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The Apache Commons Math project is a library of lightweight, self-contained mathematics and statistics components addressing the most common practical problems not immediately available in the Java programming language or commons-lang.

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/*
 * 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.OutOfRangeException;
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 Cauchy distribution.
 *
 * @see Cauchy distribution (Wikipedia)
 * @see Cauchy Distribution (MathWorld)
 * @since 1.1 (changed to concrete class in 3.0)
 */
public class CauchyDistribution extends AbstractRealDistribution {
    /**
     * Default inverse cumulative probability accuracy.
     * @since 2.1
     */
    public static final double DEFAULT_INVERSE_ABSOLUTE_ACCURACY = 1e-9;
    /** Serializable version identifier */
    private static final long serialVersionUID = 8589540077390120676L;
    /** The median of this distribution. */
    private final double median;
    /** The scale of this distribution. */
    private final double scale;
    /** Inverse cumulative probability accuracy */
    private final double solverAbsoluteAccuracy;

    /**
     * Creates a Cauchy distribution with the median equal to zero and scale
     * equal to one.
     */
    public CauchyDistribution() {
        this(0, 1);
    }

    /**
     * Creates a Cauchy distribution using the given median and scale.
     * 

* 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 median Median for this distribution. * @param scale Scale parameter for this distribution. */ public CauchyDistribution(double median, double scale) { this(median, scale, DEFAULT_INVERSE_ABSOLUTE_ACCURACY); } /** * Creates a Cauchy distribution using the given median and scale. *

* 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 median Median for this distribution. * @param scale Scale parameter for this distribution. * @param inverseCumAccuracy Maximum absolute error in inverse * cumulative probability estimates * (defaults to {@link #DEFAULT_INVERSE_ABSOLUTE_ACCURACY}). * @throws NotStrictlyPositiveException if {@code scale <= 0}. * @since 2.1 */ public CauchyDistribution(double median, double scale, double inverseCumAccuracy) { this(new Well19937c(), median, scale, inverseCumAccuracy); } /** * Creates a Cauchy distribution. * * @param rng Random number generator. * @param median Median for this distribution. * @param scale Scale parameter for this distribution. * @throws NotStrictlyPositiveException if {@code scale <= 0}. * @since 3.3 */ public CauchyDistribution(RandomGenerator rng, double median, double scale) { this(rng, median, scale, DEFAULT_INVERSE_ABSOLUTE_ACCURACY); } /** * Creates a Cauchy distribution. * * @param rng Random number generator. * @param median Median for this distribution. * @param scale Scale parameter for this distribution. * @param inverseCumAccuracy Maximum absolute error in inverse * cumulative probability estimates * (defaults to {@link #DEFAULT_INVERSE_ABSOLUTE_ACCURACY}). * @throws NotStrictlyPositiveException if {@code scale <= 0}. * @since 3.1 */ public CauchyDistribution(RandomGenerator rng, double median, double scale, double inverseCumAccuracy) { super(rng); if (scale <= 0) { throw new NotStrictlyPositiveException(LocalizedFormats.SCALE, scale); } this.scale = scale; this.median = median; solverAbsoluteAccuracy = inverseCumAccuracy; } /** {@inheritDoc} */ public double cumulativeProbability(double x) { return 0.5 + (FastMath.atan((x - median) / scale) / FastMath.PI); } /** * Access the median. * * @return the median for this distribution. */ public double getMedian() { return median; } /** * Access the scale parameter. * * @return the scale parameter for this distribution. */ public double getScale() { return scale; } /** {@inheritDoc} */ public double density(double x) { final double dev = x - median; return (1 / FastMath.PI) * (scale / (dev * dev + scale * scale)); } /** * {@inheritDoc} * * Returns {@code Double.NEGATIVE_INFINITY} when {@code p == 0} * and {@code Double.POSITIVE_INFINITY} when {@code p == 1}. */ @Override public double inverseCumulativeProbability(double p) throws OutOfRangeException { double ret; if (p < 0 || p > 1) { throw new OutOfRangeException(p, 0, 1); } else if (p == 0) { ret = Double.NEGATIVE_INFINITY; } else if (p == 1) { ret = Double.POSITIVE_INFINITY; } else { ret = median + scale * FastMath.tan(FastMath.PI * (p - .5)); } return ret; } /** {@inheritDoc} */ @Override protected double getSolverAbsoluteAccuracy() { return solverAbsoluteAccuracy; } /** * {@inheritDoc} * * The mean is always undefined no matter the parameters. * * @return mean (always Double.NaN) */ public double getNumericalMean() { return Double.NaN; } /** * {@inheritDoc} * * The variance is always undefined no matter the parameters. * * @return variance (always Double.NaN) */ public double getNumericalVariance() { return Double.NaN; } /** * {@inheritDoc} * * The lower bound of the support is always negative infinity no matter * the parameters. * * @return lower bound of the support (always Double.NEGATIVE_INFINITY) */ public double getSupportLowerBound() { return Double.NEGATIVE_INFINITY; } /** * {@inheritDoc} * * The upper bound of the support is always positive infinity no matter * the parameters. * * @return upper bound of the support (always Double.POSITIVE_INFINITY) */ public double getSupportUpperBound() { return Double.POSITIVE_INFINITY; } /** {@inheritDoc} */ public boolean isSupportLowerBoundInclusive() { return false; } /** {@inheritDoc} */ public boolean isSupportUpperBoundInclusive() { return false; } /** * {@inheritDoc} * * The support of this distribution is connected. * * @return {@code true} */ public boolean isSupportConnected() { return true; } }





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