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Java example source code file (LevyDistribution.java)

This example Java source code file (LevyDistribution.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, levydistribution, outofrangeexception, override, randomgenerator, setting, well19937c

The LevyDistribution.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.OutOfRangeException;
import org.apache.commons.math3.random.RandomGenerator;
import org.apache.commons.math3.random.Well19937c;
import org.apache.commons.math3.special.Erf;
import org.apache.commons.math3.util.FastMath;

/**
 * This class implements the <a href="http://en.wikipedia.org/wiki/L%C3%A9vy_distribution">
 * Lévy distribution</a>.
 *
 * @since 3.2
 */
public class LevyDistribution extends AbstractRealDistribution {

    /** Serializable UID. */
    private static final long serialVersionUID = 20130314L;

    /** Location parameter. */
    private final double mu;

    /** Scale parameter. */
    private final double c;  // Setting this to 1 returns a cumProb of 1.0

    /** Half of c (for calculations). */
    private final double halfC;

    /**
     * Build a new instance.
     * <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 mu location parameter
     * @param c scale parameter
     * @since 3.4
     */
    public LevyDistribution(final double mu, final double c) {
        this(new Well19937c(), mu, c);
    }

    /**
     * Creates a LevyDistribution.
     * @param rng random generator to be used for sampling
     * @param mu location
     * @param c scale parameter
     */
    public LevyDistribution(final RandomGenerator rng, final double mu, final double c) {
        super(rng);
        this.mu    = mu;
        this.c     = c;
        this.halfC = 0.5 * c;
    }

    /** {@inheritDoc}
    * <p>
    * From Wikipedia: The probability density function of the Lévy distribution
    * over the domain is
    * </p>
    * <pre>
    * f(x; μ, c) = √(c / 2π) * e<sup>-c / 2 (x - μ) / (x - μ)3/2
    * </pre>
    * <p>
    * For this distribution, {@code X}, this method returns {@code P(X < x)}.
    * If {@code x} is less than location parameter μ, {@code Double.NaN} is
    * returned, as in these cases the distribution is not defined.
    * </p>
    */
    public double density(final double x) {
        if (x < mu) {
            return Double.NaN;
        }

        final double delta = x - mu;
        final double f     = halfC / delta;
        return FastMath.sqrt(f / FastMath.PI) * FastMath.exp(-f) /delta;
    }

    /** {@inheritDoc}
     *
     * See documentation of {@link #density(double)} for computation details.
     */
    @Override
    public double logDensity(double x) {
        if (x < mu) {
            return Double.NaN;
        }

        final double delta = x - mu;
        final double f     = halfC / delta;
        return 0.5 * FastMath.log(f / FastMath.PI) - f - FastMath.log(delta);
    }

    /** {@inheritDoc}
     * <p>
     * From Wikipedia: the cumulative distribution function is
     * </p>
     * <pre>
     * f(x; u, c) = erfc (√ (c / 2 (x - u )))
     * </pre>
     */
    public double cumulativeProbability(final double x) {
        if (x < mu) {
            return Double.NaN;
        }
        return Erf.erfc(FastMath.sqrt(halfC / (x - mu)));
    }

    /** {@inheritDoc} */
    @Override
    public double inverseCumulativeProbability(final double p) throws OutOfRangeException {
        if (p < 0.0 || p > 1.0) {
            throw new OutOfRangeException(p, 0, 1);
        }
        final double t = Erf.erfcInv(p);
        return mu + halfC / (t * t);
    }

    /** Get the scale parameter of the distribution.
     * @return scale parameter of the distribution
     */
    public double getScale() {
        return c;
    }

    /** Get the location parameter of the distribution.
     * @return location parameter of the distribution
     */
    public double getLocation() {
        return mu;
    }

    /** {@inheritDoc} */
    public double getNumericalMean() {
        return Double.POSITIVE_INFINITY;
    }

    /** {@inheritDoc} */
    public double getNumericalVariance() {
        return Double.POSITIVE_INFINITY;
    }

    /** {@inheritDoc} */
    public double getSupportLowerBound() {
        return mu;
    }

    /** {@inheritDoc} */
    public double getSupportUpperBound() {
        return Double.POSITIVE_INFINITY;
    }

    /** {@inheritDoc} */
    public boolean isSupportLowerBoundInclusive() {
        // there is a division by x-mu in the computation, so density
        // is not finite at lower bound, bound must be excluded
        return false;
    }

    /** {@inheritDoc} */
    public boolean isSupportUpperBoundInclusive() {
        // upper bound is infinite, so it must be excluded
        return false;
    }

    /** {@inheritDoc} */
    public boolean isSupportConnected() {
        return true;
    }

}

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