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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  
23  /**
24   * Computes the skewness of the available values.
25   * <p>
26   * We use the following (unbiased) formula to define skewness:</p>
27   * <p>
28   * skewness = [n / (n -1) (n - 2)] sum[(x_i - mean)^3] / std^3 </p>
29   * <p>
30   * where n is the number of values, mean is the {@link Mean} and std is the 
31   * {@link StandardDeviation} </p>
32   * <p>
33   * <strong>Note that this implementation is not synchronized.</strong> If 
34   * multiple threads access an instance of this class concurrently, and at least
35   * one of the threads invokes the <code>increment()</code> or 
36   * <code>clear()</code> method, it must be synchronized externally. </p>
37   * 
38   * @version $Revision: 764209 $ $Date: 2009-04-11 11:32:18 -0400 (Sat, 11 Apr 2009) $
39   */
40  public class Skewness extends AbstractStorelessUnivariateStatistic implements Serializable {
41  
42      /** Serializable version identifier */
43      private static final long serialVersionUID = 7101857578996691352L;    
44      
45      /** Third moment on which this statistic is based */
46      protected ThirdMoment moment = null;
47  
48       /** 
49       * Determines whether or not this statistic can be incremented or cleared.
50       * <p>
51       * Statistics based on (constructed from) external moments cannot
52       * be incremented or cleared.</p>
53      */
54      protected boolean incMoment;
55  
56      /**
57       * Constructs a Skewness
58       */
59      public Skewness() {
60          incMoment = true;
61          moment = new ThirdMoment();
62      }
63  
64      /**
65       * Constructs a Skewness with an external moment
66       * @param m3 external moment
67       */
68      public Skewness(final ThirdMoment m3) {
69          incMoment = false;
70          this.moment = m3;
71      }
72       
73      /**
74       * Copy constructor, creates a new {@code Skewness} identical
75       * to the {@code original}
76       * 
77       * @param original the {@code Skewness} instance to copy
78       */
79      public Skewness(Skewness original) {
80          copy(original, this);
81      }
82  
83      /**
84       * {@inheritDoc}
85       */
86      @Override
87      public void increment(final double d) {
88          if (incMoment) {
89              moment.increment(d);
90          }
91      }
92  
93      /**
94       * Returns the value of the statistic based on the values that have been added.
95       * <p>
96       * See {@link Skewness} for the definition used in the computation.</p>
97       * 
98       * @return the skewness of the available values.
99       */
100     @Override
101     public double getResult() {
102         
103         if (moment.n < 3) {
104             return Double.NaN;
105         }
106         double variance = moment.m2 / (moment.n - 1);
107         if (variance < 10E-20) {
108             return 0.0d;
109         } else {
110             double n0 = moment.getN();
111             return  (n0 * moment.m3) /
112             ((n0 - 1) * (n0 -2) * Math.sqrt(variance) * variance);
113         }
114     }
115 
116     /**
117      * {@inheritDoc}
118      */
119     public long getN() {
120         return moment.getN();
121     }
122     
123     /**
124      * {@inheritDoc}
125      */
126     @Override
127     public void clear() {
128         if (incMoment) {
129             moment.clear();
130         }
131     }
132 
133     /**
134      * Returns the Skewness of the entries in the specifed portion of the
135      * input array.
136      * <p>
137      * See {@link Skewness} for the definition used in the computation.</p>
138      * <p>
139      * Throws <code>IllegalArgumentException</code> if the array is null.</p>
140      * 
141      * @param values the input array
142      * @param begin the index of the first array element to include
143      * @param length the number of elements to include
144      * @return the skewness of the values or Double.NaN if length is less than
145      * 3
146      * @throws IllegalArgumentException if the array is null or the array index
147      *  parameters are not valid
148      */
149     @Override
150     public double evaluate(final double[] values,final int begin, 
151             final int length) {
152 
153         // Initialize the skewness
154         double skew = Double.NaN;
155 
156         if (test(values, begin, length) && length > 2 ){
157             Mean mean = new Mean();
158             // Get the mean and the standard deviation
159             double m = mean.evaluate(values, begin, length);
160             
161             // Calc the std, this is implemented here instead
162             // of using the standardDeviation method eliminate
163             // a duplicate pass to get the mean
164             double accum = 0.0;
165             double accum2 = 0.0;
166             for (int i = begin; i < begin + length; i++) {
167                 accum += Math.pow((values[i] - m), 2.0);
168                 accum2 += (values[i] - m);
169             }
170             double stdDev = Math.sqrt((accum - (Math.pow(accum2, 2) / length)) /
171                     (length - 1));
172             
173             double accum3 = 0.0;
174             for (int i = begin; i < begin + length; i++) {
175                 accum3 += Math.pow(values[i] - m, 3.0d);
176             }
177             accum3 /= Math.pow(stdDev, 3.0d);
178             
179             // Get N
180             double n0 = length;
181             
182             // Calculate skewness
183             skew = (n0 / ((n0 - 1) * (n0 - 2))) * accum3;
184         }
185         return skew;
186     }
187     
188     /**
189      * {@inheritDoc}
190      */
191     @Override
192     public Skewness copy() {
193         Skewness result = new Skewness();
194         copy(this, result);
195         return result;
196     }
197     
198     /**
199      * Copies source to dest.
200      * <p>Neither source nor dest can be null.</p>
201      * 
202      * @param source Skewness to copy
203      * @param dest Skewness to copy to
204      * @throws NullPointerException if either source or dest is null
205      */
206     public static void copy(Skewness source, Skewness dest) {
207         dest.moment = new ThirdMoment(source.moment.copy());
208         dest.incMoment = source.incMoment;
209     }
210 }