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.stat.descriptive.AbstractStorelessUnivariateStatistic; 23 24 25 /** 26 * Computes the Kurtosis of the available values. 27 * <p> 28 * We use the following (unbiased) formula to define kurtosis:</p> 29 * <p> 30 * 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)] 31 * </p><p> 32 * where n is the number of values, mean is the {@link Mean} and std is the 33 * {@link StandardDeviation}</p> 34 * <p> 35 * Note that this statistic is undefined for n < 4. <code>Double.Nan</code> 36 * is returned when there is not sufficient data to compute the statistic.</p> 37 * <p> 38 * <strong>Note that this implementation is not synchronized.</strong> If 39 * multiple threads access an instance of this class concurrently, and at least 40 * one of the threads invokes the <code>increment()</code> or 41 * <code>clear()</code> method, it must be synchronized externally.</p> 42 * 43 * @version $Revision: 780541 $ $Date: 2009-05-31 20:47:02 -0400 (Sun, 31 May 2009) $ 44 */ 45 public class Kurtosis extends AbstractStorelessUnivariateStatistic implements Serializable { 46 47 /** Serializable version identifier */ 48 private static final long serialVersionUID = 2784465764798260919L; 49 50 /**Fourth Moment on which this statistic is based */ 51 protected FourthMoment moment; 52 53 /** 54 * Determines whether or not this statistic can be incremented or cleared. 55 * <p> 56 * Statistics based on (constructed from) external moments cannot 57 * be incremented or cleared.</p> 58 */ 59 protected boolean incMoment; 60 61 /** 62 * Construct a Kurtosis 63 */ 64 public Kurtosis() { 65 incMoment = true; 66 moment = new FourthMoment(); 67 } 68 69 /** 70 * Construct a Kurtosis from an external moment 71 * 72 * @param m4 external Moment 73 */ 74 public Kurtosis(final FourthMoment m4) { 75 incMoment = false; 76 this.moment = m4; 77 } 78 79 /** 80 * Copy constructor, creates a new {@code Kurtosis} identical 81 * to the {@code original} 82 * 83 * @param original the {@code Kurtosis} instance to copy 84 */ 85 public Kurtosis(Kurtosis original) { 86 copy(original, this); 87 } 88 89 /** 90 * {@inheritDoc} 91 */ 92 @Override 93 public void increment(final double d) { 94 if (incMoment) { 95 moment.increment(d); 96 } else { 97 throw MathRuntimeException.createIllegalStateException( 98 "statistics constructed from external moments cannot be incremented"); 99 } 100 } 101 102 /** 103 * {@inheritDoc} 104 */ 105 @Override 106 public double getResult() { 107 double kurtosis = Double.NaN; 108 if (moment.getN() > 3) { 109 double variance = moment.m2 / (moment.n - 1); 110 if (moment.n <= 3 || variance < 10E-20) { 111 kurtosis = 0.0; 112 } else { 113 double n = moment.n; 114 kurtosis = 115 (n * (n + 1) * moment.m4 - 116 3 * moment.m2 * moment.m2 * (n - 1)) / 117 ((n - 1) * (n -2) * (n -3) * variance * variance); 118 } 119 } 120 return kurtosis; 121 } 122 123 /** 124 * {@inheritDoc} 125 */ 126 @Override 127 public void clear() { 128 if (incMoment) { 129 moment.clear(); 130 } else { 131 throw MathRuntimeException.createIllegalStateException( 132 "statistics constructed from external moments cannot be cleared"); 133 } 134 } 135 136 /** 137 * {@inheritDoc} 138 */ 139 public long getN() { 140 return moment.getN(); 141 } 142 143 /* UnvariateStatistic Approach */ 144 145 /** 146 * Returns the kurtosis of the entries in the specified portion of the 147 * input array. 148 * <p> 149 * See {@link Kurtosis} for details on the computing algorithm.</p> 150 * <p> 151 * Throws <code>IllegalArgumentException</code> if the array is null.</p> 152 * 153 * @param values the input array 154 * @param begin index of the first array element to include 155 * @param length the number of elements to include 156 * @return the kurtosis of the values or Double.NaN if length is less than 157 * 4 158 * @throws IllegalArgumentException 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 // Initialize the kurtosis 164 double kurt = Double.NaN; 165 166 if (test(values, begin, length) && length > 3) { 167 168 // Compute the mean and standard deviation 169 Variance variance = new Variance(); 170 variance.incrementAll(values, begin, length); 171 double mean = variance.moment.m1; 172 double stdDev = Math.sqrt(variance.getResult()); 173 174 // Sum the ^4 of the distance from the mean divided by the 175 // standard deviation 176 double accum3 = 0.0; 177 for (int i = begin; i < begin + length; i++) { 178 accum3 += Math.pow((values[i] - mean), 4.0); 179 } 180 accum3 /= Math.pow(stdDev, 4.0d); 181 182 // Get N 183 double n0 = length; 184 185 double coefficientOne = 186 (n0 * (n0 + 1)) / ((n0 - 1) * (n0 - 2) * (n0 - 3)); 187 double termTwo = 188 ((3 * Math.pow(n0 - 1, 2.0)) / ((n0 - 2) * (n0 - 3))); 189 190 // Calculate kurtosis 191 kurt = (coefficientOne * accum3) - termTwo; 192 } 193 return kurt; 194 } 195 196 /** 197 * {@inheritDoc} 198 */ 199 @Override 200 public Kurtosis copy() { 201 Kurtosis result = new Kurtosis(); 202 copy(this, result); 203 return result; 204 } 205 206 /** 207 * Copies source to dest. 208 * <p>Neither source nor dest can be null.</p> 209 * 210 * @param source Kurtosis to copy 211 * @param dest Kurtosis to copy to 212 * @throws NullPointerException if either source or dest is null 213 */ 214 public static void copy(Kurtosis source, Kurtosis dest) { 215 dest.moment = source.moment.copy(); 216 dest.incMoment = source.incMoment; 217 } 218 219 }