    001    /*
    002     * Licensed to the Apache Software Foundation (ASF) under one or more
    003     * contributor license agreements.  See the NOTICE file distributed with
    004     * this work for additional information regarding copyright ownership.
    005     * The ASF licenses this file to You under the Apache License, Version 2.0
    006     * (the "License"); you may not use this file except in compliance with
    007     * the License.  You may obtain a copy of the License at
    008     *
    009     *      http://www.apache.org/licenses/LICENSE-2.0
    010     *
    011     * Unless required by applicable law or agreed to in writing, software
    012     * distributed under the License is distributed on an "AS IS" BASIS,
    013     * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
    014     * See the License for the specific language governing permissions and
    015     * limitations under the License.
    016     */
    017
    018    package org.apache.commons.math3.distribution;
    019
    020    import org.apache.commons.math3.exception.NotStrictlyPositiveException;
    021    import org.apache.commons.math3.exception.NumberIsTooLargeException;
    022    import org.apache.commons.math3.exception.util.LocalizedFormats;
    023    import org.apache.commons.math3.special.Erf;
    024    import org.apache.commons.math3.util.FastMath;
    025    import org.apache.commons.math3.random.RandomGenerator;
    026    import org.apache.commons.math3.random.Well19937c;
    027
    028    /**
    029     * Implementation of the normal (gaussian) distribution.
    030     *
    031     * @see <a href="http://en.wikipedia.org/wiki/Normal_distribution">Normal distribution (Wikipedia)</a>
    032     * @see <a href="http://mathworld.wolfram.com/NormalDistribution.html">Normal distribution (MathWorld)</a>
    033     * @version $Id: NormalDistribution.java 1416643 2012-12-03 19:37:14Z tn $
    034     */
    035    public class NormalDistribution extends AbstractRealDistribution {
    036        /**
    037         * Default inverse cumulative probability accuracy.
    038         * @since 2.1
    039         */
    040        public static final double DEFAULT_INVERSE_ABSOLUTE_ACCURACY = 1e-9;
    041        /** Serializable version identifier. */
    042        private static final long serialVersionUID = 8589540077390120676L;
    043        /** &radic;(2 &pi;) */
    044        private static final double SQRT2PI = FastMath.sqrt(2 * FastMath.PI);
    045        /** &radic;(2) */
    046        private static final double SQRT2 = FastMath.sqrt(2.0);
    047        /** Mean of this distribution. */
    048        private final double mean;
    049        /** Standard deviation of this distribution. */
    050        private final double standardDeviation;
    051        /** Inverse cumulative probability accuracy. */
    052        private final double solverAbsoluteAccuracy;
    053
    054        /**
    055         * Create a normal distribution with mean equal to zero and standard
    056         * deviation equal to one.
    057         */
    058        public NormalDistribution() {
    059            this(0, 1);
    060        }
    061
    062        /**
    063         * Create a normal distribution using the given mean and standard deviation.
    064         *
    065         * @param mean Mean for this distribution.
    066         * @param sd Standard deviation for this distribution.
    067         * @throws NotStrictlyPositiveException if {@code sd <= 0}.
    068         */
    069        public NormalDistribution(double mean, double sd)
    070            throws NotStrictlyPositiveException {
    071            this(mean, sd, DEFAULT_INVERSE_ABSOLUTE_ACCURACY);
    072        }
    073
    074        /**
    075         * Create a normal distribution using the given mean, standard deviation and
    076         * inverse cumulative distribution accuracy.
    077         *
    078         * @param mean Mean for this distribution.
    079         * @param sd Standard deviation for this distribution.
    080         * @param inverseCumAccuracy Inverse cumulative probability accuracy.
    081         * @throws NotStrictlyPositiveException if {@code sd <= 0}.
    082         * @since 2.1
    083         */
    084        public NormalDistribution(double mean, double sd, double inverseCumAccuracy)
    085            throws NotStrictlyPositiveException {
    086            this(new Well19937c(), mean, sd, inverseCumAccuracy);
    087        }
    088
    089        /**
    090         * Creates a normal distribution.
    091         *
    092         * @param rng Random number generator.
    093         * @param mean Mean for this distribution.
    094         * @param sd Standard deviation for this distribution.
    095         * @param inverseCumAccuracy Inverse cumulative probability accuracy.
    096         * @throws NotStrictlyPositiveException if {@code sd <= 0}.
    097         * @since 3.1
    098         */
    099        public NormalDistribution(RandomGenerator rng,
    100                                  double mean,
    101                                  double sd,
    102                                  double inverseCumAccuracy)
    103            throws NotStrictlyPositiveException {
    104            super(rng);
    105
    106            if (sd <= 0) {
    107                throw new NotStrictlyPositiveException(LocalizedFormats.STANDARD_DEVIATION, sd);
    108            }
    109
    110            this.mean = mean;
    111            standardDeviation = sd;
    112            solverAbsoluteAccuracy = inverseCumAccuracy;
    113        }
    114
    115        /**
    116         * Access the mean.
