/*
* 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.math.distribution;
import java.io.Serializable;
import org.apache.commons.math.MathException;
import org.apache.commons.math.MathRuntimeException;
import org.apache.commons.math.exception.util.LocalizedFormats;
import org.apache.commons.math.util.FastMath;
/**
* The default implementation of {@link ExponentialDistribution}.
*
* @version $Revision: 1055914 $ $Date: 2011-01-06 16:34:34 +0100 (jeu. 06 janv. 2011) $
*/
public class ExponentialDistributionImpl extends AbstractContinuousDistribution
implements ExponentialDistribution, Serializable {
/**
* 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 = 2401296428283614780L;
/** The mean of this distribution. */
private double mean;
/** Inverse cumulative probability accuracy */
private final double solverAbsoluteAccuracy;
/**
* Create a exponential distribution with the given mean.
* @param mean mean of this distribution.
*/
public ExponentialDistributionImpl(double mean) {
this(mean, DEFAULT_INVERSE_ABSOLUTE_ACCURACY);
}
/**
* Create a exponential distribution with the given mean.
* @param mean mean of this distribution.
* @param inverseCumAccuracy the maximum absolute error in inverse cumulative probability estimates
* (defaults to {@link #DEFAULT_INVERSE_ABSOLUTE_ACCURACY})
* @since 2.1
*/
public ExponentialDistributionImpl(double mean, double inverseCumAccuracy) {
super();
setMeanInternal(mean);
solverAbsoluteAccuracy = inverseCumAccuracy;
}
/**
* Modify the mean.
* @param mean the new mean.
* @throws IllegalArgumentException if <code>mean</code> is not positive.
* @deprecated as of 2.1 (class will become immutable in 3.0)
*/
@Deprecated
public void setMean(double mean) {
setMeanInternal(mean);
}
/**
* Modify the mean.
* @param newMean the new mean.
* @throws IllegalArgumentException if <code>newMean</code> is not positive.
*/
private void setMeanInternal(double newMean) {
if (newMean <= 0.0) {
throw MathRuntimeException.createIllegalArgumentException(
LocalizedFormats.NOT_POSITIVE_MEAN, newMean);
}
this.mean = newMean;
}
/**
* Access the mean.
* @return the mean.
*/
public double getMean() {
return mean;
}
/**
* Return the probability density for a particular point.
*
* @param x The point at which the density should be computed.
* @return The pdf at point x.
* @deprecated - use density(double)
*/
@Deprecated
public double density(Double x) {
return density(x.doubleValue());
}
/**
* Return the probability density for a particular point.
*
* @param x The point at which the density should be computed.
* @return The pdf at point x.
* @since 2.1
*/
@Override
public double density(double x) {
if (x < 0) {
return 0;
}
return FastMath.exp(-x / mean) / mean;
}
/**
* For this distribution, X, this method returns P(X < x).
*
* The implementation of this method is based on:
* <ul>
* <li>
* <a href="http://mathworld.wolfram.com/ExponentialDistribution.html">
* Exponential Distribution</a>, equation (1).</li>
* </ul>
*
* @param x the value at which the CDF is evaluated.
* @return CDF for this distribution.
* @throws MathException if the cumulative probability can not be
* computed due to convergence or other numerical errors.
*/
public double cumulativeProbability(double x) throws MathException{
double ret;
if (x <= 0.0) {
ret = 0.0;
} else {
ret = 1.0 - FastMath.exp(-x / mean);
}
return ret;
}
/**
* For this distribution, X, this method returns the critical point x, such
* that P(X < x) = <code>p</code>.
* <p>
* Returns 0 for p=0 and <code>Double.POSITIVE_INFINITY</code> for p=1.</p>
*
* @param p the desired probability
* @return x, such that P(X < x) = <code>p</code>
* @throws MathException if the inverse cumulative probability can not be
* computed due to convergence or other numerical errors.
* @throws IllegalArgumentException if p < 0 or p > 1.
*/
@Override
public double inverseCumulativeProbability(double p) throws MathException {
double ret;
if (p < 0.0 || p > 1.0) {
throw MathRuntimeException.createIllegalArgumentException(
LocalizedFormats.OUT_OF_RANGE_SIMPLE, p, 0.0, 1.0);
} else if (p == 1.0) {
ret = Double.POSITIVE_INFINITY;
} else {
ret = -mean * FastMath.log(1.0 - p);
}
return ret;
}
/**
* Generates a random value sampled from this distribution.
*
* <p><strong>Algorithm Description</strong>: Uses the <a
* href="http://www.jesus.ox.ac.uk/~clifford/a5/chap1/node5.html"> Inversion
* Method</a> to generate exponentially distributed random values from
* uniform deviates. </p>
*
* @return random value
* @since 2.2
* @throws MathException if an error occurs generating the random value
*/
@Override
public double sample() throws MathException {
return randomData.nextExponential(mean);
}
/**
* Access the domain value lower bound, based on <code>p</code>, used to
* bracket a CDF root.
*
* @param p the desired probability for the critical value
* @return domain value lower bound, i.e.
* P(X < <i>lower bound</i>) < <code>p</code>
*/
@Override
protected double getDomainLowerBound(double p) {
return 0;
}
/**
* Access the domain value upper bound, based on <code>p</code>, used to
* bracket a CDF root.
*
* @param p the desired probability for the critical value
* @return domain value upper bound, i.e.
* P(X < <i>upper bound</i>) > <code>p</code>
*/
@Override
protected double getDomainUpperBound(double p) {
// NOTE: exponential is skewed to the left
// NOTE: therefore, P(X < μ) > .5
if (p < .5) {
// use mean
return mean;
} else {
// use max
return Double.MAX_VALUE;
}
}
/**
* Access the initial domain value, based on <code>p</code>, used to
* bracket a CDF root.
*
* @param p the desired probability for the critical value
* @return initial domain value
*/
@Override
protected double getInitialDomain(double p) {
// TODO: try to improve on this estimate
// TODO: what should really happen here is not derive from AbstractContinuousDistribution
// TODO: because the inverse cumulative distribution is simple.
// Exponential is skewed to the left, therefore, P(X < μ) > .5
if (p < .5) {
// use 1/2 mean
return mean * .5;
} else {
// use mean
return mean;
}
}
/**
* 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;
}
/**
* Returns the lower bound of the support for the distribution.
*
* The lower bound of the support is always 0, regardless of the mean.
*
* @return lower bound of the support (always 0)
* @since 2.2
*/
public double getSupportLowerBound() {
return 0;
}
/**
* Returns the upper bound of the support for the distribution.
*
* The upper bound of the support is always positive infinity,
* regardless of the mean.
*
* @return upper bound of the support (always Double.POSITIVE_INFINITY)
* @since 2.2
*/
public double getSupportUpperBound() {
return Double.POSITIVE_INFINITY;
}
/**
* Returns the mean of the distribution.
*
* For mean parameter <code>k</code>, the mean is
* <code>k</code>
*
* @return the mean
* @since 2.2
*/
public double getNumericalMean() {
return getMean();
}
/**
* Returns the variance of the distribution.
*
* For mean parameter <code>k</code>, the variance is
* <code>k^2</code>
*
* @return the variance
* @since 2.2
*/
public double getNumericalVariance() {
final double m = getMean();
return m * m;
}
}