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The Apache Commons Math project is a library of lightweight, self-contained mathematics and statistics components addressing the most common practical problems not immediately available in the Java programming language or commons-lang.
/*
* 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.math3.distribution;
import org.apache.commons.math3.exception.NotStrictlyPositiveException;
import org.apache.commons.math3.exception.OutOfRangeException;
import org.apache.commons.math3.exception.util.LocalizedFormats;
import org.apache.commons.math3.util.FastMath;
/**
* Implementation of the exponential distribution.
*
* @see Exponential distribution (Wikipedia)
* @see Exponential distribution (MathWorld)
* @version $Id: ExponentialDistribution.java 1244107 2012-02-14 16:17:55Z erans $
*/
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 = 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 ExponentialDistribution(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 ExponentialDistribution(double mean, double inverseCumAccuracy)
throws NotStrictlyPositiveException {
if (mean <= 0) {
throw new NotStrictlyPositiveException(LocalizedFormats.MEAN, mean);
}
this.mean = mean;
solverAbsoluteAccuracy = inverseCumAccuracy;
}
/**
* Access the mean.
*
* @return the mean.
*/
public double getMean() {
return mean;
}
/**
* {@inheritDoc}
*
* For this distribution {@code P(X = x)} always evaluates to 0.
*
* @return 0
*/
public double probability(double x) {
return 0.0;
}
/** {@inheritDoc} */
public double density(double x) {
if (x < 0) {
return 0;
}
return FastMath.exp(-x / mean) / mean;
}
/**
* {@inheritDoc}
*
* The implementation of this method is based on:
*
* -
*
* Exponential Distribution, equation (1).
*
*/
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}
*
* Algorithm Description: this implementation uses the
*
* Inversion Method to generate exponentially distributed random values
* from uniform deviates.
*
* @return a random value.
* @since 2.2
*/
@Override
public double sample() {
return randomData.nextExponential(mean);
}
/** {@inheritDoc} */
@Override
protected double getSolverAbsoluteAccuracy() {
return solverAbsoluteAccuracy;
}
/**
* {@inheritDoc}
*
* For mean parameter {@code k}, the mean is {@code k}.
*/
public double getNumericalMean() {
return getMean();
}
/**
* {@inheritDoc}
*
* For mean parameter {@code k}, the variance is {@code k^2}.
*/
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)
*/
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)
*/
public double getSupportUpperBound() {
return Double.POSITIVE_INFINITY;
}
/** {@inheritDoc} */
public boolean isSupportLowerBoundInclusive() {
return true;
}
/** {@inheritDoc} */
public boolean isSupportUpperBoundInclusive() {
return false;
}
/**
* {@inheritDoc}
*
* The support of this distribution is connected.
*
* @return {@code true}
*/
public boolean isSupportConnected() {
return true;
}
}