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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  /**
22   * Computes a statistic related to the Fourth Central Moment.  Specifically,
23   * what is computed is the sum of 
24   * <p>
25   * (x_i - xbar) ^ 4, </p>
26   * <p>
27   * where the x_i are the 
28   * sample observations and xbar is the sample mean. </p>
29   * <p>
30   * The following recursive updating formula is used: </p>
31   * <p>
32   * Let <ul>
33   * <li> dev = (current obs - previous mean) </li>
34   * <li> m2 = previous value of {@link SecondMoment} </li>
35   * <li> m2 = previous value of {@link ThirdMoment} </li>
36   * <li> n = number of observations (including current obs) </li>
37   * </ul>
38   * Then </p>
39   * <p>
40   * new value = old value - 4 * (dev/n) * m3 + 6 * (dev/n)^2 * m2 + <br>
41   * [n^2 - 3 * (n-1)] * dev^4 * (n-1) / n^3 </p>
42   * <p>
43   * Returns <code>Double.NaN</code> if no data values have been added and
44   * returns <code>0</code> if there is just one value in the data set. </p>
45   * <p>
46   * <strong>Note that this implementation is not synchronized.</strong> If 
47   * multiple threads access an instance of this class concurrently, and at least
48   * one of the threads invokes the <code>increment()</code> or 
49   * <code>clear()</code> method, it must be synchronized externally. </p>
50   * 
51   * @version $Revision: 762116 $ $Date: 2009-04-05 12:48:53 -0400 (Sun, 05 Apr 2009) $
52   */
53  public class FourthMoment extends ThirdMoment implements Serializable{
54  
55      /** Serializable version identifier */
56      private static final long serialVersionUID = 4763990447117157611L;
57          
58      /** fourth moment of values that have been added */
59      protected double m4;
60  
61      /**
62       * Create a FourthMoment instance
63       */
64      public FourthMoment() {
65          super();
66          m4 = Double.NaN;
67      }
68      
69      /**
70       * Copy constructor, creates a new {@code FourthMoment} identical
71       * to the {@code original}
72       * 
73       * @param original the {@code FourthMoment} instance to copy
74       */
75       public FourthMoment(FourthMoment original) {
76           super();
77           copy(original, this);
78       }
79      
80      /**
81       * {@inheritDoc}
82       */
83       @Override
84      public void increment(final double d) {
85          if (n < 1) {
86              m4 = 0.0;
87              m3 = 0.0;
88              m2 = 0.0;
89              m1 = 0.0;
90          }
91  
92          double prevM3 = m3;
93          double prevM2 = m2;
94          
95          super.increment(d);
96          
97          double n0 = n;
98  
99          m4 = m4 - 4.0 * nDev * prevM3 + 6.0 * nDevSq * prevM2 +
100             ((n0 * n0) - 3 * (n0 -1)) * (nDevSq * nDevSq * (n0 - 1) * n0);
101     }
102 
103     /**
104      * {@inheritDoc}
105      */
106     @Override
107     public double getResult() {
108         return m4;
109     }
110 
111     /**
112      * {@inheritDoc}
113      */
114     @Override
115     public void clear() {
116         super.clear();
117         m4 = Double.NaN;
118     }
119     
120     /**
121      * {@inheritDoc}
122      */
123     @Override
124     public FourthMoment copy() {
125         FourthMoment result = new FourthMoment();
126         copy(this, result);
127         return result;
128     }
129     
130     /**
131      * Copies source to dest.
132      * <p>Neither source nor dest can be null.</p>
133      * 
134      * @param source FourthMoment to copy
135      * @param dest FourthMoment to copy to
136      * @throws NullPointerException if either source or dest is null
137      */
138     public static void copy(FourthMoment source, FourthMoment dest) {
139         ThirdMoment.copy(source, dest);
140         dest.m4 = source.m4;
141     }  
142 }