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.math.distribution;
018
019 import org.apache.commons.math.MathException;
020 import org.apache.commons.math.MathRuntimeException;
021 import org.apache.commons.math.exception.util.LocalizedFormats;
022 import org.apache.commons.math.special.Gamma;
023 import org.apache.commons.math.special.Beta;
024 import org.apache.commons.math.util.FastMath;
025
026 /**
027 * Implements the Beta distribution.
028 * <p>
029 * References:
030 * <ul>
031 * <li><a href="http://en.wikipedia.org/wiki/Beta_distribution">
032 * Beta distribution</a></li>
033 * </ul>
034 * </p>
035 * @version $Revision: 1054524 $ $Date: 2011-01-03 05:59:18 +0100 (lun. 03 janv. 2011) $
036 * @since 2.0
037 */
038 public class BetaDistributionImpl
039 extends AbstractContinuousDistribution implements BetaDistribution {
040
041 /**
042 * Default inverse cumulative probability accuracy
043 * @since 2.1
044 */
045 public static final double DEFAULT_INVERSE_ABSOLUTE_ACCURACY = 1e-9;
046
047 /** Serializable version identifier. */
048 private static final long serialVersionUID = -1221965979403477668L;
049
050 /** First shape parameter. */
051 private double alpha;
052
053 /** Second shape parameter. */
054 private double beta;
055
056 /** Normalizing factor used in density computations.
057 * updated whenever alpha or beta are changed.
058 */
059 private double z;
060
061 /** Inverse cumulative probability accuracy */
062 private final double solverAbsoluteAccuracy;
063
064 /**
065 * Build a new instance.
066 * @param alpha first shape parameter (must be positive)
067 * @param beta second shape parameter (must be positive)
068 * @param inverseCumAccuracy the maximum absolute error in inverse cumulative probability estimates
069 * (defaults to {@link #DEFAULT_INVERSE_ABSOLUTE_ACCURACY})
070 * @since 2.1
071 */
072 public BetaDistributionImpl(double alpha, double beta, double inverseCumAccuracy) {
073 this.alpha = alpha;
074 this.beta = beta;
075 z = Double.NaN;
076 solverAbsoluteAccuracy = inverseCumAccuracy;
077 }
078
079 /**
080 * Build a new instance.
081 * @param alpha first shape parameter (must be positive)
082 * @param beta second shape parameter (must be positive)
083 */
084 public BetaDistributionImpl(double alpha, double beta) {
085 this(alpha, beta, DEFAULT_INVERSE_ABSOLUTE_ACCURACY);
086 }
087
088 /** {@inheritDoc}
089 * @deprecated as of 2.1 (class will become immutable in 3.0)
090 */
091 @Deprecated
092 public void setAlpha(double alpha) {
093 this.alpha = alpha;
094 z = Double.NaN;
095 }
096
097 /** {@inheritDoc} */
098 public double getAlpha() {
099 return alpha;
100 }
101
102 /** {@inheritDoc}
103 * @deprecated as of 2.1 (class will become immutable in 3.0)
104 */
105 @Deprecated
106 public void setBeta(double beta) {
107 this.beta = beta;
108 z = Double.NaN;
109 }
110
111 /** {@inheritDoc} */
112 public double getBeta() {
113 return beta;
114 }
115
116 /**
117 * Recompute the normalization factor.
118 */
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 /**
126 * Return the probability density for a particular point.
127 *
128 * @param x The point at which the density should be computed.
129 * @return The pdf at point x.
130 * @deprecated
131 */
132 @Deprecated
133 public double density(Double x) {
134 return density(x.doubleValue());
135 }
136
137 /**
138 * Return the probability density for a particular point.
139 *
140 * @param x The point at which the density should be computed.
141 * @return The pdf at point x.
