NormalDistribution.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.  */

  18. package org.apache.commons.math3.distribution;

  20. import org.apache.commons.math3.exception.NotStrictlyPositiveException;
  21. import org.apache.commons.math3.exception.NumberIsTooLargeException;
  22. import org.apache.commons.math3.exception.OutOfRangeException;
  23. import org.apache.commons.math3.exception.util.LocalizedFormats;
  24. import org.apache.commons.math3.random.RandomGenerator;
  25. import org.apache.commons.math3.random.Well19937c;
  26. import org.apache.commons.math3.special.Erf;
  27. import org.apache.commons.math3.util.FastMath;

  29. /**
  30.  * Implementation of the normal (gaussian) distribution.
  31.  *
  32.  * @see <a href="http://en.wikipedia.org/wiki/Normal_distribution">Normal distribution (Wikipedia)</a>
  33.  * @see <a href="http://mathworld.wolfram.com/NormalDistribution.html">Normal distribution (MathWorld)</a>
  34.  */
  35. public class NormalDistribution extends AbstractRealDistribution {
  36.     /**
  37.      * Default inverse cumulative probability accuracy.
  38.      * @since 2.1
  39.      */
  40.     public static final double DEFAULT_INVERSE_ABSOLUTE_ACCURACY = 1e-9;
  41.     /** Serializable version identifier. */
  42.     private static final long serialVersionUID = 8589540077390120676L;
  43.     /** &radic;(2) */
  44.     private static final double SQRT2 = FastMath.sqrt(2.0);
  45.     /** Mean of this distribution. */
  46.     private final double mean;
  47.     /** Standard deviation of this distribution. */
  48.     private final double standardDeviation;
  49.     /** The value of {@code log(sd) + 0.5*log(2*pi)} stored for faster computation. */
  50.     private final double logStandardDeviationPlusHalfLog2Pi;
  51.     /** Inverse cumulative probability accuracy. */
  52.     private final double solverAbsoluteAccuracy;

  54.     /**
  55.      * Create a normal distribution with mean equal to zero and standard
  56.      * deviation equal to one.
  57.      * <p>
  58.      * <b>Note:</b> this constructor will implicitly create an instance of
  59.      * {@link Well19937c} as random generator to be used for sampling only (see
  60.      * {@link #sample()} and {@link #sample(int)}). In case no sampling is
  61.      * needed for the created distribution, it is advised to pass {@code null}
  62.      * as random generator via the appropriate constructors to avoid the
  63.      * additional initialisation overhead.
  64.      */
  65.     public NormalDistribution() {
  66.         this(0, 1);
  67.     }

  69.     /**
  70.      * Create a normal distribution using the given mean and standard deviation.
  71.      * <p>
  72.      * <b>Note:</b> this constructor will implicitly create an instance of
  73.      * {@link Well19937c} as random generator to be used for sampling only (see
  74.      * {@link #sample()} and {@link #sample(int)}). In case no sampling is
  75.      * needed for the created distribution, it is advised to pass {@code null}
  76.      * as random generator via the appropriate constructors to avoid the
  77.      * additional initialisation overhead.
  78.      *
  79.      * @param mean Mean for this distribution.
  80.      * @param sd Standard deviation for this distribution.
  81.      * @throws NotStrictlyPositiveException if {@code sd <= 0}.
  82.      */
  83.     public NormalDistribution(double mean, double sd)
  84.         throws NotStrictlyPositiveException {
  85.         this(mean, sd, DEFAULT_INVERSE_ABSOLUTE_ACCURACY);
  86.     }

