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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    *      https://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  
18  /*
19   * This is not the original file distributed by the Apache Software Foundation
20   * It has been modified by the Hipparchus project
21   */
22  package org.hipparchus.stat.descriptive.moment;
23  
24  import java.io.Serializable;
25  
26  import org.hipparchus.exception.MathIllegalArgumentException;
27  import org.hipparchus.exception.NullArgumentException;
28  import org.hipparchus.stat.descriptive.AbstractStorelessUnivariateStatistic;
29  import org.hipparchus.util.FastMath;
30  import org.hipparchus.util.MathArrays;
31  import org.hipparchus.util.MathUtils;
32  
33  
34  /**
35   * Computes the Kurtosis of the available values.
36   * <p>
37   * We use the following (unbiased) formula to define kurtosis:
38   * <p>
39   * 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)]
40   * <p>
41   * where n is the number of values, mean is the {@link Mean} and std is the
42   * {@link StandardDeviation}.
43   * <p>
44   * Note that this statistic is undefined for n &lt; 4.  <code>Double.Nan</code>
45   * is returned when there is not sufficient data to compute the statistic.
46   * Note that Double.NaN may also be returned if the input includes NaN
47   * and / or infinite values.
48   * <p>
49   * <strong>Note that this implementation is not synchronized.</strong> If
50   * multiple threads access an instance of this class concurrently, and at least
51   * one of the threads invokes the <code>increment()</code> or
52   * <code>clear()</code> method, it must be synchronized externally.
53   */
54  public class Kurtosis extends AbstractStorelessUnivariateStatistic  implements Serializable {
55  
56      /** Serializable version identifier */
57      private static final long serialVersionUID = 20150412L;
58  
59      /**Fourth Moment on which this statistic is based */
60      protected final FourthMoment moment;
61  
62      /**
63       * Determines whether or not this statistic can be incremented or cleared.
64       * <p>
65       * Statistics based on (constructed from) external moments cannot
66       * be incremented or cleared.
67       */
68      protected final boolean incMoment;
69  
70      /**
71       * Construct a Kurtosis.
72       */
73      public Kurtosis() {
74          moment    = new FourthMoment();
75          incMoment = true;
76      }
77  
78      /**
79       * Construct a Kurtosis from an external moment.
80       *
81       * @param m4 external Moment
82       */
83      public Kurtosis(final FourthMoment m4) {
84          this.moment = m4;
85          incMoment   = false;
86      }
87  
88      /**
89       * Copy constructor, creates a new {@code Kurtosis} identical
90       * to the {@code original}.
91       *
92       * @param original the {@code Kurtosis} instance to copy
93       * @throws NullArgumentException if original is null
94       */
95      public Kurtosis(Kurtosis original) throws NullArgumentException {
96          MathUtils.checkNotNull(original);
97          this.moment    = original.moment.copy();
98          this.incMoment = original.incMoment;
99      }
100 
101     /**
102      * {@inheritDoc}
103      * <p>Note that when {@link #Kurtosis(FourthMoment)} is used to
104      * create a Variance, this method does nothing. In that case, the
105      * FourthMoment should be incremented directly.</p>
106      */
107     @Override
108     public void increment(final double d) {
109         if (incMoment) {
110             moment.increment(d);
111         }
112     }
113 
114     /** {@inheritDoc} */
115     @Override
116     public double getResult() {
117         double kurtosis = Double.NaN;
118         if (moment.getN() > 3) {
119             double variance = moment.m2 / (moment.n - 1);
120                 if (moment.n <= 3 || variance < 10E-20) {
121                     kurtosis = 0.0;
122                 } else {
123                     double n = moment.n;
124                     kurtosis =
125                         (n * (n + 1) * moment.getResult() -
126                                 3 * moment.m2 * moment.m2 * (n - 1)) /
127                                 ((n - 1) * (n -2) * (n -3) * variance * variance);
128                 }
129         }
130         return kurtosis;
131     }
132 
133     /** {@inheritDoc} */
134     @Override
135     public void clear() {
136         if (incMoment) {
137             moment.clear();
138         }
139     }
140 
141     /** {@inheritDoc} */
142     @Override
143     public long getN() {
144         return moment.getN();
145     }
146 
147     /* UnvariateStatistic Approach  */
148 
149     /**
150      * Returns the kurtosis of the entries in the specified portion of the
151      * input array.
152      * <p>
153      * See {@link Kurtosis} for details on the computing algorithm.</p>
154      * <p>
155      * Throws <code>IllegalArgumentException</code> if the array is null.</p>
156      *
157      * @param values the input array
158      * @param begin index of the first array element to include
159      * @param length the number of elements to include
160      * @return the kurtosis of the values or Double.NaN if length is less than 4
161      * @throws MathIllegalArgumentException if the input array is null or the array
162      * index parameters are not valid
163      */
164     @Override
165     public double evaluate(final double[] values, final int begin, final int length)
166         throws MathIllegalArgumentException {
167 
168         // Initialize the kurtosis
169         double kurt = Double.NaN;
170 
171         if (MathArrays.verifyValues(values, begin, length) && length > 3) {
172             // Compute the mean and standard deviation
173             Variance variance = new Variance();
174             variance.incrementAll(values, begin, length);
175             double mean = variance.moment.m1;
176             double stdDev = FastMath.sqrt(variance.getResult());
177 
178             // Sum the ^4 of the distance from the mean divided by the
179             // standard deviation
180             double accum3 = 0.0;
181             for (int i = begin; i < begin + length; i++) {
182                 accum3 += FastMath.pow(values[i] - mean, 4.0);
183             }
184             accum3 /= FastMath.pow(stdDev, 4.0d);
185 
186             // Get N
187             double n0 = length;
188 
189             double coefficientOne =
190                 (n0 * (n0 + 1)) / ((n0 - 1) * (n0 - 2) * (n0 - 3));
191             double termTwo =
192                 (3 * FastMath.pow(n0 - 1, 2.0)) / ((n0 - 2) * (n0 - 3));
193 
194             // Calculate kurtosis
195             kurt = (coefficientOne * accum3) - termTwo;
196         }
197         return kurt;
198     }
199 
200     /** {@inheritDoc} */
201     @Override
202     public Kurtosis copy() {
203         return new Kurtosis(this);
204     }
205 
206 }