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.stat.descriptive.AbstractStorelessUnivariateStatistic; 023 024 025 /** 026 * Computes the Kurtosis of the available values. 027 * <p> 028 * We use the following (unbiased) formula to define kurtosis:</p> 029 * <p> 030 * 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)] 031 * </p><p> 032 * where n is the number of values, mean is the {@link Mean} and std is the 033 * {@link StandardDeviation}</p> 034 * <p> 035 * Note that this statistic is undefined for n < 4. <code>Double.Nan</code> 036 * is returned when there is not sufficient data to compute the statistic.</p> 037 * <p> 038 * <strong>Note that this implementation is not synchronized.</strong> If 039 * multiple threads access an instance of this class concurrently, and at least 040 * one of the threads invokes the <code>increment()</code> or 041 * <code>clear()</code> method, it must be synchronized externally.</p> 042 * 043 * @version $Revision: 811833 $ $Date: 2009-09-06 12:27:50 -0400 (Sun, 06 Sep 2009) $ 044 */ 045 public class Kurtosis extends AbstractStorelessUnivariateStatistic implements Serializable { 046 047 /** Serializable version identifier */ 048 private static final long serialVersionUID = 2784465764798260919L; 049 050 /**Fourth Moment on which this statistic is based */ 051 protected FourthMoment moment; 052 053 /** 054 * Determines whether or not this statistic can be incremented or cleared. 055 * <p> 056 * Statistics based on (constructed from) external moments cannot 057 * be incremented or cleared.</p> 058 */ 059 protected boolean incMoment; 060 061 /** 062 * Construct a Kurtosis 063 */ 064 public Kurtosis() { 065 incMoment = true; 066 moment = new FourthMoment(); 067 } 068 069 /** 070 * Construct a Kurtosis from an external moment 071 * 072 * @param m4 external Moment 073 */ 074 public Kurtosis(final FourthMoment m4) { 075 incMoment = false; 076 this.moment = m4; 077 } 078 079 /** 080 * Copy constructor, creates a new {@code Kurtosis} identical 081 * to the {@code original} 082 * 083 * @param original the {@code Kurtosis} instance to copy 084 */ 085 public Kurtosis(Kurtosis original) { 086 copy(original, this); 087 } 088 089 /** 090 * {@inheritDoc} 091 */ 092 @Override 093 public void increment(final double d) { 094 if (incMoment) { 095 moment.increment(d); 096 } else { 097 throw MathRuntimeException.createIllegalStateException( 098 "statistics constructed from external moments cannot be incremented"); 099 } 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 }