CauchyDistribution.java

  1. /*
  2.  * Licensed to the Apache Software Foundation (ASF) under one or more
  3.  * contributor license agreements.  See the NOTICE file distributed with
  4.  * this work for additional information regarding copyright ownership.
  5.  * The ASF licenses this file to You under the Apache License, Version 2.0
  6.  * (the "License"); you may not use this file except in compliance with
  7.  * the License.  You may obtain a copy of the License at
  8.  *
  9.  *      http://www.apache.org/licenses/LICENSE-2.0
  10.  *
  11.  * Unless required by applicable law or agreed to in writing, software
  12.  * distributed under the License is distributed on an "AS IS" BASIS,
  13.  * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
  14.  * See the License for the specific language governing permissions and
  15.  * limitations under the License.
  16.  */
  17. package org.apache.commons.math3.distribution;

  19. import org.apache.commons.math3.exception.NotStrictlyPositiveException;
  20. import org.apache.commons.math3.exception.OutOfRangeException;
  21. import org.apache.commons.math3.exception.util.LocalizedFormats;
  22. import org.apache.commons.math3.random.RandomGenerator;
  23. import org.apache.commons.math3.random.Well19937c;
  24. import org.apache.commons.math3.util.FastMath;

  26. /**
  27.  * Implementation of the Cauchy distribution.
  28.  *
  29.  * @see <a href="http://en.wikipedia.org/wiki/Cauchy_distribution">Cauchy distribution (Wikipedia)</a>
  30.  * @see <a href="http://mathworld.wolfram.com/CauchyDistribution.html">Cauchy Distribution (MathWorld)</a>
  31.  * @since 1.1 (changed to concrete class in 3.0)
  32.  */
  33. public class CauchyDistribution extends AbstractRealDistribution {
  34.     /**
  35.      * Default inverse cumulative probability accuracy.
  36.      * @since 2.1
  37.      */
  38.     public static final double DEFAULT_INVERSE_ABSOLUTE_ACCURACY = 1e-9;
  39.     /** Serializable version identifier */
  40.     private static final long serialVersionUID = 8589540077390120676L;
  41.     /** The median of this distribution. */
  42.     private final double median;
  43.     /** The scale of this distribution. */
  44.     private final double scale;
  45.     /** Inverse cumulative probability accuracy */
  46.     private final double solverAbsoluteAccuracy;

  48.     /**
  49.      * Creates a Cauchy distribution with the median equal to zero and scale
  50.      * equal to one.
  51.      */
  52.     public CauchyDistribution() {
  53.         this(0, 1);
  54.     }

  56.     /**
  57.      * Creates a Cauchy distribution using the given median and scale.
  58.      * <p>
  59.      * <b>Note:</b> this constructor will implicitly create an instance of
  60.      * {@link Well19937c} as random generator to be used for sampling only (see
  61.      * {@link #sample()} and {@link #sample(int)}). In case no sampling is
  62.      * needed for the created distribution, it is advised to pass {@code null}
  63.      * as random generator via the appropriate constructors to avoid the
  64.      * additional initialisation overhead.
  65.      *
  66.      * @param median Median for this distribution.
  67.      * @param scale Scale parameter for this distribution.
  68.      */
  69.     public CauchyDistribution(double median, double scale) {
  70.         this(median, scale, DEFAULT_INVERSE_ABSOLUTE_ACCURACY);
  71.     }

  73.     /**
  74.      * Creates a Cauchy distribution using the given median and scale.
  75.      * <p>
  76.      * <b>Note:</b> this constructor will implicitly create an instance of
  77.      * {@link Well19937c} as random generator to be used for sampling only (see
  78.      * {@link #sample()} and {@link #sample(int)}). In case no sampling is
  79.      * needed for the created distribution, it is advised to pass {@code null}
  80.      * as random generator via the appropriate constructors to avoid the
  81.      * additional initialisation overhead.
  82.      *
  83.      * @param median Median for this distribution.
  84.      * @param scale Scale parameter for this distribution.
  85.      * @param inverseCumAccuracy Maximum absolute error in inverse
  86.      * cumulative probability estimates
  87.      * (defaults to {@link #DEFAULT_INVERSE_ABSOLUTE_ACCURACY}).
  88.      * @throws NotStrictlyPositiveException if {@code scale <= 0}.
  89.      * @since 2.1
  90.      */
  91.     public CauchyDistribution(double median, double scale,
  92.                               double inverseCumAccuracy) {
  93.         this(new Well19937c(), median, scale, inverseCumAccuracy);
  94.     }

  96.     /**
  97.      * Creates a Cauchy distribution.
  98.      *
  99.      * @param rng Random number generator.
  100.      * @param median Median for this distribution.
  101.      * @param scale Scale parameter for this distribution.
  102.      * @throws NotStrictlyPositiveException if {@code scale <= 0}.
  103.      * @since 3.3
  104.      */
  105.     public CauchyDistribution(RandomGenerator rng, double median, double scale) {
  106.         this(rng, median, scale, DEFAULT_INVERSE_ABSOLUTE_ACCURACY);
  107.     }

