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 */
17package org.apache.commons.math.stat.descriptive.moment;
18
19import java.io.Serializable;
20
21import org.apache.commons.math.MathRuntimeException;
22import org.apache.commons.math.exception.util.LocalizedFormats;
23import org.apache.commons.math.stat.descriptive.AbstractStorelessUnivariateStatistic;
24import org.apache.commons.math.util.FastMath;
25
26
27/**
28 * Computes the Kurtosis of the available values.
29 * <p>
30 * We use the following (unbiased) formula to define kurtosis:</p>
31 *  <p>
32 *  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)]
33 *  </p><p>
34 *  where n is the number of values, mean is the {@link Mean} and std is the
35 * {@link StandardDeviation}</p>
36 * <p>
37 *  Note that this statistic is undefined for n < 4.  <code>Double.Nan</code>
38 *  is returned when there is not sufficient data to compute the statistic.</p>
39 * <p>
40 * <strong>Note that this implementation is not synchronized.</strong> If
41 * multiple threads access an instance of this class concurrently, and at least
42 * one of the threads invokes the <code>increment()</code> or
43 * <code>clear()</code> method, it must be synchronized externally.</p>
44 *
45 * @version $Revision: 1006299 $ $Date: 2010-10-10 16:47:17 +0200 (dim. 10 oct. 2010) $
46 */
47public class Kurtosis extends AbstractStorelessUnivariateStatistic  implements Serializable {
48
49    /** Serializable version identifier */
50    private static final long serialVersionUID = 2784465764798260919L;
51
52    /**Fourth Moment on which this statistic is based */
53    protected FourthMoment moment;
54
55    /**
56     * Determines whether or not this statistic can be incremented or cleared.
57     * <p>
58     * Statistics based on (constructed from) external moments cannot
59     * be incremented or cleared.</p>
60    */
61    protected boolean incMoment;
62
63    /**
64     * Construct a Kurtosis
65     */
66    public Kurtosis() {
67        incMoment = true;
68        moment = new FourthMoment();
69    }
70
71    /**
72     * Construct a Kurtosis from an external moment
73     *
74     * @param m4 external Moment
75     */
76    public Kurtosis(final FourthMoment m4) {
77        incMoment = false;
78        this.moment = m4;
79    }
80
81    /**
82     * Copy constructor, creates a new {@code Kurtosis} identical
83     * to the {@code original}
84     *
85     * @param original the {@code Kurtosis} instance to copy
86     */
87    public Kurtosis(Kurtosis original) {
88        copy(original, this);
89    }
90
91    /**
92     * {@inheritDoc}
93     */
94    @Override
95    public void increment(final double d) {
96        if (incMoment) {
97            moment.increment(d);
98        }  else  {
99            throw MathRuntimeException.createIllegalStateException(
100                    LocalizedFormats.CANNOT_INCREMENT_STATISTIC_CONSTRUCTED_FROM_EXTERNAL_MOMENTS);
101        }
102    }
103
104    /**
105     * {@inheritDoc}
106     */
107    @Override
108    public double getResult() {
109        double kurtosis = Double.NaN;
110        if (moment.getN() > 3) {
111            double variance = moment.m2 / (moment.n - 1);
112                if (moment.n <= 3 || variance < 10E-20) {
113                    kurtosis = 0.0;
114                } else {
115                    double n = moment.n;
116                    kurtosis =
117                        (n * (n + 1) * moment.m4 -
118                                3 * moment.m2 * moment.m2 * (n - 1)) /
119                                ((n - 1) * (n -2) * (n -3) * variance * variance);
120                }
121        }
122        return kurtosis;
123    }
124
125    /**
126     * {@inheritDoc}
127     */
128    @Override
129    public void clear() {
130        if (incMoment) {
131            moment.clear();
132        } else  {
133            throw MathRuntimeException.createIllegalStateException(
134                    LocalizedFormats.CANNOT_CLEAR_STATISTIC_CONSTRUCTED_FROM_EXTERNAL_MOMENTS);
135        }
136    }
137
138    /**
139     * {@inheritDoc}
140     */
141    public long getN() {
142        return moment.getN();
143    }
144
145    /* UnvariateStatistic Approach  */
146
147    /**
148     * Returns the kurtosis of the entries in the specified portion of the
149     * input array.
150     * <p>
151     * See {@link Kurtosis} for details on the computing algorithm.</p>
152     * <p>
153     * Throws <code>IllegalArgumentException</code> if the array is null.</p>
154     *
155     * @param values the input array
156     * @param begin index of the first array element to include
157     * @param length the number of elements to include
158     * @return the kurtosis of the values or Double.NaN if length is less than
159     * 4
160     * @throws IllegalArgumentException if the input array is null or the array
161     * index parameters are not valid
162     */
163    @Override
164    public double evaluate(final double[] values,final int begin, final int length) {
165        // Initialize the kurtosis
166        double kurt = Double.NaN;
167
168        if (test(values, begin, length) && length > 3) {
169
170            // Compute the mean and standard deviation
171            Variance variance = new Variance();
172            variance.incrementAll(values, begin, length);
173            double mean = variance.moment.m1;
174            double stdDev = FastMath.sqrt(variance.getResult());
175
176            // Sum the ^4 of the distance from the mean divided by the
177            // standard deviation
178            double accum3 = 0.0;
179            for (int i = begin; i < begin + length; i++) {
180                accum3 += FastMath.pow(values[i] - mean, 4.0);
181            }
182            accum3 /= FastMath.pow(stdDev, 4.0d);
183
184            // Get N
185            double n0 = length;
186
187            double coefficientOne =
188                (n0 * (n0 + 1)) / ((n0 - 1) * (n0 - 2) * (n0 - 3));
189            double termTwo =
190                (3 * FastMath.pow(n0 - 1, 2.0)) / ((n0 - 2) * (n0 - 3));
191
192            // Calculate kurtosis
193            kurt = (coefficientOne * accum3) - termTwo;
194        }
195        return kurt;
196    }
197
198    /**
199     * {@inheritDoc}
200     */
201    @Override
202    public Kurtosis copy() {
203        Kurtosis result = new Kurtosis();
204        copy(this, result);
205        return result;
206    }
207
208    /**
209     * Copies source to dest.
210     * <p>Neither source nor dest can be null.</p>
211     *
212     * @param source Kurtosis to copy
213     * @param dest Kurtosis to copy to
214     * @throws NullPointerException if either source or dest is null
215     */
216    public static void copy(Kurtosis source, Kurtosis dest) {
217        dest.setData(source.getDataRef());
218        dest.moment = source.moment.copy();
219        dest.incMoment = source.incMoment;
220    }
221
222}
223