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.math3.stat.descriptive.moment;
018
019 import java.io.Serializable;
020
021 import org.apache.commons.math3.exception.MathIllegalArgumentException;
022 import org.apache.commons.math3.exception.NullArgumentException;
023 import org.apache.commons.math3.stat.descriptive.AbstractStorelessUnivariateStatistic;
024 import org.apache.commons.math3.util.FastMath;
025 import org.apache.commons.math3.util.MathUtils;
026
027
028 /**
029 * Computes the Kurtosis of the available values.
030 * <p>
031 * We use the following (unbiased) formula to define kurtosis:</p>
032 * <p>
033 * 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)]
034 * </p><p>
035 * where n is the number of values, mean is the {@link Mean} and std is the
036 * {@link StandardDeviation}</p>
037 * <p>
038 * Note that this statistic is undefined for n < 4. <code>Double.Nan</code>
039 * is returned when there is not sufficient data to compute the statistic.</p>
040 * <p>
041 * <strong>Note that this implementation is not synchronized.</strong> If
042 * multiple threads access an instance of this class concurrently, and at least
043 * one of the threads invokes the <code>increment()</code> or
044 * <code>clear()</code> method, it must be synchronized externally.</p>
045 *
046 * @version $Id: Kurtosis.java 1416643 2012-12-03 19:37:14Z tn $
047 */
048 public class Kurtosis extends AbstractStorelessUnivariateStatistic implements Serializable {
049
050 /** Serializable version identifier */
051 private static final long serialVersionUID = 2784465764798260919L;
052
053 /**Fourth Moment on which this statistic is based */
054 protected FourthMoment moment;
055
056 /**
057 * Determines whether or not this statistic can be incremented or cleared.
058 * <p>
059 * Statistics based on (constructed from) external moments cannot
060 * be incremented or cleared.</p>
061 */
062 protected boolean incMoment;
063
064 /**
065 * Construct a Kurtosis
066 */
067 public Kurtosis() {
068 incMoment = true;
069 moment = new FourthMoment();
070 }
071
072 /**
073 * Construct a Kurtosis from an external moment
074 *
075 * @param m4 external Moment
076 */
077 public Kurtosis(final FourthMoment m4) {
078 incMoment = false;
079 this.moment = m4;
080 }
081
082 /**
083 * Copy constructor, creates a new {@code Kurtosis} identical
084 * to the {@code original}
085 *
086 * @param original the {@code Kurtosis} instance to copy
087 * @throws NullArgumentException if original is null
088 */
089 public Kurtosis(Kurtosis original) throws NullArgumentException {
090 copy(original, this);
091 }
092
093 /**
094 * {@inheritDoc}
095 * <p>Note that when {@link #Kurtosis(FourthMoment)} is used to
096 * create a Variance, this method does nothing. In that case, the
097 * FourthMoment should be incremented directly.</p>
098 */
099 @Override
100 public void increment(final double d) {
101 if (incMoment) {
102 moment.increment(d);
103 }
104 }
105
106 /**
107 * {@inheritDoc}
108 */
109 @Override
110 public double getResult() {
111 double kurtosis = Double.NaN;
112 if (moment.getN() > 3) {
113 double variance = moment.m2 / (moment.n - 1);
114 if (moment.n <= 3 || variance < 10E-20) {
115 kurtosis = 0.0;
116 } else {
117 double n = moment.n;
118 kurtosis =
119 (n * (n + 1) * moment.getResult() -
120 3 * moment.m2 * moment.m2 * (n - 1)) /
121 ((n - 1) * (n -2) * (n -3) * variance * variance);
122 }
123 }
124 return kurtosis;
125 }
126
127 /**
128 * {@inheritDoc}
129 */
130 @Override
131 public void clear() {
132 if (incMoment) {
133 moment.clear();
134 }
135 }
136
137 /**
138 * {@inheritDoc}
139 */
140 public long getN() {
141 return moment.getN();
142 }
143
144 /* UnvariateStatistic Approach */
145
146 /**
147 * Returns the kurtosis of the entries in the specified portion of the
148 * input array.
149 * <p>
150 * See {@link Kurtosis} for details on the computing algorithm.</p>
151 * <p>
152 * Throws <code>IllegalArgumentException</code> if the array is null.</p>
153 *
154 * @param values the input array
155 * @param begin index of the first array element to include
156 * @param length the number of elements to include
157 * @return the kurtosis of the values or Double.NaN if length is less than 4
158 * @throws MathIllegalArgumentException 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 throws MathIllegalArgumentException {
164 // Initialize the kurtosis
165 double kurt = Double.NaN;
166
167 if (test(values, begin, length) && length > 3) {
168
169 // Compute the mean and standard deviation
170 Variance variance = new Variance();
171 variance.incrementAll(values, begin, length);
172 double mean = variance.moment.m1;
173 double stdDev = FastMath.sqrt(variance.getResult());
174
175 // Sum the ^4 of the distance from the mean divided by the
176 // standard deviation
177 double accum3 = 0.0;
178 for (int i = begin; i < begin + length; i++) {
179 accum3 += FastMath.pow(values[i] - mean, 4.0);
180 }
181 accum3 /= FastMath.pow(stdDev, 4.0d);
182
183 // Get N
184 double n0 = length;
185
186 double coefficientOne =
187 (n0 * (n0 + 1)) / ((n0 - 1) * (n0 - 2) * (n0 - 3));
188 double termTwo =
189 (3 * FastMath.pow(n0 - 1, 2.0)) / ((n0 - 2) * (n0 - 3));
190
191 // Calculate kurtosis
192 kurt = (coefficientOne * accum3) - termTwo;
193 }
194 return kurt;
195 }
196
197 /**
198 * {@inheritDoc}
199 */
200 @Override
201 public Kurtosis copy() {
202 Kurtosis result = new Kurtosis();
203 // No try-catch because args are guaranteed non-null
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 NullArgumentException if either source or dest is null
215 */
216 public static void copy(Kurtosis source, Kurtosis dest)
217 throws NullArgumentException {
218 MathUtils.checkNotNull(source);
219 MathUtils.checkNotNull(dest);
220 dest.setData(source.getDataRef());
221 dest.moment = source.moment.copy();
222 dest.incMoment = source.incMoment;
223 }
224
225 }