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.exception.util.LocalizedFormats; 23 import org.apache.commons.math.stat.descriptive.AbstractStorelessUnivariateStatistic; 24 import 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 */ 47 public 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 */ Kurtosis()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 */ Kurtosis(final FourthMoment m4)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 */ Kurtosis(Kurtosis original)87 public Kurtosis(Kurtosis original) { 88 copy(original, this); 89 } 90 91 /** 92 * {@inheritDoc} 93 */ 94 @Override increment(final double d)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 getResult()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 clear()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 */ getN()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 evaluate(final double[] values,final int begin, final int length)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 copy()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 */ copy(Kurtosis source, Kurtosis dest)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