    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    package org.apache.commons.math3.stat.descriptive.moment;
    018
    019    import java.io.Serializable;
    020
    021    import org.apache.commons.math3.exception.MathIllegalArgumentException;
    022    import org.apache.commons.math3.exception.NullArgumentException;
    023    import org.apache.commons.math3.stat.descriptive.AbstractStorelessUnivariateStatistic;
    024    import org.apache.commons.math3.util.FastMath;
    025    import org.apache.commons.math3.util.MathUtils;
    026
    027    /**
    028     * Computes the skewness of the available values.
    029     * <p>
    030     * We use the following (unbiased) formula to define skewness:</p>
    031     * <p>
    032     * skewness = [n / (n -1) (n - 2)] sum[(x_i - mean)^3] / std^3 </p>
    033     * <p>
    034     * where n is the number of values, mean is the {@link Mean} and std is the
    035     * {@link StandardDeviation} </p>
    036     * <p>
    037     * <strong>Note that this implementation is not synchronized.</strong> If
    038     * multiple threads access an instance of this class concurrently, and at least
    039     * one of the threads invokes the <code>increment()</code> or
    040     * <code>clear()</code> method, it must be synchronized externally. </p>
    041     *
    042     * @version $Id: Skewness.java 1416643 2012-12-03 19:37:14Z tn $
    043     */
    044    public class Skewness extends AbstractStorelessUnivariateStatistic implements Serializable {
    045
    046        /** Serializable version identifier */
    047        private static final long serialVersionUID = 7101857578996691352L;
    048
    049        /** Third moment on which this statistic is based */
    050        protected ThirdMoment moment = null;
    051
    052         /**
    053         * Determines whether or not this statistic can be incremented or cleared.
    054         * <p>
    055         * Statistics based on (constructed from) external moments cannot
    056         * be incremented or cleared.</p>
    057        */
    058        protected boolean incMoment;
    059
    060        /**
    061         * Constructs a Skewness
    062         */
    063        public Skewness() {
    064            incMoment = true;
    065            moment = new ThirdMoment();
    066        }
    067
    068        /**
    069         * Constructs a Skewness with an external moment
    070         * @param m3 external moment
    071         */
    072        public Skewness(final ThirdMoment m3) {
    073            incMoment = false;
    074            this.moment = m3;
    075        }
    076
    077        /**
    078         * Copy constructor, creates a new {@code Skewness} identical
    079         * to the {@code original}
    080         *
    081         * @param original the {@code Skewness} instance to copy
    082         * @throws NullArgumentException if original is null
    083         */
    084        public Skewness(Skewness original) throws NullArgumentException {
    085            copy(original, this);
    086        }
    087
    088        /**
    089         * {@inheritDoc}
    090         * <p>Note that when {@link #Skewness(ThirdMoment)} is used to
    091         * create a Skewness, this method does nothing. In that case, the
    092         * ThirdMoment should be incremented directly.</p>
    093         */
    094        @Override
    095        public void increment(final double d) {
    096            if (incMoment) {
    097                moment.increment(d);
    098            }
    099        }
    100
    101        /**
    102         * Returns the value of the statistic based on the values that have been added.
    103         * <p>
    104         * See {@link Skewness} for the definition used in the computation.</p>
    105         *
    106         * @return the skewness of the available values.
    107         */
    108        @Override
    109        public double getResult() {
    110
    111            if (moment.n < 3) {
    112                return Double.NaN;
    113            }
    114            double variance = moment.m2 / (moment.n - 1);
    115            if (variance < 10E-20) {
    116                return 0.0d;
    117            } else {
    118                double n0 = moment.getN();
    119                return  (n0 * moment.m3) /
    120                ((n0 - 1) * (n0 -2) * FastMath.sqrt(variance) * variance);
    121            }
    122        }
    123
    124        /**
    125         * {@inheritDoc}
    126         */
    127        public long getN() {
    128            return moment.getN();
    129        }
    130
    131        /**
    132         * {@inheritDoc}
    133         */
    134        @Override
    135        public void clear() {
    136            if (incMoment) {
    137                moment.clear();
    138            }
    139        }
    140
    141        /**
    142         * Returns the Skewness of the entries in the specifed portion of the
    143         * input array.
    144         * <p>
    145         * See {@link Skewness} for the definition used in the computation.</p>
    146         * <p>
    147         * Throws <code>IllegalArgumentException</code> if the array is null.</p>
    148         *
    149         * @param values the input array
    150         * @param begin the index of the first array element to include
    151         * @param length the number of elements to include
    152         * @return the skewness of the values or Double.NaN if length is less than
    153         * 3
    154         * @throws MathIllegalArgumentException if the array is null or the array index
    155         *  parameters are not valid
    156         */
    157        @Override
    158        public double evaluate(final double[] values,final int begin,
    159                final int length) throws MathIllegalArgumentException {
    160
    161            // Initialize the skewness
    162            double skew = Double.NaN;
    163
    164            if (test(values, begin, length) && length > 2 ){
    165                Mean mean = new Mean();
    166                // Get the mean and the standard deviation
    167                double m = mean.evaluate(values, begin, length);
    168
    169                // Calc the std, this is implemented here instead
    170                // of using the standardDeviation method eliminate
    171                // a duplicate pass to get the mean
    172                double accum = 0.0;
    173                double accum2 = 0.0;
    174                for (int i = begin; i < begin + length; i++) {
    175                    final double d = values[i] - m;
    176                    accum  += d * d;
    177                    accum2 += d;
    178                }
    179                final double variance = (accum - (accum2 * accum2 / length)) / (length - 1);
    180
    181                double accum3 = 0.0;
    182                for (int i = begin; i < begin + length; i++) {
    183                    final double d = values[i] - m;
    184                    accum3 += d * d * d;
    185                }
    186                accum3 /= variance * FastMath.sqrt(variance);
    187
    188                // Get N
    189                double n0 = length;
    190
    191                // Calculate skewness
    192                skew = (n0 / ((n0 - 1) * (n0 - 2))) * accum3;
    193            }
    194            return skew;
    195        }
    196
    197        /**
    198         * {@inheritDoc}
    199         */
    200        @Override
    201        public Skewness copy() {
    202            Skewness result = new Skewness();
    203            // No try-catch or advertised exception because args are guaranteed non-null
    204            copy(this, result);
    205            return result;
    206        }
    207
    208        /**
    209         * Copies source to dest.
    210         * <p>Neither source nor dest can be null.</p>
    211         *
    212         * @param source Skewness to copy
    213         * @param dest Skewness to copy to
    214         * @throws NullArgumentException if either source or dest is null
    215         */
    216        public static void copy(Skewness source, Skewness dest)
    217            throws NullArgumentException {
    218            MathUtils.checkNotNull(source);
    219            MathUtils.checkNotNull(dest);
    220            dest.setData(source.getDataRef());
    221            dest.moment = new ThirdMoment(source.moment.copy());
    222            dest.incMoment = source.incMoment;
    223        }
    224    }