  88.     /**
  89.      * Create a normal distribution using the given mean, standard deviation and
  90.      * inverse cumulative distribution accuracy.
  91.      * <p>
  92.      * <b>Note:</b> this constructor will implicitly create an instance of
  93.      * {@link Well19937c} as random generator to be used for sampling only (see
  94.      * {@link #sample()} and {@link #sample(int)}). In case no sampling is
  95.      * needed for the created distribution, it is advised to pass {@code null}
  96.      * as random generator via the appropriate constructors to avoid the
  97.      * additional initialisation overhead.
  98.      *
  99.      * @param mean Mean for this distribution.
  100.      * @param sd Standard deviation for this distribution.
  101.      * @param inverseCumAccuracy Inverse cumulative probability accuracy.
  102.      * @throws NotStrictlyPositiveException if {@code sd <= 0}.
  103.      * @since 2.1
  104.      */
  105.     public NormalDistribution(double mean, double sd, double inverseCumAccuracy)
  106.         throws NotStrictlyPositiveException {
  107.         this(new Well19937c(), mean, sd, inverseCumAccuracy);
  108.     }

  110.     /**
  111.      * Creates a normal distribution.
  112.      *
  113.      * @param rng Random number generator.
  114.      * @param mean Mean for this distribution.
  115.      * @param sd Standard deviation for this distribution.
  116.      * @throws NotStrictlyPositiveException if {@code sd <= 0}.
  117.      * @since 3.3
  118.      */
  119.     public NormalDistribution(RandomGenerator rng, double mean, double sd)
  120.         throws NotStrictlyPositiveException {
  121.         this(rng, mean, sd, DEFAULT_INVERSE_ABSOLUTE_ACCURACY);
  122.     }

  124.     /**
  125.      * Creates a normal distribution.
  126.      *
  127.      * @param rng Random number generator.
  128.      * @param mean Mean for this distribution.
  129.      * @param sd Standard deviation for this distribution.
  130.      * @param inverseCumAccuracy Inverse cumulative probability accuracy.
  131.      * @throws NotStrictlyPositiveException if {@code sd <= 0}.
  132.      * @since 3.1
  133.      */
  134.     public NormalDistribution(RandomGenerator rng,
  135.                               double mean,
  136.                               double sd,
  137.                               double inverseCumAccuracy)
  138.         throws NotStrictlyPositiveException {
  139.         super(rng);

  141.         if (sd <= 0) {
  142.             throw new NotStrictlyPositiveException(LocalizedFormats.STANDARD_DEVIATION, sd);
  143.         }

  145.         this.mean = mean;
  146.         standardDeviation = sd;
  147.         logStandardDeviationPlusHalfLog2Pi = FastMath.log(sd) + 0.5 * FastMath.log(2 * FastMath.PI);
  148.         solverAbsoluteAccuracy = inverseCumAccuracy;
  149.     }

  151.     /**
  152.      * Access the mean.
  153.      *
  154.      * @return the mean for this distribution.
  155.      */
  156.     public double getMean() {
  157.         return mean;
  158.     }

  160.     /**
  161.      * Access the standard deviation.
  162.      *
  163.      * @return the standard deviation for this distribution.
  164.      */
  165.     public double getStandardDeviation() {
  166.         return standardDeviation;
  167.     }

  169.     /** {@inheritDoc} */
  170.     public double density(double x) {
  171.         return FastMath.exp(logDensity(x));
  172.     }

  174.     /** {@inheritDoc} */
  175.     @Override
  176.     public double logDensity(double x) {
  177.         final double x0 = x - mean;
  178.         final double x1 = x0 / standardDeviation;
  179.         return -0.5 * x1 * x1 - logStandardDeviationPlusHalfLog2Pi;
  180.     }

  182.     /**
  183.      * {@inheritDoc}
  184.      *
  185.      * If {@code x} is more than 40 standard deviations from the mean, 0 or 1
  186.      * is returned, as in these cases the actual value is within
  187.      * {@code Double.MIN_VALUE} of 0 or 1.
  188.      */
  189.     public double cumulativeProbability(double x)  {
  190.         final double dev = x - mean;
  191.         if (FastMath.abs(dev) > 40 * standardDeviation) {
  192.             return dev < 0 ? 0.0d : 1.0d;
  193.         }
  194.         return 0.5 * (1 + Erf.erf(dev / (standardDeviation * SQRT2)));
  195.     }

