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 java.io.Serializable;
020    
021    import org.apache.commons.math.MathException;
022    import org.apache.commons.math.MathRuntimeException;
023    import org.apache.commons.math.exception.util.LocalizedFormats;
024    import org.apache.commons.math.special.Beta;
025    import org.apache.commons.math.util.FastMath;
026    
027    /**
028     * The default implementation of {@link BinomialDistribution}.
029     *
030     * @version $Revision: 1054524 $ $Date: 2011-01-03 05:59:18 +0100 (lun. 03 janv. 2011) $
031     */
032    public class BinomialDistributionImpl extends AbstractIntegerDistribution
033            implements BinomialDistribution, Serializable {
034    
035        /** Serializable version identifier */
036        private static final long serialVersionUID = 6751309484392813623L;
037    
038        /** The number of trials. */
039        private int numberOfTrials;
040    
041        /** The probability of success. */
042        private double probabilityOfSuccess;
043    
044        /**
045         * Create a binomial distribution with the given number of trials and
046         * probability of success.
047         *
048         * @param trials the number of trials.
049         * @param p the probability of success.
050         */
051        public BinomialDistributionImpl(int trials, double p) {
052            super();
053            setNumberOfTrialsInternal(trials);
054            setProbabilityOfSuccessInternal(p);
055        }
056    
057        /**
058         * Access the number of trials for this distribution.
059         *
060         * @return the number of trials.
061         */
062        public int getNumberOfTrials() {
063            return numberOfTrials;
064        }
065    
066        /**
067         * Access the probability of success for this distribution.
068         *
069         * @return the probability of success.
070         */
071        public double getProbabilityOfSuccess() {
072            return probabilityOfSuccess;
073        }
074    
075        /**
076         * Change the number of trials for this distribution.
077         *
078         * @param trials the new number of trials.
079         * @throws IllegalArgumentException if <code>trials</code> is not a valid
080         *             number of trials.
081         * @deprecated as of 2.1 (class will become immutable in 3.0)
082         */
083        @Deprecated
084        public void setNumberOfTrials(int trials) {
085            setNumberOfTrialsInternal(trials);
086        }
087    
088        /**
089         * Change the number of trials for this distribution.
090         *
091         * @param trials the new number of trials.
092         * @throws IllegalArgumentException if <code>trials</code> is not a valid
093         *             number of trials.
094         */
095        private void setNumberOfTrialsInternal(int trials) {
096            if (trials < 0) {
097                throw MathRuntimeException.createIllegalArgumentException(
098                        LocalizedFormats.NEGATIVE_NUMBER_OF_TRIALS, trials);
099            }
100            numberOfTrials = trials;
101        }
102    
103        /**
104         * Change the probability of success for this distribution.
105         *
106         * @param p the new probability of success.
107         * @throws IllegalArgumentException if <code>p</code> is not a valid
108         *             probability.
109         * @deprecated as of 2.1 (class will become immutable in 3.0)
110         */
111        @Deprecated
112        public void setProbabilityOfSuccess(double p) {
113            setProbabilityOfSuccessInternal(p);
114        }
115    
116        /**
117         * Change the probability of success for this distribution.
118         *
119         * @param p the new probability of success.
120         * @throws IllegalArgumentException if <code>p</code> is not a valid
121         *             probability.
122         */
123        private void setProbabilityOfSuccessInternal(double p) {
124            if (p < 0.0 || p > 1.0) {
125                throw MathRuntimeException.createIllegalArgumentException(
126                        LocalizedFormats.OUT_OF_RANGE_SIMPLE, p, 0.0, 1.0);
127            }
128            probabilityOfSuccess = p;
129        }
130    
131        /**
132         * Access the domain value lower bound, based on <code>p</code>, used to
133         * bracket a PDF root.
134         *
135         * @param p the desired probability for the critical value
136         * @return domain value lower bound, i.e. P(X &lt; <i>lower bound</i>) &lt;
137         *         <code>p</code>
138         */
139        @Override
140        protected int getDomainLowerBound(double p) {
141            return -1;
142        }
143    
144        /**
145         * Access the domain value upper bound, based on <code>p</code>, used to
146         * bracket a PDF root.
