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    
024    /**
025     * The default implementation of {@link ExponentialDistribution}.
026     *
027     * @version $Revision: 925900 $ $Date: 2010-03-21 17:10:07 -0400 (Sun, 21 Mar 2010) $
028     */
029    public class ExponentialDistributionImpl extends AbstractContinuousDistribution
030        implements ExponentialDistribution, Serializable {
031    
032        /**
033         * Default inverse cumulative probability accuracy
034         * @since 2.1
035         */
036        public static final double DEFAULT_INVERSE_ABSOLUTE_ACCURACY = 1e-9;
037    
038        /** Serializable version identifier */
039        private static final long serialVersionUID = 2401296428283614780L;
040    
041        /** The mean of this distribution. */
042        private double mean;
043    
044        /** Inverse cumulative probability accuracy */
045        private final double solverAbsoluteAccuracy;
046    
047        /**
048         * Create a exponential distribution with the given mean.
049         * @param mean mean of this distribution.
050         */
051        public ExponentialDistributionImpl(double mean) {
052            this(mean, DEFAULT_INVERSE_ABSOLUTE_ACCURACY);
053        }
054    
055        /**
056         * Create a exponential distribution with the given mean.
057         * @param mean mean of this distribution.
058         * @param inverseCumAccuracy the maximum absolute error in inverse cumulative probability estimates
059         * (defaults to {@link #DEFAULT_INVERSE_ABSOLUTE_ACCURACY})
060         * @since 2.1
061         */
062        public ExponentialDistributionImpl(double mean, double inverseCumAccuracy) {
063            super();
064            setMeanInternal(mean);
065            solverAbsoluteAccuracy = inverseCumAccuracy;
066        }
067    
068        /**
069         * Modify the mean.
070         * @param mean the new mean.
071         * @throws IllegalArgumentException if <code>mean</code> is not positive.
072         * @deprecated as of 2.1 (class will become immutable in 3.0)
073         */
074        @Deprecated
075        public void setMean(double mean) {
076            setMeanInternal(mean);
077        }
078        /**
079         * Modify the mean.
080         * @param newMean the new mean.
081         * @throws IllegalArgumentException if <code>newMean</code> is not positive.
082         */
083        private void setMeanInternal(double newMean) {
084            if (newMean <= 0.0) {
085                throw MathRuntimeException.createIllegalArgumentException(
086                      "mean must be positive ({0})", newMean);
087            }
088            this.mean = newMean;
089        }
090    
091        /**
092         * Access the mean.
093         * @return the mean.
094         */
095        public double getMean() {
096            return mean;
097        }
098    
099        /**
100         * Return the probability density for a particular point.
101         *
102         * @param x The point at which the density should be computed.
103         * @return The pdf at point x.
104         * @deprecated - use density(double)
105         */
106        public double density(Double x) {
107            return density(x.doubleValue());
108        }
109    
110        /**
111         * Return the probability density for a particular point.
112         *
113         * @param x The point at which the density should be computed.
114         * @return The pdf at point x.
115         * @since 2.1
116         */
117        @Override
118        public double density(double x) {
119            if (x < 0) {
120                return 0;
121            }
122            return Math.exp(-x / mean) / mean;
123        }
124    
125        /**
126         * For this distribution, X, this method returns P(X &lt; x).
127         *
128         * The implementation of this method is based on:
129         * <ul>
130         * <li>
131         * <a href="http://mathworld.wolfram.com/ExponentialDistribution.html">
132         * Exponential Distribution</a>, equation (1).</li>
133         * </ul>
134         *
135         * @param x the value at which the CDF is evaluated.
136         * @return CDF for this distribution.
137         * @throws MathException if the cumulative probability can not be
138         *            computed due to convergence or other numerical errors.
139         */
140        public double cumulativeProbability(double x) throws MathException{
141            double ret;
142            if (x <= 0.0) {
143                ret = 0.0;
144            } else {
145                ret = 1.0 - Math.exp(-x / mean);
146            }
147            return ret;
148        }
149    
150        /**
151         * For this distribution, X, this method returns the critical point x, such
152         * that P(X &lt; x) = <code>p</code>.
153         * <p>
154         * Returns 0 for p=0 and <code>Double.POSITIVE_INFINITY</code> for p=1.</p>
155         *
156         * @param p the desired probability
157         * @return x, such that P(X &lt; x) = <code>p</code>
158         * @throws MathException if the inverse cumulative probability can not be
159         *            computed due to convergence or other numerical errors.
160         * @throws IllegalArgumentException if p < 0 or p > 1.
161         */
162        @Override
163        public double inverseCumulativeProbability(double p) throws MathException {
164            double ret;
165    
166            if (p < 0.0 || p > 1.0) {
167                throw MathRuntimeException.createIllegalArgumentException(
168                      "{0} out of [{1}, {2}] range", p, 0.0, 1.0);
169            } else if (p == 1.0) {
170                ret = Double.POSITIVE_INFINITY;
171            } else {
172                ret = -mean * Math.log(1.0 - p);
173            }
174    
175            return ret;
176        }
177    
178        /**
179         * Access the domain value lower bound, based on <code>p</code>, used to
180         * bracket a CDF root.
181         *
182         * @param p the desired probability for the critical value
183         * @return domain value lower bound, i.e.
184         *         P(X &lt; <i>lower bound</i>) &lt; <code>p</code>
185         */
186        @Override
187        protected double getDomainLowerBound(double p) {
188            return 0;
189        }
190    
191        /**
192         * Access the domain value upper bound, based on <code>p</code>, used to
193         * bracket a CDF root.
194         *
195         * @param p the desired probability for the critical value
196         * @return domain value upper bound, i.e.
197         *         P(X &lt; <i>upper bound</i>) &gt; <code>p</code>
198         */
199        @Override
200        protected double getDomainUpperBound(double p) {
201            // NOTE: exponential is skewed to the left
202            // NOTE: therefore, P(X < &mu;) > .5
203    
204            if (p < .5) {
205                // use mean
206                return mean;
207            } else {
208                // use max
209                return Double.MAX_VALUE;
210            }
211        }
212    
213        /**
214         * Access the initial domain value, based on <code>p</code>, used to
215         * bracket a CDF root.
216         *
217         * @param p the desired probability for the critical value
218         * @return initial domain value
219         */
220        @Override
221        protected double getInitialDomain(double p) {
222            // TODO: try to improve on this estimate
223            // TODO: what should really happen here is not derive from AbstractContinuousDistribution
224            // TODO: because the inverse cumulative distribution is simple.
225            // Exponential is skewed to the left, therefore, P(X < &mu;) > .5
226            if (p < .5) {
227                // use 1/2 mean
228                return mean * .5;
229            } else {
230                // use mean
231                return mean;
232            }
233        }
234    
235        /**
236         * Return the absolute accuracy setting of the solver used to estimate
237         * inverse cumulative probabilities.
238         *
239         * @return the solver absolute accuracy
240         * @since 2.1
241         */
242        @Override
243        protected double getSolverAbsoluteAccuracy() {
244            return solverAbsoluteAccuracy;
245        }
246    }