001    /*
002     * Licensed to the Apache Software Foundation (ASF) under one or more
003     * contributor license agreements.  See the NOTICE file distributed with
004     * this work for additional information regarding copyright ownership.
005     * The ASF licenses this file to You under the Apache License, Version 2.0
006     * (the "License"); you may not use this file except in compliance with
007     * the License.  You may obtain a copy of the License at
008     *
009     *      http://www.apache.org/licenses/LICENSE-2.0
010     *
011     * Unless required by applicable law or agreed to in writing, software
012     * distributed under the License is distributed on an "AS IS" BASIS,
013     * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
014     * See the License for the specific language governing permissions and
015     * limitations under the License.
016     */
017    package org.apache.commons.math.stat.descriptive.moment;
018    
019    import java.io.Serializable;
020    
021    import org.apache.commons.math.MathRuntimeException;
022    import org.apache.commons.math.exception.util.LocalizedFormats;
023    import org.apache.commons.math.stat.descriptive.AbstractStorelessUnivariateStatistic;
024    import org.apache.commons.math.util.FastMath;
025    
026    
027    /**
028     * Computes the Kurtosis of the available values.
029     * <p>
030     * We use the following (unbiased) formula to define kurtosis:</p>
031     *  <p>
032     *  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)]
033     *  </p><p>
034     *  where n is the number of values, mean is the {@link Mean} and std is the
035     * {@link StandardDeviation}</p>
036     * <p>
037     *  Note that this statistic is undefined for n < 4.  <code>Double.Nan</code>
038     *  is returned when there is not sufficient data to compute the statistic.</p>
039     * <p>
040     * <strong>Note that this implementation is not synchronized.</strong> If
041     * multiple threads access an instance of this class concurrently, and at least
042     * one of the threads invokes the <code>increment()</code> or
043     * <code>clear()</code> method, it must be synchronized externally.</p>
044     *
045     * @version $Revision: 1006299 $ $Date: 2010-10-10 16:47:17 +0200 (dim. 10 oct. 2010) $
046     */
047    public class Kurtosis extends AbstractStorelessUnivariateStatistic  implements Serializable {
048    
049        /** Serializable version identifier */
050        private static final long serialVersionUID = 2784465764798260919L;
051    
052        /**Fourth Moment on which this statistic is based */
053        protected FourthMoment moment;
054    
055        /**
056         * Determines whether or not this statistic can be incremented or cleared.
057         * <p>
058         * Statistics based on (constructed from) external moments cannot
059         * be incremented or cleared.</p>
060        */
061        protected boolean incMoment;
062    
063        /**
064         * Construct a Kurtosis
065         */
066        public Kurtosis() {
067            incMoment = true;
068            moment = new FourthMoment();
069        }
070    
071        /**
072         * Construct a Kurtosis from an external moment
073         *
074         * @param m4 external Moment
075         */
076        public Kurtosis(final FourthMoment m4) {
077            incMoment = false;
078            this.moment = m4;
079        }
080    
081        /**
082         * Copy constructor, creates a new {@code Kurtosis} identical
083         * to the {@code original}
084         *
085         * @param original the {@code Kurtosis} instance to copy
086         */
087        public Kurtosis(Kurtosis original) {
088            copy(original, this);
089        }
090    
091        /**
092         * {@inheritDoc}
093         */
094        @Override
095        public void increment(final double d) {
096            if (incMoment) {
097                moment.increment(d);
098            }  else  {
099                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    }