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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.MathRuntimeException;
22  import org.apache.commons.math.stat.descriptive.AbstractStorelessUnivariateStatistic;
23  
24  
25  /**
26   * Computes the Kurtosis of the available values.
27   * <p>
28   * We use the following (unbiased) formula to define kurtosis:</p>
29   *  <p>
30   *  kurtosis = { [n(n+1) / (n -1)(n - 2)(n-3)] sum[(x_i - mean)^4] / std^4 } - [3(n-1)^2 / (n-2)(n-3)]
31   *  </p><p>
32   *  where n is the number of values, mean is the {@link Mean} and std is the
33   * {@link StandardDeviation}</p>
34   * <p>
35   *  Note that this statistic is undefined for n < 4.  <code>Double.Nan</code>
36   *  is returned when there is not sufficient data to compute the statistic.</p>
37   * <p>
38   * <strong>Note that this implementation is not synchronized.</strong> If 
39   * multiple threads access an instance of this class concurrently, and at least
40   * one of the threads invokes the <code>increment()</code> or 
41   * <code>clear()</code> method, it must be synchronized externally.</p>
42   * 
43   * @version $Revision: 780541 $ $Date: 2009-05-31 20:47:02 -0400 (Sun, 31 May 2009) $
44   */
45  public class Kurtosis extends AbstractStorelessUnivariateStatistic  implements Serializable {
46  
47      /** Serializable version identifier */
48      private static final long serialVersionUID = 2784465764798260919L;  
49        
50      /**Fourth Moment on which this statistic is based */
51      protected FourthMoment moment;
52  
53      /** 
54       * Determines whether or not this statistic can be incremented or cleared.
55       * <p>
56       * Statistics based on (constructed from) external moments cannot
57       * be incremented or cleared.</p>
58      */
59      protected boolean incMoment;
60  
61      /**
62       * Construct a Kurtosis
63       */
64      public Kurtosis() {
65          incMoment = true;
66          moment = new FourthMoment();
67      }
68  
69      /**
70       * Construct a Kurtosis from an external moment
71       * 
72       * @param m4 external Moment
73       */
74      public Kurtosis(final FourthMoment m4) {
75          incMoment = false;
76          this.moment = m4;
77      }
78      
79      /**
80       * Copy constructor, creates a new {@code Kurtosis} identical
81       * to the {@code original}
82       * 
83       * @param original the {@code Kurtosis} instance to copy
84       */
85      public Kurtosis(Kurtosis original) {
86          copy(original, this);
87      }
88  
89      /**
90       * {@inheritDoc}
91       */
92      @Override
93      public void increment(final double d) {
94          if (incMoment) {
95              moment.increment(d);
96          }  else  {
97              throw MathRuntimeException.createIllegalStateException(
98                      "statistics constructed from external moments cannot be incremented");
99          }
100     }
101 
102     /**
103      * {@inheritDoc}
104      */
105     @Override
106     public double getResult() {
107         double kurtosis = Double.NaN;
108         if (moment.getN() > 3) {
109             double variance = moment.m2 / (moment.n - 1);
110                 if (moment.n <= 3 || variance < 10E-20) {
111                     kurtosis = 0.0;
112                 } else {
113                     double n = moment.n;
114                     kurtosis =
115                         (n * (n + 1) * moment.m4 -
116                                 3 * moment.m2 * moment.m2 * (n - 1)) /
117                                 ((n - 1) * (n -2) * (n -3) * variance * variance);
118                 }
119         }
120         return kurtosis;
121     }
122 
123     /**
124      * {@inheritDoc}
125      */
126     @Override
127     public void clear() {
128         if (incMoment) {
129             moment.clear();
130         } else  {
131             throw MathRuntimeException.createIllegalStateException(
132                     "statistics constructed from external moments cannot be cleared");
133         }
134     }
135 
136     /**
137      * {@inheritDoc}
138      */
139     public long getN() {
140         return moment.getN();
141     }
142     
143     /* UnvariateStatistic Approach  */
144 
145     /**
146      * Returns the kurtosis of the entries in the specified portion of the
147      * input array.  
148      * <p>
149      * See {@link Kurtosis} for details on the computing algorithm.</p>
150      * <p>
151      * Throws <code>IllegalArgumentException</code> if the array is null.</p>
152      * 
153      * @param values the input array
154      * @param begin index of the first array element to include
155      * @param length the number of elements to include
156      * @return the kurtosis of the values or Double.NaN if length is less than
157      * 4
158      * @throws IllegalArgumentException if the input array is null or the array
159      * index parameters are not valid
160      */
161     @Override
162     public double evaluate(final double[] values,final int begin, final int length) {
163         // Initialize the kurtosis  
164         double kurt = Double.NaN;   
165         
166         if (test(values, begin, length) && length > 3) {       
167             
168             // Compute the mean and standard deviation
169             Variance variance = new Variance();
170             variance.incrementAll(values, begin, length);
171             double mean = variance.moment.m1;
172             double stdDev = Math.sqrt(variance.getResult());
173             
174             // Sum the ^4 of the distance from the mean divided by the
175             // standard deviation
176             double accum3 = 0.0;
177             for (int i = begin; i < begin + length; i++) {
178                 accum3 += Math.pow((values[i] - mean), 4.0);
179             }
180             accum3 /= Math.pow(stdDev, 4.0d);
181             
182             // Get N
183             double n0 = length;
184             
185             double coefficientOne =
186                 (n0 * (n0 + 1)) / ((n0 - 1) * (n0 - 2) * (n0 - 3));
187             double termTwo =
188                 ((3 * Math.pow(n0 - 1, 2.0)) / ((n0 - 2) * (n0 - 3)));
189             
190             // Calculate kurtosis
191             kurt = (coefficientOne * accum3) - termTwo;
192         }       
193         return kurt;
194     }
195     
196     /**
197      * {@inheritDoc}
198      */
199     @Override
200     public Kurtosis copy() {
201         Kurtosis result = new Kurtosis();
202         copy(this, result);
203         return result;
204     }
205     
206     /**
207      * Copies source to dest.
208      * <p>Neither source nor dest can be null.</p>
209      * 
210      * @param source Kurtosis to copy
211      * @param dest Kurtosis to copy to
212      * @throws NullPointerException if either source or dest is null
213      */
214     public static void copy(Kurtosis source, Kurtosis dest) {
215         dest.moment = source.moment.copy();
216         dest.incMoment = source.incMoment;
217     }
218 
219 }