    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    /**
    029     * Computes the Kurtosis of the available values.
    030     * <p>
    031     * We use the following (unbiased) formula to define kurtosis:</p>
    032     *  <p>
    033     *  kurtosis = { [n(n+1) / (n -1)(n - 2)(n-3)] sum[(x_i - mean)^4] / std^4 } - [3(n-1)^2 / (n-2)(n-3)]
    034     *  </p><p>
    035     *  where n is the number of values, mean is the {@link Mean} and std is the
    036     * {@link StandardDeviation}</p>
    037     * <p>
    038     *  Note that this statistic is undefined for n < 4.  <code>Double.Nan</code>
    039     *  is returned when there is not sufficient data to compute the statistic.</p>
    040     * <p>
    041     * <strong>Note that this implementation is not synchronized.</strong> If
    042     * multiple threads access an instance of this class concurrently, and at least
    043     * one of the threads invokes the <code>increment()</code> or
    044     * <code>clear()</code> method, it must be synchronized externally.</p>
    045     *
    046     * @version $Id: Kurtosis.java 1416643 2012-12-03 19:37:14Z tn $
    047     */
    048    public class Kurtosis extends AbstractStorelessUnivariateStatistic  implements Serializable {
    049
    050        /** Serializable version identifier */
    051        private static final long serialVersionUID = 2784465764798260919L;
    052
    053        /**Fourth Moment on which this statistic is based */
    054        protected FourthMoment moment;
    055
    056        /**
    057         * Determines whether or not this statistic can be incremented or cleared.
    058         * <p>
    059         * Statistics based on (constructed from) external moments cannot
    060         * be incremented or cleared.</p>
    061        */
    062        protected boolean incMoment;
    063
    064        /**
    065         * Construct a Kurtosis
    066         */
    067        public Kurtosis() {
    068            incMoment = true;
    069            moment = new FourthMoment();
    070        }
    071
    072        /**
    073         * Construct a Kurtosis from an external moment
    074         *
    075         * @param m4 external Moment
    076         */
    077        public Kurtosis(final FourthMoment m4) {
    078            incMoment = false;
    079            this.moment = m4;
    080        }
    081
    082        /**
    083         * Copy constructor, creates a new {@code Kurtosis} identical
    084         * to the {@code original}
    085         *
    086         * @param original the {@code Kurtosis} instance to copy
    087         * @throws NullArgumentException if original is null
    088         */
    089        public Kurtosis(Kurtosis original) throws NullArgumentException {
    090            copy(original, this);
    091        }
    092
    093        /**
    094         * {@inheritDoc}
    095         * <p>Note that when {@link #Kurtosis(FourthMoment)} is used to
    096         * create a Variance, this method does nothing. In that case, the
    097         * FourthMoment should be incremented directly.</p>
    098         */
    099        @Override
    100        public void increment(final double d) {
    101            if (incMoment) {
    102                moment.increment(d);
    103            }
    104        }
    105
    106        /**
    107         * {@inheritDoc}
    108         */
    109        @Override
    110        public double getResult() {
    111            double kurtosis = Double.NaN;
    112            if (moment.getN() > 3) {
    113                double variance = moment.m2 / (moment.n - 1);
    114                    if (moment.n <= 3 || variance < 10E-20) {
    115                        kurtosis = 0.0;
    116                    } else {
    117                        double n = moment.n;
    118                        kurtosis =
    119                            (n * (n + 1) * moment.getResult() -
    120                                    3 * moment.m2 * moment.m2 * (n - 1)) /
    121                                    ((n - 1) * (n -2) * (n -3) * variance * variance);
    122                    }
    123            }
    124            return kurtosis;
    125        }
    126
    127        /**
    128         * {@inheritDoc}
    129         */
    130        @Override
    131        public void clear() {
    132            if (incMoment) {
    133                moment.clear();
    134            }
    135        }
    136
    137        /**
    138         * {@inheritDoc}
    139         */
    140        public long getN() {
    141            return moment.getN();
    142        }
    143
    144        /* UnvariateStatistic Approach  */
    145
    146        /**
    147         * Returns the kurtosis of the entries in the specified portion of the
    148         * input array.
    149         * <p>
    150         * See {@link Kurtosis} for details on the computing algorithm.</p>
    151         * <p>
    152         * Throws <code>IllegalArgumentException</code> if the array is null.</p>
    153         *
    154         * @param values the input array
    155         * @param begin index of the first array element to include
    156         * @param length the number of elements to include
    157         * @return the kurtosis of the values or Double.NaN if length is less than 4
    158         * @throws MathIllegalArgumentException if the input array is null or the array
    159         * index parameters are not valid
    160         */
    161        @Override
    162        public double evaluate(final double[] values,final int begin, final int length)
    163        throws MathIllegalArgumentException {
    164            // Initialize the kurtosis
    165            double kurt = Double.NaN;
    166
    167            if (test(values, begin, length) && length > 3) {
    168
    169                // Compute the mean and standard deviation
    170                Variance variance = new Variance();
    171                variance.incrementAll(values, begin, length);
    172                double mean = variance.moment.m1;
    173                double stdDev = FastMath.sqrt(variance.getResult());
    174
    175                // Sum the ^4 of the distance from the mean divided by the
    176                // standard deviation
    177                double accum3 = 0.0;
    178                for (int i = begin; i < begin + length; i++) {
    179                    accum3 += FastMath.pow(values[i] - mean, 4.0);
    180                }
    181                accum3 /= FastMath.pow(stdDev, 4.0d);
    182
    183                // Get N
    184                double n0 = length;
    185
    186                double coefficientOne =
    187                    (n0 * (n0 + 1)) / ((n0 - 1) * (n0 - 2) * (n0 - 3));
    188                double termTwo =
    189                    (3 * FastMath.pow(n0 - 1, 2.0)) / ((n0 - 2) * (n0 - 3));
    190
    191                // Calculate kurtosis
    192                kurt = (coefficientOne * accum3) - termTwo;
    193            }
    194            return kurt;
    195        }
    196
    197        /**
    198         * {@inheritDoc}
    199         */
    200        @Override
    201        public Kurtosis copy() {
    202            Kurtosis result = new Kurtosis();
    203            // No try-catch 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 Kurtosis to copy
    213         * @param dest Kurtosis to copy to
    214         * @throws NullArgumentException if either source or dest is null
    215         */
    216        public static void copy(Kurtosis source, Kurtosis dest)
    217            throws NullArgumentException {
    218            MathUtils.checkNotNull(source);
    219            MathUtils.checkNotNull(dest);
    220            dest.setData(source.getDataRef());
    221            dest.moment = source.moment.copy();
    222            dest.incMoment = source.incMoment;
    223        }
    224
    225    }