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1   /*
2    * Copyright 2003-2004 The Apache Software Foundation.
3    *
4    * Licensed under the Apache License, Version 2.0 (the "License");
5    * you may not use this file except in compliance with the License.
6    * You may obtain a copy of the License at
7    *
8    *      http://www.apache.org/licenses/LICENSE-2.0
9    *
10   * Unless required by applicable law or agreed to in writing, software
11   * distributed under the License is distributed on an "AS IS" BASIS,
12   * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
13   * See the License for the specific language governing permissions and
14   * limitations under the License.
15   */
16  package org.apache.commons.math.stat.descriptive.moment;
17  
18  import java.io.Serializable;
19  
20  /**
21   * Computes a statistic related to the Fourth Central Moment.  Specifically,
22   * what is computed is the sum of 
23   * <p>
24   * (x_i - xbar) ^ 4,
25   * <p>
26   * where the x_i are the 
27   * sample observations and xbar is the sample mean.
28   * <p>
29   * The following recursive updating formula is used:
30   * <p>
31   * Let <ul>
32   * <li> dev = (current obs - previous mean) </li>
33   * <li> m2 = previous value of {@link SecondMoment} </li>
34   * <li> m2 = previous value of {@link ThirdMoment} </li>
35   * <li> n = number of observations (including current obs) </li>
36   * </ul>
37   * Then
38   * <p>
39   * new value = old value - 4 * (dev/n) * m3 + 6 * (dev/n)^2 * m2 + <br>
40   * [n^2 - 3 * (n-1)] * dev^4 * (n-1) / n^3
41   * <p>
42   * Returns <code>Double.NaN</code> if no data values have been added and
43   * returns <code>0</code> if there is just one value in the data set.
44   * <p>
45   * <strong>Note that this implementation is not synchronized.</strong> If 
46   * multiple threads access an instance of this class concurrently, and at least
47   * one of the threads invokes the <code>increment()</code> or 
48   * <code>clear()</code> method, it must be synchronized externally.
49   * 
50   * @version $Revision: 348519 $ $Date: 2005-11-23 12:12:18 -0700 (Wed, 23 Nov 2005) $
51   */
52  public class FourthMoment extends ThirdMoment implements Serializable{
53  
54      /** Serializable version identifier */
55      private static final long serialVersionUID = 4763990447117157611L;
56          
57      /** fourth moment of values that have been added */
58      protected double m4;
59  
60      /**
61       * Create a FourthMoment instance
62       */
63      public FourthMoment() {
64          super();
65          m4 = Double.NaN;
66      }
67      
68      /**
69       * @see org.apache.commons.math.stat.descriptive.StorelessUnivariateStatistic#increment(double)
70       */
71      public void increment(final double d) {
72          if (n < 1) {
73              m4 = 0.0;
74              m3 = 0.0;
75              m2 = 0.0;
76              m1 = 0.0;
77          }
78  
79          double prevM3 = m3;
80          double prevM2 = m2;
81          
82          super.increment(d);
83          
84          double n0 = (double) n;
85  
86          m4 = m4 - 4.0 * nDev * prevM3 + 6.0 * nDevSq * prevM2 +
87              ((n0 * n0) - 3 * (n0 -1)) * (nDevSq * nDevSq * (n0 - 1) * n0);
88      }
89  
90      /**
91       * @see org.apache.commons.math.stat.descriptive.StorelessUnivariateStatistic#getResult()
92       */
93      public double getResult() {
94          return m4;
95      }
96  
97      /**
98       * @see org.apache.commons.math.stat.descriptive.StorelessUnivariateStatistic#clear()
99       */
100     public void clear() {
101         super.clear();
102         m4 = Double.NaN;
103     }
104 
105 }