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 }