  109.     /**
  110.      * Creates a Cauchy distribution.
  111.      *
  112.      * @param rng Random number generator.
  113.      * @param median Median for this distribution.
  114.      * @param scale Scale parameter for this distribution.
  115.      * @param inverseCumAccuracy Maximum absolute error in inverse
  116.      * cumulative probability estimates
  117.      * (defaults to {@link #DEFAULT_INVERSE_ABSOLUTE_ACCURACY}).
  118.      * @throws NotStrictlyPositiveException if {@code scale <= 0}.
  119.      * @since 3.1
  120.      */
  121.     public CauchyDistribution(RandomGenerator rng,
  122.                               double median,
  123.                               double scale,
  124.                               double inverseCumAccuracy) {
  125.         super(rng);
  126.         if (scale <= 0) {
  127.             throw new NotStrictlyPositiveException(LocalizedFormats.SCALE, scale);
  128.         }
  129.         this.scale = scale;
  130.         this.median = median;
  131.         solverAbsoluteAccuracy = inverseCumAccuracy;
  132.     }

  134.     /** {@inheritDoc} */
  135.     public double cumulativeProbability(double x) {
  136.         return 0.5 + (FastMath.atan((x - median) / scale) / FastMath.PI);
  137.     }

  139.     /**
  140.      * Access the median.
  141.      *
  142.      * @return the median for this distribution.
  143.      */
  144.     public double getMedian() {
  145.         return median;
  146.     }

  148.     /**
  149.      * Access the scale parameter.
  150.      *
  151.      * @return the scale parameter for this distribution.
  152.      */
  153.     public double getScale() {
  154.         return scale;
  155.     }

  157.     /** {@inheritDoc} */
  158.     public double density(double x) {
  159.         final double dev = x - median;
  160.         return (1 / FastMath.PI) * (scale / (dev * dev + scale * scale));
  161.     }

  163.     /**
  164.      * {@inheritDoc}
  165.      *
  166.      * Returns {@code Double.NEGATIVE_INFINITY} when {@code p == 0}
  167.      * and {@code Double.POSITIVE_INFINITY} when {@code p == 1}.
  168.      */
  169.     @Override
  170.     public double inverseCumulativeProbability(double p) throws OutOfRangeException {
  171.         double ret;
  172.         if (p < 0 || p > 1) {
  173.             throw new OutOfRangeException(p, 0, 1);
  174.         } else if (p == 0) {
  175.             ret = Double.NEGATIVE_INFINITY;
  176.         } else  if (p == 1) {
  177.             ret = Double.POSITIVE_INFINITY;
  178.         } else {
  179.             ret = median + scale * FastMath.tan(FastMath.PI * (p - .5));
  180.         }
  181.         return ret;
  182.     }

  184.     /** {@inheritDoc} */
  185.     @Override
  186.     protected double getSolverAbsoluteAccuracy() {
  187.         return solverAbsoluteAccuracy;
  188.     }

  190.     /**
  191.      * {@inheritDoc}
  192.      *
  193.      * The mean is always undefined no matter the parameters.
  194.      *
  195.      * @return mean (always Double.NaN)
  196.      */
  197.     public double getNumericalMean() {
  198.         return Double.NaN;
  199.     }

  201.     /**
  202.      * {@inheritDoc}
  203.      *
  204.      * The variance is always undefined no matter the parameters.
  205.      *
  206.      * @return variance (always Double.NaN)
  207.      */
  208.     public double getNumericalVariance() {
  209.         return Double.NaN;
  210.     }

  212.     /**
  213.      * {@inheritDoc}
  214.      *
  215.      * The lower bound of the support is always negative infinity no matter
  216.      * the parameters.
  217.      *
  218.      * @return lower bound of the support (always Double.NEGATIVE_INFINITY)
  219.      */
  220.     public double getSupportLowerBound() {
  221.         return Double.NEGATIVE_INFINITY;
  222.     }

  224.     /**
  225.      * {@inheritDoc}
  226.      *
  227.      * The upper bound of the support is always positive infinity no matter
  228.      * the parameters.
  229.      *
  230.      * @return upper bound of the support (always Double.POSITIVE_INFINITY)
  231.      */
  232.     public double getSupportUpperBound() {
  233.         return Double.POSITIVE_INFINITY;
  234.     }

  236.     /** {@inheritDoc} */
  237.     public boolean isSupportLowerBoundInclusive() {
  238.         return false;
  239.     }

  241.     /** {@inheritDoc} */
  242.     public boolean isSupportUpperBoundInclusive() {
  243.         return false;
  244.     }

  246.     /**
  247.      * {@inheritDoc}
  248.      *
  249.      * The support of this distribution is connected.
  250.      *
  251.      * @return {@code true}
  252.      */
  253.     public boolean isSupportConnected() {
  254.         return true;
  255.     }
  256. }
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