147         *
148         * @param p the desired probability for the critical value
149         * @return domain value upper bound, i.e. P(X &lt; <i>upper bound</i>) &gt;
150         *         <code>p</code>
151         */
152        @Override
153        protected int getDomainUpperBound(double p) {
154            return numberOfTrials;
155        }
156    
157        /**
158         * For this distribution, X, this method returns P(X &le; x).
159         *
160         * @param x the value at which the PDF is evaluated.
161         * @return PDF for this distribution.
162         * @throws MathException if the cumulative probability can not be computed
163         *             due to convergence or other numerical errors.
164         */
165        @Override
166        public double cumulativeProbability(int x) throws MathException {
167            double ret;
168            if (x < 0) {
169                ret = 0.0;
170            } else if (x >= numberOfTrials) {
171                ret = 1.0;
172            } else {
173                ret = 1.0 - Beta.regularizedBeta(getProbabilityOfSuccess(),
174                        x + 1.0, numberOfTrials - x);
175            }
176            return ret;
177        }
178    
179        /**
180         * For this distribution, X, this method returns P(X = x).
181         *
182         * @param x the value at which the PMF is evaluated.
183         * @return PMF for this distribution.
184         */
185        public double probability(int x) {
186            double ret;
187            if (x < 0 || x > numberOfTrials) {
188                ret = 0.0;
189            } else {
190                ret = FastMath.exp(SaddlePointExpansion.logBinomialProbability(x,
191                        numberOfTrials, probabilityOfSuccess,
192                        1.0 - probabilityOfSuccess));
193            }
194            return ret;
195        }
196    
197        /**
198         * For this distribution, X, this method returns the largest x, such that
199         * P(X &le; x) &le; <code>p</code>.
200         * <p>
201         * Returns <code>-1</code> for p=0 and <code>Integer.MAX_VALUE</code> for
202         * p=1.
203         * </p>
204         *
205         * @param p the desired probability
206         * @return the largest x such that P(X &le; x) <= p
207         * @throws MathException if the inverse cumulative probability can not be
208         *             computed due to convergence or other numerical errors.
209         * @throws IllegalArgumentException if p < 0 or p > 1
210         */
211        @Override
212        public int inverseCumulativeProbability(final double p)
213                throws MathException {
214            // handle extreme values explicitly
215            if (p == 0) {
216                return -1;
217            }
218            if (p == 1) {
219                return Integer.MAX_VALUE;
220            }
221    
222            // use default bisection impl
223            return super.inverseCumulativeProbability(p);
224        }
225    
226        /**
227         * Returns the lower bound of the support for the distribution.
228         *
229         * The lower bound of the support is always 0 no matter the number of trials
230         * and probability parameter.
231         *
232         * @return lower bound of the support (always 0)
233         * @since 2.2
234         */
235        public int getSupportLowerBound() {
236            return 0;
237        }
238    
239        /**
240         * Returns the upper bound of the support for the distribution.
241         *
242         * The upper bound of the support is the number of trials.
243         *
244         * @return upper bound of the support (equal to number of trials)
245         * @since 2.2
246         */
247        public int getSupportUpperBound() {
248            return getNumberOfTrials();
249        }
250    
251        /**
252         * Returns the mean.
253         *
254         * For <code>n</code> number of trials and
255         * probability parameter <code>p</code>, the mean is
256         * <code>n * p</code>
257         *
258         * @return the mean
259         * @since 2.2
260         */
261        public double getNumericalMean() {
262            return (double)getNumberOfTrials() * getProbabilityOfSuccess();
263        }
264    
265        /**
266         * Returns the variance.
267         *
268         * For <code>n</code> number of trials and
269         * probability parameter <code>p</code>, the variance is
270         * <code>n * p * (1 - p)</code>
271         *
272         * @return the variance
273         * @since 2.2
274         */
275        public double getNumericalVariance() {
276            final double p = getProbabilityOfSuccess();
277            return (double)getNumberOfTrials() * p * (1 - p);
278        }
279    }