math/distribution/ExponentialDistributionImpl.java

/*
 * 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 &lt; 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 &lt; 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 &lt; 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 &lt; <i>lower bound</i>) &lt; <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 &lt; <i>upper bound</i>) &gt; <code>p</code>
     */
    @Override
    protected double getDomainUpperBound(double p) {
        // NOTE: exponential is skewed to the left
        // NOTE: therefore, P(X < &mu;) > .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 < &mu;) > .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;
    }

}