  197.     /** {@inheritDoc}
  198.      * @since 3.2
  199.      */
  200.     @Override
  201.     public double inverseCumulativeProbability(final double p) throws OutOfRangeException {
  202.         if (p < 0.0 || p > 1.0) {
  203.             throw new OutOfRangeException(p, 0, 1);
  204.         }
  205.         return mean + standardDeviation * SQRT2 * Erf.erfInv(2 * p - 1);
  206.     }

  208.     /**
  209.      * {@inheritDoc}
  210.      *
  211.      * @deprecated See {@link RealDistribution#cumulativeProbability(double,double)}
  212.      */
  213.     @Override@Deprecated
  214.     public double cumulativeProbability(double x0, double x1)
  215.         throws NumberIsTooLargeException {
  216.         return probability(x0, x1);
  217.     }

  219.     /** {@inheritDoc} */
  220.     @Override
  221.     public double probability(double x0,
  222.                               double x1)
  223.         throws NumberIsTooLargeException {
  224.         if (x0 > x1) {
  225.             throw new NumberIsTooLargeException(LocalizedFormats.LOWER_ENDPOINT_ABOVE_UPPER_ENDPOINT,
  226.                                                 x0, x1, true);
  227.         }
  228.         final double denom = standardDeviation * SQRT2;
  229.         final double v0 = (x0 - mean) / denom;
  230.         final double v1 = (x1 - mean) / denom;
  231.         return 0.5 * Erf.erf(v0, v1);
  232.     }

  234.     /** {@inheritDoc} */
  235.     @Override
  236.     protected double getSolverAbsoluteAccuracy() {
  237.         return solverAbsoluteAccuracy;
  238.     }

  240.     /**
  241.      * {@inheritDoc}
  242.      *
  243.      * For mean parameter {@code mu}, the mean is {@code mu}.
  244.      */
  245.     public double getNumericalMean() {
  246.         return getMean();
  247.     }

  249.     /**
  250.      * {@inheritDoc}
  251.      *
  252.      * For standard deviation parameter {@code s}, the variance is {@code s^2}.
  253.      */
  254.     public double getNumericalVariance() {
  255.         final double s = getStandardDeviation();
  256.         return s * s;
  257.     }

  259.     /**
  260.      * {@inheritDoc}
  261.      *
  262.      * The lower bound of the support is always negative infinity
  263.      * no matter the parameters.
  264.      *
  265.      * @return lower bound of the support (always
  266.      * {@code Double.NEGATIVE_INFINITY})
  267.      */
  268.     public double getSupportLowerBound() {
  269.         return Double.NEGATIVE_INFINITY;
  270.     }

  272.     /**
  273.      * {@inheritDoc}
  274.      *
  275.      * The upper bound of the support is always positive infinity
  276.      * no matter the parameters.
  277.      *
  278.      * @return upper bound of the support (always
  279.      * {@code Double.POSITIVE_INFINITY})
  280.      */
  281.     public double getSupportUpperBound() {
  282.         return Double.POSITIVE_INFINITY;
  283.     }

  285.     /** {@inheritDoc} */
  286.     public boolean isSupportLowerBoundInclusive() {
  287.         return false;
  288.     }

  290.     /** {@inheritDoc} */
  291.     public boolean isSupportUpperBoundInclusive() {
  292.         return false;
  293.     }

  295.     /**
  296.      * {@inheritDoc}
  297.      *
  298.      * The support of this distribution is connected.
  299.      *
  300.      * @return {@code true}
  301.      */
  302.     public boolean isSupportConnected() {
  303.         return true;
  304.     }

  306.     /** {@inheritDoc} */
  307.     @Override
  308.     public double sample()  {
  309.         return standardDeviation * random.nextGaussian() + mean;
  310.     }
  311. }
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