| /* |
| * 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:</strong> |
| * 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 <em>scale</em> parameter: this is the minimum possible value of {@code X},</li> |
| * <li>{@code α} is the <em>shape</em> parameter: this is the Pareto index</li> |
| * </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:</b> 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:</b> 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> |
| * <li>{@code α * k^α / x^(α + 1)} otherwise.</li> |
| * </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> |
| * <li>{@code 1 - (k / x)^α} otherwise.</li> |
| * </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> |
| * <li>{@code α * k / (α - 1)} otherwise.</li> |
| * </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> |
| * <li>{@code k^2 * α / ((α - 1)^2 * (α - 2))} otherwise.</li> |
| * </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); |
| } |
| } |
