/*
* 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.exception.NotStrictlyPositiveException;
import org.apache.commons.math.exception.OutOfRangeException;
import org.apache.commons.math.exception.util.LocalizedFormats;
import org.apache.commons.math.util.FastMath;
/**
* The default implementation of {@link ExponentialDistribution}.
*
* @version $Id: ExponentialDistributionImpl.java 1131229 2011-06-03 20:49:25Z luc $
*/
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 final 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 Maximum absolute error in inverse
* cumulative probability estimates (defaults to
* {@link #DEFAULT_INVERSE_ABSOLUTE_ACCURACY}).
* @throws NotStrictlyPositiveException if {@code mean <= 0}.
* @since 2.1
*/
public ExponentialDistributionImpl(double mean, double inverseCumAccuracy) {
if (mean <= 0) {
throw new NotStrictlyPositiveException(LocalizedFormats.MEAN, mean);
}
this.mean = mean;
solverAbsoluteAccuracy = inverseCumAccuracy;
}
/**
* {@inheritDoc}
*/
public double getMean() {
return mean;
}
/**
* {@inheritDoc}
*/
@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 Value at which the CDF is evaluated.
* @return the 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 {@code P(X < x) = p}.
* It will return 0 when p = 0 and {@code Double.POSITIVE_INFINITY}
* when p = 1.
*
* @param p Desired probability.
* @return {@code x}, such that {@code P(X < x) = p}.
* @throws MathException if the inverse cumulative probability can not be
* computed due to convergence or other numerical errors.
* @throws OutOfRangeException if {@code p < 0} or {@code p > 1}.
*/
@Override
public double inverseCumulativeProbability(double p) throws MathException {
double ret;
if (p < 0.0 || p > 1.0) {
throw new OutOfRangeException(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 a random value.
* @throws MathException if an error occurs generating the random value.
* @since 2.2
*/
@Override
public double sample() throws MathException {
return randomData.nextExponential(mean);
}
/**
* Access the domain value lower bound, based on {@code p}, used to
* bracket a CDF root.
*
* @param p Desired probability for the critical value.
* @return the domain value lower bound, i.e. {@code P(X < 'lower bound') < p}.
*/
@Override
protected double getDomainLowerBound(double p) {
return 0;
}
/**
* Access the domain value upper bound, based on {@code p}, used to
* bracket a CDF root.
*
* @param p Desired probability for the critical value.
* @return the domain value upper bound, i.e. {@code P(X < 'upper bound') > p}.
*/
@Override
protected double getDomainUpperBound(double p) {
// NOTE: exponential is skewed to the left
// NOTE: therefore, P(X < μ) > .5
if (p < 0.5) {
// use mean
return mean;
} else {
// use max
return Double.MAX_VALUE;
}
}
/**
* Access the initial domain value, based on {@code p}, used to
* bracket a CDF root.
*
* @param p Desired probability for the critical value.
* @return the 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 < 0.5) {
// use 1/2 mean
return mean * 0.5;
} 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;
}
/**
* {@inheritDoc}
*
* The lower bound of the support is always 0 no matter the mean parameter.
*
* @return lower bound of the support (always 0)
*/
@Override
public double getSupportLowerBound() {
return 0;
}
/**
* {@inheritDoc}
*
* The upper bound of the support is always positive infinity
* no matter the mean parameter.
*
* @return upper bound of the support (always Double.POSITIVE_INFINITY)
*/
@Override
public double getSupportUpperBound() {
return Double.POSITIVE_INFINITY;
}
/**
* {@inheritDoc}
*
* For mean parameter <code>k</code>, the mean is
* <code>k</code>
*
* @return {@inheritDoc}
*/
@Override
protected double calculateNumericalMean() {
return getMean();
}
/**
* {@inheritDoc}
*
* For mean parameter <code>k</code>, the variance is
* <code>k^2</code>
*
* @return {@inheritDoc}
*/
@Override
protected double calculateNumericalVariance() {
final double m = getMean();
return m * m;
}
/**
* {@inheritDoc}
*/
@Override
public boolean isSupportLowerBoundInclusive() {
return true;
}
/**
* {@inheritDoc}
*/
@Override
public boolean isSupportUpperBoundInclusive() {
return false;
}
}