/*
* 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.math4.distribution;
import org.apache.commons.math4.exception.NotStrictlyPositiveException;
import org.apache.commons.math4.exception.OutOfRangeException;
import org.apache.commons.math4.exception.util.LocalizedFormats;
import org.apache.commons.math4.util.FastMath;
import org.apache.commons.rng.UniformRandomProvider;
import org.apache.commons.rng.sampling.distribution.ContinuousSampler;
import org.apache.commons.rng.sampling.distribution.AhrensDieterExponentialSampler;
/**
* Implementation of the exponential distribution.
*
* @see <a href="http://en.wikipedia.org/wiki/Exponential_distribution">Exponential distribution (Wikipedia)</a>
* @see <a href="http://mathworld.wolfram.com/ExponentialDistribution.html">Exponential distribution (MathWorld)</a>
*/
public class ExponentialDistribution extends AbstractRealDistribution {
/**
* 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 = 20160311L;
/** The mean of this distribution. */
private final double mean;
/** The logarithm of the mean, stored to reduce computing time. **/
private final double logMean;
/** Inverse cumulative probability accuracy. */
private final double solverAbsoluteAccuracy;
/**
* Creates a distribution.
*
* @param mean mean of this distribution.
*/
public ExponentialDistribution(double mean) {
this(mean, DEFAULT_INVERSE_ABSOLUTE_ACCURACY);
}
/**
* Creates a distribution.
*
* @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 ExponentialDistribution(double mean,
double inverseCumAccuracy)
throws NotStrictlyPositiveException {
if (mean <= 0) {
throw new NotStrictlyPositiveException(LocalizedFormats.MEAN, mean);
}
this.mean = mean;
logMean = FastMath.log(mean);
solverAbsoluteAccuracy = inverseCumAccuracy;
}
/**
* Access the mean.
*
* @return the mean.
*/
public double getMean() {
return mean;
}
/** {@inheritDoc} */
@Override
public double density(double x) {
final double logDensity = logDensity(x);
return logDensity == Double.NEGATIVE_INFINITY ? 0 : FastMath.exp(logDensity);
}
/** {@inheritDoc} **/
@Override
public double logDensity(double x) {
if (x < 0) {
return Double.NEGATIVE_INFINITY;
}
return -x / mean - logMean;
}
/**
* {@inheritDoc}
*
* 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>
*/
@Override
public double cumulativeProbability(double x) {
double ret;
if (x <= 0.0) {
ret = 0.0;
} else {
ret = 1.0 - FastMath.exp(-x / mean);
}
return ret;
}
/**
* {@inheritDoc}
*
* Returns {@code 0} when {@code p= = 0} and
* {@code Double.POSITIVE_INFINITY} when {@code p == 1}.
*/
@Override
public double inverseCumulativeProbability(double p) throws OutOfRangeException {
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;
}
/** {@inheritDoc} */
@Override
protected double getSolverAbsoluteAccuracy() {
return solverAbsoluteAccuracy;
}
/**
* {@inheritDoc}
*
* For mean parameter {@code k}, the mean is {@code k}.
*/
@Override
public double getNumericalMean() {
return getMean();
}
/**
* {@inheritDoc}
*
* For mean parameter {@code k}, the variance is {@code k^2}.
*/
@Override
public double getNumericalVariance() {
final double m = getMean();
return m * m;
}
/**
* {@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}
*
* The support of this distribution is connected.
*
* @return {@code true}
*/
@Override
public boolean isSupportConnected() {
return true;
}
/**
* {@inheritDoc}
*
* <p>Sampling algorithm 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>
*/
@Override
public RealDistribution.Sampler createSampler(final UniformRandomProvider rng) {
return new RealDistribution.Sampler() {
/**
* Exponential distribution sampler.
*/
private final ContinuousSampler sampler =
new AhrensDieterExponentialSampler(rng, mean);
/**{@inheritDoc} */
@Override
public double sample() {
return sampler.sample();
}
};
}
}