Java tutorial
/* * 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; } }