142 * @since 2.1
143 */
144 @Override
145 public double density(double x) {
146 recomputeZ();
147 if (x < 0 || x > 1) {
148 return 0;
149 } else if (x == 0) {
150 if (alpha < 1) {
151 throw MathRuntimeException.createIllegalArgumentException(
152 LocalizedFormats.CANNOT_COMPUTE_BETA_DENSITY_AT_0_FOR_SOME_ALPHA, alpha);
153 }
154 return 0;
155 } else if (x == 1) {
156 if (beta < 1) {
157 throw MathRuntimeException.createIllegalArgumentException(
158 LocalizedFormats.CANNOT_COMPUTE_BETA_DENSITY_AT_1_FOR_SOME_BETA, beta);
159 }
160 return 0;
161 } else {
162 double logX = FastMath.log(x);
163 double log1mX = FastMath.log1p(-x);
164 return FastMath.exp((alpha - 1) * logX + (beta - 1) * log1mX - z);
165 }
166 }
167
168 /** {@inheritDoc} */
169 @Override
170 public double inverseCumulativeProbability(double p) throws MathException {
171 if (p == 0) {
172 return 0;
173 } else if (p == 1) {
174 return 1;
175 } else {
176 return super.inverseCumulativeProbability(p);
177 }
178 }
179
180 /** {@inheritDoc} */
181 @Override
182 protected double getInitialDomain(double p) {
183 return p;
184 }
185
186 /** {@inheritDoc} */
187 @Override
188 protected double getDomainLowerBound(double p) {
189 return 0;
190 }
191
192 /** {@inheritDoc} */
193 @Override
194 protected double getDomainUpperBound(double p) {
195 return 1;
196 }
197
198 /** {@inheritDoc} */
199 public double cumulativeProbability(double x) throws MathException {
200 if (x <= 0) {
201 return 0;
202 } else if (x >= 1) {
203 return 1;
204 } else {
205 return Beta.regularizedBeta(x, alpha, beta);
206 }
207 }
208
209 /** {@inheritDoc} */
210 @Override
211 public double cumulativeProbability(double x0, double x1) throws MathException {
212 return cumulativeProbability(x1) - cumulativeProbability(x0);
213 }
214
215 /**
216 * Return the absolute accuracy setting of the solver used to estimate
217 * inverse cumulative probabilities.
218 *
219 * @return the solver absolute accuracy
220 * @since 2.1
221 */
222 @Override
223 protected double getSolverAbsoluteAccuracy() {
224 return solverAbsoluteAccuracy;
225 }
226
227 /**
228 * Returns the lower bound of the support for this distribution.
229 * The support of the Beta distribution is always [0, 1], regardless
230 * of the parameters, so this method always returns 0.
231 *
232 * @return lower bound of the support (always 0)
233 * @since 2.2
234 */
235 public double getSupportLowerBound() {
236 return 0;
237 }
238
239 /**
240 * Returns the upper bound of the support for this distribution.
241 * The support of the Beta distribution is always [0, 1], regardless
242 * of the parameters, so this method always returns 1.
243 *
244 * @return lower bound of the support (always 1)
245 * @since 2.2
246 */
247 public double getSupportUpperBound() {
248 return 1;
249 }
250
251 /**
252 * Returns the mean.
253 *
254 * For first shape parameter <code>s1</code> and
255 * second shape parameter <code>s2</code>, the mean is
256 * <code>s1 / (s1 + s2)</code>
257 *
258 * @return the mean
259 * @since 2.2
260 */
261 public double getNumericalMean() {
262 final double a = getAlpha();
263 return a / (a + getBeta());
264 }
265
266 /**
267 * Returns the variance.
268 *
269 * For first shape parameter <code>s1</code> and
270 * second shape parameter <code>s2</code>,
271 * the variance is
272 * <code>[ s1 * s2 ] / [ (s1 + s2)^2 * (s1 + s2 + 1) ]</code>
273 *
274 * @return the variance
275 * @since 2.2
276 */
277 public double getNumericalVariance() {
278 final double a = getAlpha();
279 final double b = getBeta();
280 final double alphabetasum = a + b;
281 return (a * b) / ((alphabetasum * alphabetasum) * (alphabetasum + 1));
282 }
283
284 }