    117         *
    118         * @return the mean for this distribution.
    119         */
    120        public double getMean() {
    121            return mean;
    122        }
    123
    124        /**
    125         * Access the standard deviation.
    126         *
    127         * @return the standard deviation for this distribution.
    128         */
    129        public double getStandardDeviation() {
    130            return standardDeviation;
    131        }
    132
    133        /** {@inheritDoc} */
    134        public double density(double x) {
    135            final double x0 = x - mean;
    136            final double x1 = x0 / standardDeviation;
    137            return FastMath.exp(-0.5 * x1 * x1) / (standardDeviation * SQRT2PI);
    138        }
    139
    140        /**
    141         * {@inheritDoc}
    142         *
    143         * If {@code x} is more than 40 standard deviations from the mean, 0 or 1
    144         * is returned, as in these cases the actual value is within
    145         * {@code Double.MIN_VALUE} of 0 or 1.
    146         */
    147        public double cumulativeProbability(double x)  {
    148            final double dev = x - mean;
    149            if (FastMath.abs(dev) > 40 * standardDeviation) {
    150                return dev < 0 ? 0.0d : 1.0d;
    151            }
    152            return 0.5 * (1 + Erf.erf(dev / (standardDeviation * SQRT2)));
    153        }
    154
    155        /**
    156         * {@inheritDoc}
    157         *
    158         * @deprecated See {@link RealDistribution#cumulativeProbability(double,double)}
    159         */
    160        @Override@Deprecated
    161        public double cumulativeProbability(double x0, double x1)
    162            throws NumberIsTooLargeException {
    163            return probability(x0, x1);
    164        }
    165
    166        /** {@inheritDoc} */
    167        @Override
    168        public double probability(double x0,
    169                                  double x1)
    170            throws NumberIsTooLargeException {
    171            if (x0 > x1) {
    172                throw new NumberIsTooLargeException(LocalizedFormats.LOWER_ENDPOINT_ABOVE_UPPER_ENDPOINT,
    173                                                    x0, x1, true);
    174            }
    175            final double denom = standardDeviation * SQRT2;
    176            final double v0 = (x0 - mean) / denom;
    177            final double v1 = (x1 - mean) / denom;
    178            return 0.5 * Erf.erf(v0, v1);
    179        }
    180
    181        /** {@inheritDoc} */
    182        @Override
    183        protected double getSolverAbsoluteAccuracy() {
    184            return solverAbsoluteAccuracy;
    185        }
    186
    187        /**
    188         * {@inheritDoc}
    189         *
    190         * For mean parameter {@code mu}, the mean is {@code mu}.
    191         */
    192        public double getNumericalMean() {
    193            return getMean();
    194        }
    195
    196        /**
    197         * {@inheritDoc}
    198         *
    199         * For standard deviation parameter {@code s}, the variance is {@code s^2}.
    200         */
    201        public double getNumericalVariance() {
    202            final double s = getStandardDeviation();
    203            return s * s;
    204        }
    205
    206        /**
    207         * {@inheritDoc}
    208         *
    209         * The lower bound of the support is always negative infinity
    210         * no matter the parameters.
    211         *
    212         * @return lower bound of the support (always
    213         * {@code Double.NEGATIVE_INFINITY})
    214         */
    215        public double getSupportLowerBound() {
    216            return Double.NEGATIVE_INFINITY;
    217        }
    218
    219        /**
    220         * {@inheritDoc}
    221         *
    222         * The upper bound of the support is always positive infinity
    223         * no matter the parameters.
    224         *
    225         * @return upper bound of the support (always
    226         * {@code Double.POSITIVE_INFINITY})
    227         */
    228        public double getSupportUpperBound() {
    229            return Double.POSITIVE_INFINITY;
    230        }
    231
    232        /** {@inheritDoc} */
    233        public boolean isSupportLowerBoundInclusive() {
    234            return false;
    235        }
    236
    237        /** {@inheritDoc} */
    238        public boolean isSupportUpperBoundInclusive() {
    239            return false;
    240        }
    241
    242        /**
    243         * {@inheritDoc}
    244         *
    245         * The support of this distribution is connected.
    246         *
    247         * @return {@code true}
    248         */
    249        public boolean isSupportConnected() {
    250            return true;
    251        }
    252
    253        /** {@inheritDoc} */
    254        @Override
    255        public double sample()  {
    256            return standardDeviation * random.nextGaussian() + mean;
    257        }
    258    }