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Java example source code file (LogNormalDistribution.java)

This example Java source code file (LogNormalDistribution.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, lognormaldistribution, notstrictlypositiveexception, numberistoolargeexception, override, override@deprecated, sqrt2, sqrt2pi, well19937c

The LogNormalDistribution.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.NumberIsTooLargeException;
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.special.Erf;
import org.apache.commons.math3.util.FastMath;

/**
 * Implementation of the log-normal (gaussian) distribution.
 *
 * <p>
 * <strong>Parameters:
 * {@code X} is log-normally distributed if its natural logarithm {@code log(X)}
 * is normally distributed. The probability distribution function of {@code X}
 * is given by (for {@code x > 0})
 * </p>
 * <p>
 * {@code exp(-0.5 * ((ln(x) - m) / s)^2) / (s * sqrt(2 * pi) * x)}
 * </p>
 * <ul>
 * <li>{@code m} is the scale parameter: this is the mean of the
 * normally distributed natural logarithm of this distribution,</li>
 * <li>{@code s} is the shape parameter: this is the standard
 * deviation of the normally distributed natural logarithm of this
 * distribution.
 * </ul>
 *
 * @see <a href="http://en.wikipedia.org/wiki/Log-normal_distribution">
 * Log-normal distribution (Wikipedia)</a>
 * @see <a href="http://mathworld.wolfram.com/LogNormalDistribution.html">
 * Log Normal distribution (MathWorld)</a>
 *
 * @since 3.0
 */
public class LogNormalDistribution extends AbstractRealDistribution {
    /** Default inverse cumulative probability accuracy. */
    public static final double DEFAULT_INVERSE_ABSOLUTE_ACCURACY = 1e-9;

    /** Serializable version identifier. */
    private static final long serialVersionUID = 20120112;

    /** √(2 π) */
    private static final double SQRT2PI = FastMath.sqrt(2 * FastMath.PI);

    /** √(2) */
    private static final double SQRT2 = FastMath.sqrt(2.0);

    /** The scale parameter of this distribution. */
    private final double scale;

    /** The shape parameter of this distribution. */
    private final double shape;
    /** The value of {@code log(shape) + 0.5 * log(2*PI)} stored for faster computation. */
    private final double logShapePlusHalfLog2Pi;

    /** Inverse cumulative probability accuracy. */
    private final double solverAbsoluteAccuracy;

    /**
     * Create a log-normal distribution, where the mean and standard deviation
     * of the {@link NormalDistribution normally distributed} natural
     * logarithm of the log-normal distribution are equal to zero and one
     * respectively. In other words, the scale of the returned distribution is
     * {@code 0}, while its shape is {@code 1}.
     * <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.
     */
    public LogNormalDistribution() {
        this(0, 1);
    }

    /**
     * Create a log-normal distribution using the specified scale and shape.
     * <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 scale the scale parameter of this distribution
     * @param shape the shape parameter of this distribution
     * @throws NotStrictlyPositiveException if {@code shape <= 0}.
     */
    public LogNormalDistribution(double scale, double shape)
        throws NotStrictlyPositiveException {
        this(scale, shape, DEFAULT_INVERSE_ABSOLUTE_ACCURACY);
    }

    /**
     * Create a log-normal distribution using the specified scale, shape and
     * inverse cumulative distribution accuracy.
     * <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 scale the scale parameter of this distribution
     * @param shape the shape parameter of this distribution
     * @param inverseCumAccuracy Inverse cumulative probability accuracy.
     * @throws NotStrictlyPositiveException if {@code shape <= 0}.
     */
    public LogNormalDistribution(double scale, double shape, double inverseCumAccuracy)
        throws NotStrictlyPositiveException {
        this(new Well19937c(), scale, shape, inverseCumAccuracy);
    }

    /**
     * Creates a log-normal distribution.
     *
     * @param rng Random number generator.
     * @param scale Scale parameter of this distribution.
     * @param shape Shape parameter of this distribution.
     * @throws NotStrictlyPositiveException if {@code shape <= 0}.
     * @since 3.3
     */
    public LogNormalDistribution(RandomGenerator rng, double scale, double shape)
        throws NotStrictlyPositiveException {
        this(rng, scale, shape, DEFAULT_INVERSE_ABSOLUTE_ACCURACY);
    }

    /**
     * Creates a log-normal distribution.
     *
     * @param rng Random number generator.
     * @param scale Scale parameter of this distribution.
     * @param shape Shape parameter of this distribution.
     * @param inverseCumAccuracy Inverse cumulative probability accuracy.
     * @throws NotStrictlyPositiveException if {@code shape <= 0}.
     * @since 3.1
     */
    public LogNormalDistribution(RandomGenerator rng,
                                 double scale,
                                 double shape,
                                 double inverseCumAccuracy)
        throws NotStrictlyPositiveException {
        super(rng);

        if (shape <= 0) {
            throw new NotStrictlyPositiveException(LocalizedFormats.SHAPE, shape);
        }

        this.scale = scale;
        this.shape = shape;
        this.logShapePlusHalfLog2Pi = FastMath.log(shape) + 0.5 * FastMath.log(2 * FastMath.PI);
        this.solverAbsoluteAccuracy = inverseCumAccuracy;
    }

