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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.math3.stat.descriptive.moment;
18  
19  import java.io.Serializable;
20  
21  import org.apache.commons.math3.exception.MathIllegalArgumentException;
22  import org.apache.commons.math3.exception.NullArgumentException;
23  import org.apache.commons.math3.stat.descriptive.AbstractStorelessUnivariateStatistic;
24  import org.apache.commons.math3.util.FastMath;
25  import org.apache.commons.math3.util.MathUtils;
26  
27  /**
28   * Computes the skewness of the available values.
29   * <p>
30   * We use the following (unbiased) formula to define skewness:</p>
31   * <p>
32   * skewness = [n / (n -1) (n - 2)] sum[(x_i - mean)^3] / std^3 </p>
33   * <p>
34   * where n is the number of values, mean is the {@link Mean} and std is the
35   * {@link StandardDeviation} </p>
36   * <p>
37   * <strong>Note that this implementation is not synchronized.</strong> If
38   * multiple threads access an instance of this class concurrently, and at least
39   * one of the threads invokes the <code>increment()</code> or
40   * <code>clear()</code> method, it must be synchronized externally. </p>
41   *
42   * @version $Id: Skewness.java 1416643 2012-12-03 19:37:14Z tn $
43   */
44  public class Skewness extends AbstractStorelessUnivariateStatistic implements Serializable {
45  
46      /** Serializable version identifier */
47      private static final long serialVersionUID = 7101857578996691352L;
48  
49      /** Third moment on which this statistic is based */
50      protected ThirdMoment moment = null;
51  
52       /**
53       * Determines whether or not this statistic can be incremented or cleared.
54       * <p>
55       * Statistics based on (constructed from) external moments cannot
56       * be incremented or cleared.</p>
57      */
58      protected boolean incMoment;
59  
60      /**
61       * Constructs a Skewness
62       */
63      public Skewness() {
64          incMoment = true;
65          moment = new ThirdMoment();
66      }
67  
68      /**
69       * Constructs a Skewness with an external moment
70       * @param m3 external moment
71       */
72      public Skewness(final ThirdMoment m3) {
73          incMoment = false;
74          this.moment = m3;
75      }
76  
77      /**
78       * Copy constructor, creates a new {@code Skewness} identical
79       * to the {@code original}
80       *
81       * @param original the {@code Skewness} instance to copy
82       * @throws NullArgumentException if original is null
83       */
84      public Skewness(Skewness original) throws NullArgumentException {
85          copy(original, this);
86      }
87  
88      /**
89       * {@inheritDoc}
90       * <p>Note that when {@link #Skewness(ThirdMoment)} is used to
91       * create a Skewness, this method does nothing. In that case, the
92       * ThirdMoment should be incremented directly.</p>
93       */
94      @Override
95      public void increment(final double d) {
96          if (incMoment) {
97              moment.increment(d);
98          }
99      }
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 }