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Diffstat (limited to 'src/main/java/org/apache/commons/math3/distribution/ParetoDistribution.java')
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diff --git a/src/main/java/org/apache/commons/math3/distribution/ParetoDistribution.java b/src/main/java/org/apache/commons/math3/distribution/ParetoDistribution.java new file mode 100644 index 0000000..c4d5d58 --- /dev/null +++ b/src/main/java/org/apache/commons/math3/distribution/ParetoDistribution.java @@ -0,0 +1,315 @@ +/* + * 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>{@code α} is the <em>shape</em> 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:</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>{@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} + * + * <p>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); + } +} |