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Java example source code file (ParetoDistribution.java)

This example Java source code file (ParetoDistribution.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, deprecated, notstrictlypositiveexception, numberistoolargeexception, override, paretodistribution, well19937c

The ParetoDistribution.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.util.FastMath;

/**
 * Implementation of the Pareto distribution.
 *
 * <p>
 * <strong>Parameters:
 * The probability distribution function of {@code X} is given by (for {@code x >= k}):
 * <pre>
 *  α * k^α / x^(α + 1)
 * </pre>
 * <p>
 * <ul>
 * <li>{@code k} is the scale parameter: this is the minimum possible value of {@code X},
 * <li>{@code α} is the shape parameter: this is the Pareto index
 * </ul>
 *
 * @see <a href="http://en.wikipedia.org/wiki/Pareto_distribution">
 * Pareto distribution (Wikipedia)</a>
 * @see <a href="http://mathworld.wolfram.com/ParetoDistribution.html">
 * Pareto distribution (MathWorld)</a>
 *
 * @since 3.3
 */
public class ParetoDistribution 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 = 20130424;

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

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

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

    /**
     * Create a Pareto distribution with a scale of {@code 1} and a shape of {@code 1}.
     */
    public ParetoDistribution() {
        this(1, 1);
    }

    /**
     * Create a Pareto 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 scale <= 0} or {@code shape <= 0}.
     */
    public ParetoDistribution(double scale, double shape)
        throws NotStrictlyPositiveException {
        this(scale, shape, DEFAULT_INVERSE_ABSOLUTE_ACCURACY);
    }

    /**
     * Create a Pareto 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 scale <= 0} or {@code shape <= 0}.
     */
    public ParetoDistribution(double scale, double shape, double inverseCumAccuracy)
        throws NotStrictlyPositiveException {
        this(new Well19937c(), scale, shape, inverseCumAccuracy);
    }

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

    /**
     * Creates a Pareto 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 scale <= 0} or {@code shape <= 0}.
     */
    public ParetoDistribution(RandomGenerator rng,
                              double scale,
                              double shape,
                              double inverseCumAccuracy)
        throws NotStrictlyPositiveException {
        super(rng);

        if (scale <= 0) {
            throw new NotStrictlyPositiveException(LocalizedFormats.SCALE, scale);
        }

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

        this.scale = scale;
        this.shape = shape;
        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}
     * <p>
     * For scale {@code k}, and shape {@code α} of this distribution, the PDF
     * is given by
     * <ul>
     * <li>{@code 0} if {@code x < k},
     * <li>{@code α * k^α / x^(α + 1)} otherwise.
     * </ul>
     */
    public double density(double x) {
        if (x < scale) {
            return 0;
        }
        return FastMath.pow(scale, shape) / FastMath.pow(x, shape + 1) * shape;
    }

    /** {@inheritDoc}
     *
     * See documentation of {@link #density(double)} for computation details.
     */
    @Override
    public double logDensity(double x) {
        if (x < scale) {
            return Double.NEGATIVE_INFINITY;
        }
        return FastMath.log(scale) * shape - FastMath.log(x) * (shape + 1) + FastMath.log(shape);
    }

    /**
     * {@inheritDoc}
     * <p>
     * For scale {@code k}, and shape {@code α} of this distribution, the CDF is given by
     * <ul>
     * <li>{@code 0} if {@code x < k},
     * <li>{@code 1 - (k / x)^α} otherwise.
     * </ul>
     */
    public double cumulativeProbability(double x)  {
        if (x <= scale) {
            return 0;
        }
        return 1 - FastMath.pow(scale / x, shape);
    }

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

    /**
     * {@inheritDoc}
     * <p>
     * For scale {@code k} and shape {@code α}, the mean is given by
     * <ul>
     * <li>{@code ∞} if {@code α <= 1},
     * <li>{@code α * k / (α - 1)} otherwise.
     * </ul>
     */
    public double getNumericalMean() {
        if (shape <= 1) {
            return Double.POSITIVE_INFINITY;
        }
        return shape * scale / (shape - 1);
    }

    /**
     * {@inheritDoc}
     * <p>
     * For scale {@code k} and shape {@code α}, the variance is given by
     * <ul>
     * <li>{@code ∞} if {@code 1 < α <= 2},
     * <li>{@code k^2 * α / ((α - 1)^2 * (α - 2))} otherwise.
     * </ul>
     */
    public double getNumericalVariance() {
        if (shape <= 2) {
            return Double.POSITIVE_INFINITY;
        }
        double s = shape - 1;
        return scale * scale * shape / (s * s) / (shape - 2);
    }

    /**
     * {@inheritDoc}
     * <p>
     * The lower bound of the support is equal to the scale parameter {@code k}.
     *
     * @return lower bound of the support
     */
    public double getSupportLowerBound() {
        return scale;
    }

    /**
     * {@inheritDoc}
     * <p>
     * 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}
     * <p>
     * The support of this distribution is connected.
     *
     * @return {@code true}
     */
    public boolean isSupportConnected() {
        return true;
    }

    /** {@inheritDoc} */
    @Override
    public double sample()  {
        final double n = random.nextDouble();
        return scale / FastMath.pow(n, 1 / shape);
    }
}

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