound of the support (always 1)
212 */
213 public double getSupportUpperBound() {
214 return 1;
215 }
216
217 /** {@inheritDoc} */
218 public boolean isSupportLowerBoundInclusive() {
219 return false;
220 }
221
222 /** {@inheritDoc} */
223 public boolean isSupportUpperBoundInclusive() {
224 return false;
225 }
226
227 /**
228 * {@inheritDoc}
229 *
230 * The support of this distribution is connected.
231 *
232 * @return {@code true}
233 */
234 public boolean isSupportConnected() {
235 return true;
236 }
237 }