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

    /**
     * Returns the shape parameter of this distribution.
     *
     * @return the shape parameter
     */
    public double getShape() {
        return shape;
    }

    /**
     * {@inheritDoc}
     *
     * For scale {@code m}, and shape {@code s} of this distribution, the PDF
     * is given by
     * <ul>
     * <li>{@code 0} if {@code x <= 0},
     * <li>{@code exp(-0.5 * ((ln(x) - m) / s)^2) / (s * sqrt(2 * pi) * x)}
     * otherwise.</li>
     * </ul>
     */
    public double density(double x) {
        if (x <= 0) {
            return 0;
        }
        final double x0 = FastMath.log(x) - scale;
        final double x1 = x0 / shape;
        return FastMath.exp(-0.5 * x1 * x1) / (shape * SQRT2PI * x);
    }

    /** {@inheritDoc}
     *
     * See documentation of {@link #density(double)} for computation details.
     */
    @Override
    public double logDensity(double x) {
        if (x <= 0) {
            return Double.NEGATIVE_INFINITY;
        }
        final double logX = FastMath.log(x);
        final double x0 = logX - scale;
        final double x1 = x0 / shape;
        return -0.5 * x1 * x1 - (logShapePlusHalfLog2Pi + logX);
    }

    /**
     * {@inheritDoc}
     *
     * For scale {@code m}, and shape {@code s} of this distribution, the CDF
     * is given by
     * <ul>
     * <li>{@code 0} if {@code x <= 0},
     * <li>{@code 0} if {@code ln(x) - m < 0} and {@code m - ln(x) > 40 * s}, as
     * in these cases the actual value is within {@code Double.MIN_VALUE} of 0,
     * <li>{@code 1} if {@code ln(x) - m >= 0} and {@code ln(x) - m > 40 * s},
     * as in these cases the actual value is within {@code Double.MIN_VALUE} of
     * 1,</li>
     * <li>{@code 0.5 + 0.5 * erf((ln(x) - m) / (s * sqrt(2))} otherwise.
     * </ul>
     */
    public double cumulativeProbability(double x)  {
        if (x <= 0) {
            return 0;
        }
        final double dev = FastMath.log(x) - scale;
        if (FastMath.abs(dev) > 40 * shape) {
            return dev < 0 ? 0.0d : 1.0d;
        }
        return 0.5 + 0.5 * Erf.erf(dev / (shape * SQRT2));
    }

    /**
     * {@inheritDoc}
     *
     * @deprecated See {@link RealDistribution#cumulativeProbability(double,double)}
     */
    @Override@Deprecated
    public double cumulativeProbability(double x0, double x1)
        throws NumberIsTooLargeException {
        return probability(x0, x1);
    }

    /** {@inheritDoc} */
    @Override
    public double probability(double x0,
                              double x1)
        throws NumberIsTooLargeException {
        if (x0 > x1) {
            throw new NumberIsTooLargeException(LocalizedFormats.LOWER_ENDPOINT_ABOVE_UPPER_ENDPOINT,
                                                x0, x1, true);
        }
        if (x0 <= 0 || x1 <= 0) {
            return super.probability(x0, x1);
        }
        final double denom = shape * SQRT2;
        final double v0 = (FastMath.log(x0) - scale) / denom;
        final double v1 = (FastMath.log(x1) - scale) / denom;
        return 0.5 * Erf.erf(v0, v1);
    }

    /** {@inheritDoc} */
    @Override
    protected double getSolverAbsoluteAccuracy() {
        return solverAbsoluteAccuracy;
    }

    /**
     * {@inheritDoc}
     *
     * For scale {@code m} and shape {@code s}, the mean is
     * {@code exp(m + s^2 / 2)}.
     */
    public double getNumericalMean() {
        double s = shape;
        return FastMath.exp(scale + (s * s / 2));
    }

    /**
     * {@inheritDoc}
     *
     * For scale {@code m} and shape {@code s}, the variance is
     * {@code (exp(s^2) - 1) * exp(2 * m + s^2)}.
     */
    public double getNumericalVariance() {
        final double s = shape;
        final double ss = s * s;
        return (FastMath.expm1(ss)) * FastMath.exp(2 * scale + ss);
    }

    /**
     * {@inheritDoc}
     *
     * The lower bound of the support is always 0 no matter the parameters.
     *
     * @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 parameters.
     *
     * @return upper bound of the support (always
     * {@code 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;
    }

    /** {@inheritDoc} */
    @Override
    public double sample()  {
        final double n = random.nextGaussian();
        return FastMath.exp(scale + shape * n);
    }
}

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