    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.math.stat.descriptive.moment;
    018
    019    import java.io.Serializable;
    020
    021    import org.apache.commons.math.stat.descriptive.AbstractStorelessUnivariateStatistic;
    022    import org.apache.commons.math.util.FastMath;
    023
    024    /**
    025     * Computes the skewness of the available values.
    026     * <p>
    027     * We use the following (unbiased) formula to define skewness:</p>
    028     * <p>
    029     * skewness = [n / (n -1) (n - 2)] sum[(x_i - mean)^3] / std^3 </p>
    030     * <p>
    031     * where n is the number of values, mean is the {@link Mean} and std is the
    032     * {@link StandardDeviation} </p>
    033     * <p>
    034     * <strong>Note that this implementation is not synchronized.</strong> If
    035     * multiple threads access an instance of this class concurrently, and at least
    036     * one of the threads invokes the <code>increment()</code> or
    037     * <code>clear()</code> method, it must be synchronized externally. </p>
    038     *
    039     * @version $Revision: 1006299 $ $Date: 2010-10-10 16:47:17 +0200 (dim. 10 oct. 2010) $
    040     */
    041    public class Skewness extends AbstractStorelessUnivariateStatistic implements Serializable {
    042
    043        /** Serializable version identifier */
    044        private static final long serialVersionUID = 7101857578996691352L;
    045
    046        /** Third moment on which this statistic is based */
    047        protected ThirdMoment moment = null;
    048
    049         /**
    050         * Determines whether or not this statistic can be incremented or cleared.
    051         * <p>
    052         * Statistics based on (constructed from) external moments cannot
    053         * be incremented or cleared.</p>
    054        */
    055        protected boolean incMoment;
    056
    057        /**
    058         * Constructs a Skewness
    059         */
    060        public Skewness() {
    061            incMoment = true;
    062            moment = new ThirdMoment();
    063        }
    064
    065        /**
    066         * Constructs a Skewness with an external moment
    067         * @param m3 external moment
    068         */
    069        public Skewness(final ThirdMoment m3) {
    070            incMoment = false;
    071            this.moment = m3;
    072        }
    073
    074        /**
    075         * Copy constructor, creates a new {@code Skewness} identical
    076         * to the {@code original}
    077         *
    078         * @param original the {@code Skewness} instance to copy
    079         */
    080        public Skewness(Skewness original) {
    081            copy(original, this);
    082        }
    083
    084        /**
    085         * {@inheritDoc}
    086         */
    087        @Override
    088        public void increment(final double d) {
    089            if (incMoment) {
    090                moment.increment(d);
    091            }
    092        }
    093
    094        /**
    095         * Returns the value of the statistic based on the values that have been added.
    096         * <p>
    097         * See {@link Skewness} for the definition used in the computation.</p>
    098         *
    099         * @return the skewness of the available values.
    100         */
    101        @Override
    102        public double getResult() {
    103
    104            if (moment.n < 3) {
    105                return Double.NaN;
    106            }
    107            double variance = moment.m2 / (moment.n - 1);
    108            if (variance < 10E-20) {
    109                return 0.0d;
    110            } else {
    111                double n0 = moment.getN();
    112                return  (n0 * moment.m3) /
    113                ((n0 - 1) * (n0 -2) * FastMath.sqrt(variance) * variance);
    114            }
    115        }
    116
    117        /**
    118         * {@inheritDoc}
    119         */
    120        public long getN() {
    121            return moment.getN();
    122        }
    123
    124        /**
    125         * {@inheritDoc}
    126         */
    127        @Override
    128        public void clear() {
    129            if (incMoment) {
    130                moment.clear();
    131            }
    132        }
    133
    134        /**
    135         * Returns the Skewness of the entries in the specifed portion of the
    136         * input array.
    137         * <p>
    138         * See {@link Skewness} for the definition used in the computation.</p>
    139         * <p>
    140         * Throws <code>IllegalArgumentException</code> if the array is null.</p>
    141         *
    142         * @param values the input array
    143         * @param begin the index of the first array element to include
    144         * @param length the number of elements to include
    145         * @return the skewness of the values or Double.NaN if length is less than
    146         * 3
    147         * @throws IllegalArgumentException if the array is null or the array index
    148         *  parameters are not valid
    149         */
    150        @Override
    151        public double evaluate(final double[] values,final int begin,
    152                final int length) {
    153
    154            // Initialize the skewness
    155            double skew = Double.NaN;
    156
    157            if (test(values, begin, length) && length > 2 ){
    158                Mean mean = new Mean();
    159                // Get the mean and the standard deviation
    160                double m = mean.evaluate(values, begin, length);
    161
    162                // Calc the std, this is implemented here instead
    163                // of using the standardDeviation method eliminate
    164                // a duplicate pass to get the mean
    165                double accum = 0.0;
    166                double accum2 = 0.0;
    167                for (int i = begin; i < begin + length; i++) {
    168                    final double d = values[i] - m;
    169                    accum  += d * d;
    170                    accum2 += d;
    171                }
    172                final double variance = (accum - (accum2 * accum2 / length)) / (length - 1);
    173
    174                double accum3 = 0.0;
    175                for (int i = begin; i < begin + length; i++) {
    176                    final double d = values[i] - m;
    177                    accum3 += d * d * d;
    178                }
    179                accum3 /= variance * FastMath.sqrt(variance);
    180
    181                // Get N
    182                double n0 = length;
    183
    184                // Calculate skewness
    185                skew = (n0 / ((n0 - 1) * (n0 - 2))) * accum3;
    186            }
    187            return skew;
    188        }
    189
    190        /**
    191         * {@inheritDoc}
    192         */
    193        @Override
    194        public Skewness copy() {
    195            Skewness result = new Skewness();
    196            copy(this, result);
    197            return result;
    198        }
    199
    200        /**
    201         * Copies source to dest.
    202         * <p>Neither source nor dest can be null.</p>
    203         *
    204         * @param source Skewness to copy
    205         * @param dest Skewness to copy to
    206         * @throws NullPointerException if either source or dest is null
    207         */
    208        public static void copy(Skewness source, Skewness dest) {
    209            dest.setData(source.getDataRef());
    210            dest.moment = new ThirdMoment(source.moment.copy());
    211            dest.incMoment = source.incMoment;
    212        }
    213    }