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 */ 017package org.apache.commons.math3.stat.descriptive.moment; 018 019import java.io.Serializable; 020 021import org.apache.commons.math3.exception.MathIllegalArgumentException; 022import org.apache.commons.math3.exception.NullArgumentException; 023import org.apache.commons.math3.stat.descriptive.AbstractStorelessUnivariateStatistic; 024import org.apache.commons.math3.util.FastMath; 025import 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. 040 * Note that Double.NaN may also be returned if the input includes NaN 041 * and / or infinite values.</p> 042 * <p> 043 * <strong>Note that this implementation is not synchronized.</strong> If 044 * multiple threads access an instance of this class concurrently, and at least 045 * one of the threads invokes the <code>increment()</code> or 046 * <code>clear()</code> method, it must be synchronized externally.</p> 047 * 048 */ 049public class Kurtosis extends AbstractStorelessUnivariateStatistic implements Serializable { 050 051 /** Serializable version identifier */ 052 private static final long serialVersionUID = 2784465764798260919L; 053 054 /**Fourth Moment on which this statistic is based */ 055 protected FourthMoment moment; 056 057 /** 058 * Determines whether or not this statistic can be incremented or cleared. 059 * <p> 060 * Statistics based on (constructed from) external moments cannot 061 * be incremented or cleared.</p> 062 */ 063 protected boolean incMoment; 064 065 /** 066 * Construct a Kurtosis 067 */ 068 public Kurtosis() { 069 incMoment = true; 070 moment = new FourthMoment(); 071 } 072 073 /** 074 * Construct a Kurtosis from an external moment 075 * 076 * @param m4 external Moment 077 */ 078 public Kurtosis(final FourthMoment m4) { 079 incMoment = false; 080 this.moment = m4; 081 } 082 083 /** 084 * Copy constructor, creates a new {@code Kurtosis} identical 085 * to the {@code original} 086 * 087 * @param original the {@code Kurtosis} instance to copy 088 * @throws NullArgumentException if original is null 089 */ 090 public Kurtosis(Kurtosis original) throws NullArgumentException { 091 copy(original, this); 092 } 093 094 /** 095 * {@inheritDoc} 096 * <p>Note that when {@link #Kurtosis(FourthMoment)} is used to 097 * create a Variance, this method does nothing. In that case, the 098 * FourthMoment should be incremented directly.</p> 099 */ 100 @Override 101 public void increment(final double d) { 102 if (incMoment) { 103 moment.increment(d); 104 } 105 } 106 107 /** 108 * {@inheritDoc} 109 */ 110 @Override 111 public double getResult() { 112 double kurtosis = Double.NaN; 113 if (moment.getN() > 3) { 114 double variance = moment.m2 / (moment.n - 1); 115 if (moment.n <= 3 || variance < 10E-20) { 116 kurtosis = 0.0; 117 } else { 118 double n = moment.n; 119 kurtosis = 120 (n * (n + 1) * moment.getResult() - 121 3 * moment.m2 * moment.m2 * (n - 1)) / 122 ((n - 1) * (n -2) * (n -3) * variance * variance); 123 } 124 } 125 return kurtosis; 126 } 127 128 /** 129 * {@inheritDoc} 130 */ 131 @Override 132 public void clear() { 133 if (incMoment) { 134 moment.clear(); 135 } 136 } 137 138 /** 139 * {@inheritDoc} 140 */ 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 4 159 * @throws MathIllegalArgumentException if the input array is null or the array 160 * index parameters are not valid 161 */ 162 @Override 163 public double evaluate(final double[] values,final int begin, final int length) 164 throws MathIllegalArgumentException { 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 202 public Kurtosis copy() { 203 Kurtosis result = new Kurtosis(); 204 // No try-catch because args are guaranteed non-null 205 copy(this, result); 206 return result; 207 } 208 209 /** 210 * Copies source to dest. 211 * <p>Neither source nor dest can be null.</p> 212 * 213 * @param source Kurtosis to copy 214 * @param dest Kurtosis to copy to 215 * @throws NullArgumentException if either source or dest is null 216 */ 217 public static void copy(Kurtosis source, Kurtosis dest) 218 throws NullArgumentException { 219 MathUtils.checkNotNull(source); 220 MathUtils.checkNotNull(dest); 221 dest.setData(source.getDataRef()); 222 dest.moment = source.moment.copy(); 223 dest.incMoment = source.incMoment; 224 } 225 226}