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      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  */
     17 package org.apache.commons.math.stat.descriptive.moment;
     18 
     19 import java.io.Serializable;
     20 
     21 import org.apache.commons.math.stat.descriptive.AbstractStorelessUnivariateStatistic;
     22 import org.apache.commons.math.util.FastMath;
     23 
     24 /**
     25  * Computes the skewness of the available values.
     26  * <p>
     27  * We use the following (unbiased) formula to define skewness:</p>
     28  * <p>
     29  * skewness = [n / (n -1) (n - 2)] sum[(x_i - mean)^3] / std^3 </p>
     30  * <p>
     31  * where n is the number of values, mean is the {@link Mean} and std is the
     32  * {@link StandardDeviation} </p>
     33  * <p>
     34  * <strong>Note that this implementation is not synchronized.</strong> If
     35  * multiple threads access an instance of this class concurrently, and at least
     36  * one of the threads invokes the <code>increment()</code> or
     37  * <code>clear()</code> method, it must be synchronized externally. </p>
     38  *
     39  * @version $Revision: 1006299 $ $Date: 2010-10-10 16:47:17 +0200 (dim. 10 oct. 2010) $
     40  */
     41 public class Skewness extends AbstractStorelessUnivariateStatistic implements Serializable {
     42 
     43     /** Serializable version identifier */
     44     private static final long serialVersionUID = 7101857578996691352L;
     45 
     46     /** Third moment on which this statistic is based */
     47     protected ThirdMoment moment = null;
     48 
     49      /**
     50      * Determines whether or not this statistic can be incremented or cleared.
     51      * <p>
     52      * Statistics based on (constructed from) external moments cannot
     53      * be incremented or cleared.</p>
     54     */
     55     protected boolean incMoment;
     56 
     57     /**
     58      * Constructs a Skewness
     59      */
     60     public Skewness() {
     61         incMoment = true;
     62         moment = new ThirdMoment();
     63     }
     64 
     65     /**
     66      * Constructs a Skewness with an external moment
     67      * @param m3 external moment
     68      */
     69     public Skewness(final ThirdMoment m3) {
     70         incMoment = false;
     71         this.moment = m3;
     72     }
     73 
     74     /**
     75      * Copy constructor, creates a new {@code Skewness} identical
     76      * to the {@code original}
     77      *
     78      * @param original the {@code Skewness} instance to copy
     79      */
     80     public Skewness(Skewness original) {
     81         copy(original, this);
     82     }
     83 
     84     /**
     85      * {@inheritDoc}
     86      */
     87     @Override
     88     public void increment(final double d) {
     89         if (incMoment) {
     90             moment.increment(d);
     91         }
     92     }
     93 
     94     /**
     95      * Returns the value of the statistic based on the values that have been added.
     96      * <p>
     97      * See {@link Skewness} for the definition used in the computation.</p>
     98      *
     99      * @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 }
    214