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Java example source code file (ExponentialDistribution.java)

This example Java source code file (ExponentialDistribution.java) is included in the alvinalexander.com "Java Source Code Warehouse" project. The intent of this project is to help you "Learn Java by Example" TM.

Learn more about this Java project at its project page.

Java - Java tags/keywords

abstractrealdistribution, default_inverse_absolute_accuracy, ensured, exponential_sa_qi, exponentialdistribution, ln2, notstrictlypositiveexception, outofrangeexception, override, resizabledoublearray, should, well19937c

The ExponentialDistribution.java Java example source code

/*
 * 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.random.RandomGenerator;
import org.apache.commons.math3.random.Well19937c;
import org.apache.commons.math3.util.CombinatoricsUtils;
import org.apache.commons.math3.util.FastMath;
import org.apache.commons.math3.util.ResizableDoubleArray;

/**
 * Implementation of the exponential distribution.
 *
 * @see <a href="http://en.wikipedia.org/wiki/Exponential_distribution">Exponential distribution (Wikipedia)
 * @see <a href="http://mathworld.wolfram.com/ExponentialDistribution.html">Exponential distribution (MathWorld)
 */
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;
    /**
     * Used when generating Exponential samples.
     * Table containing the constants
     * q_i = sum_{j=1}^i (ln 2)^j/j! = ln 2 + (ln 2)^2/2 + ... + (ln 2)^i/i!
     * until the largest representable fraction below 1 is exceeded.
     *
     * Note that
     * 1 = 2 - 1 = exp(ln 2) - 1 = sum_{n=1}^infty (ln 2)^n / n!
     * thus q_i -> 1 as i -> +inf,
     * so the higher i, the closer to one we get (the series is not alternating).
     *
     * By trying, n = 16 in Java is enough to reach 1.0.
     */
    private static final double[] EXPONENTIAL_SA_QI;
    /** 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;

    /**
     * Initialize tables.
     */
    static {
        /**
         * Filling EXPONENTIAL_SA_QI table.
         * Note that we don't want qi = 0 in the table.
         */
        final double LN2 = FastMath.log(2);
        double qi = 0;
        int i = 1;

        /**
         * ArithmeticUtils provides factorials up to 20, so let's use that
         * limit together with Precision.EPSILON to generate the following
         * code (a priori, we know that there will be 16 elements, but it is
         * better to not hardcode it).
         */
        final ResizableDoubleArray ra = new ResizableDoubleArray(20);

        while (qi < 1) {
            qi += FastMath.pow(LN2, i) / CombinatoricsUtils.factorial(i);
            ra.addElement(qi);
            ++i;
        }

        EXPONENTIAL_SA_QI = ra.getElements();
    }

    /**
     * Create an exponential distribution with the given mean.
     * <p>
     * <b>Note: this constructor will implicitly create an instance of
     * {@link Well19937c} as random generator to be used for sampling only (see
     * {@link #sample()} and {@link #sample(int)}). In case no sampling is
     * needed for the created distribution, it is advised to pass {@code null}
     * as random generator via the appropriate constructors to avoid the
     * additional initialisation overhead.
     *
     * @param mean mean of this distribution.
     */
    public ExponentialDistribution(double mean) {
        this(mean, DEFAULT_INVERSE_ABSOLUTE_ACCURACY);
    }

    /**
     * Create an exponential distribution with the given mean.
     * <p>
     * <b>Note: this constructor will implicitly create an instance of
     * {@link Well19937c} as random generator to be used for sampling only (see
     * {@link #sample()} and {@link #sample(int)}). In case no sampling is
     * needed for the created distribution, it is advised to pass {@code null}
     * as random generator via the appropriate constructors to avoid the
     * additional initialisation overhead.
     *
     * @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) {
        this(new Well19937c(), mean, inverseCumAccuracy);
    }

    /**
     * Creates an exponential distribution.
     *
     * @param rng Random number generator.
     * @param mean Mean of this distribution.
     * @throws NotStrictlyPositiveException if {@code mean <= 0}.
     * @since 3.3
     */
    public ExponentialDistribution(RandomGenerator rng, double mean)
        throws NotStrictlyPositiveException {
        this(rng, mean, DEFAULT_INVERSE_ABSOLUTE_ACCURACY);
    }

    /**
     * Creates an exponential distribution.
     *
     * @param rng Random number generator.
     * @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 3.1
     */
    public ExponentialDistribution(RandomGenerator rng,
                                   double mean,
                                   double inverseCumAccuracy)
        throws NotStrictlyPositiveException {
        super(rng);

        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} */
    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).
     * </ul>
     */
    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}
     *
     * <p>Algorithm Description: this implementation 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.
     * @since 2.2
     */
    @Override
    public double sample() {
        // Step 1:
        double a = 0;
        double u = random.nextDouble();

        // Step 2 and 3:
        while (u < 0.5) {
            a += EXPONENTIAL_SA_QI[0];
            u *= 2;
        }

        // Step 4 (now u >= 0.5):
        u += u - 1;

        // Step 5:
        if (u <= EXPONENTIAL_SA_QI[0]) {
            return mean * (a + u);
        }

        // Step 6:
        int i = 0; // Should be 1, be we iterate before it in while using 0
        double u2 = random.nextDouble();
        double umin = u2;

        // Step 7 and 8:
        do {
            ++i;
            u2 = random.nextDouble();

            if (u2 < umin) {
                umin = u2;
            }

            // Step 8:
        } while (u > EXPONENTIAL_SA_QI[i]); // Ensured to exit since EXPONENTIAL_SA_QI[MAX] = 1

        return mean * (a + umin * EXPONENTIAL_SA_QI[0]);
    }

    /** {@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;
    }
}

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