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 org.apache.commons.math.stat.descriptive.AbstractStorelessUnivariateStatistic; 20 21 /** 22 * Computes the Kurtosis of the available values. 23 * <p> 24 * We use the following (unbiased) formula to define kurtosis:</p> 25 * <p> 26 * 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)] 27 * </p><p> 28 * where n is the number of values, mean is the {@link Mean} and std is the 29 * {@link StandardDeviation}</p> 30 * <p> 31 * Note that this statistic is undefined for n < 4. <code>Double.Nan</code> 32 * is returned when there is not sufficient data to compute the statistic.</p> 33 * <p> 34 * <strong>Note that this implementation is not synchronized.</strong> If 35 * multiple threads access an instance of this class concurrently, and at least 36 * one of the threads invokes the <code>increment()</code> or 37 * <code>clear()</code> method, it must be synchronized externally.</p> 38 * 39 * @version $Revision: 617953 $ $Date: 2008-02-02 22:54:00 -0700 (Sat, 02 Feb 2008) $ 40 */ 41 public class Kurtosis extends AbstractStorelessUnivariateStatistic { 42 43 /** Serializable version identifier */ 44 private static final long serialVersionUID = 2784465764798260919L; 45 46 /**Fourth Moment on which this statistic is based */ 47 protected FourthMoment moment; 48 49 /** 50 * Determines whether or not this statistic can be incremented or cleared. 51 * <p> 52 * Statistics based on (constructed from) external moments cannot 53 * be incremented or cleared.</p> 54 */ 55 protected boolean incMoment; 56 57 /** 58 * Construct a Kurtosis 59 */ 60 public Kurtosis() { 61 incMoment = true; 62 moment = new FourthMoment(); 63 } 64 65 /** 66 * Construct a Kurtosis from an external moment 67 * 68 * @param m4 external Moment 69 */ 70 public Kurtosis(final FourthMoment m4) { 71 incMoment = false; 72 this.moment = m4; 73 } 74 75 /** 76 * @see org.apache.commons.math.stat.descriptive.StorelessUnivariateStatistic#increment(double) 77 */ 78 public void increment(final double d) { 79 if (incMoment) { 80 moment.increment(d); 81 } else { 82 throw new IllegalStateException 83 ("Statistics constructed from external moments cannot be incremented"); 84 } 85 } 86 87 /** 88 * @see org.apache.commons.math.stat.descriptive.StorelessUnivariateStatistic#getResult() 89 */ 90 public double getResult() { 91 double kurtosis = Double.NaN; 92 if (moment.getN() > 3) { 93 double variance = moment.m2 / (double) (moment.n - 1); 94 if (moment.n <= 3 || variance < 10E-20) { 95 kurtosis = 0.0; 96 } else { 97 double n = (double) moment.n; 98 kurtosis = 99 (n * (n + 1) * moment.m4 - 100 3 * moment.m2 * moment.m2 * (n - 1)) / 101 ((n - 1) * (n -2) * (n -3) * variance * variance); 102 } 103 } 104 return kurtosis; 105 } 106 107 /** 108 * @see org.apache.commons.math.stat.descriptive.StorelessUnivariateStatistic#clear() 109 */ 110 public void clear() { 111 if (incMoment) { 112 moment.clear(); 113 } else { 114 throw new IllegalStateException 115 ("Statistics constructed from external moments cannot be cleared"); 116 } 117 } 118 119 /** 120 * @see org.apache.commons.math.stat.descriptive.StorelessUnivariateStatistic#getN() 121 */ 122 public long getN() { 123 return moment.getN(); 124 } 125 126 /* UnvariateStatistic Approach */ 127 128 /** 129 * Returns the kurtosis of the entries in the specified portion of the 130 * input array. 131 * <p> 132 * See {@link Kurtosis} for details on the computing algorithm.</p> 133 * <p> 134 * Throws <code>IllegalArgumentException</code> if the array is null.</p> 135 * 136 * @param values the input array 137 * @param begin index of the first array element to include 138 * @param length the number of elements to include 139 * @return the kurtosis of the values or Double.NaN if length is less than 140 * 4 141 * @throws IllegalArgumentException if the input array is null or the array 142 * index parameters are not valid 143 */ 144 public double evaluate(final double[] values,final int begin, final int length) { 145 // Initialize the kurtosis 146 double kurt = Double.NaN; 147 148 if (test(values, begin, length) && length > 3) { 149 150 // Compute the mean and standard deviation 151 Variance variance = new Variance(); 152 variance.incrementAll(values, begin, length); 153 double mean = variance.moment.m1; 154 double stdDev = Math.sqrt(variance.getResult()); 155 156 // Sum the ^4 of the distance from the mean divided by the 157 // standard deviation 158 double accum3 = 0.0; 159 for (int i = begin; i < begin + length; i++) { 160 accum3 += Math.pow((values[i] - mean), 4.0); 161 } 162 accum3 /= Math.pow(stdDev, 4.0d); 163 164 // Get N 165 double n0 = length; 166 167 double coefficientOne = 168 (n0 * (n0 + 1)) / ((n0 - 1) * (n0 - 2) * (n0 - 3)); 169 double termTwo = 170 ((3 * Math.pow(n0 - 1, 2.0)) / ((n0 - 2) * (n0 - 3))); 171 172 // Calculate kurtosis 173 kurt = (coefficientOne * accum3) - termTwo; 174 } 175 return kurt; 176 } 177 178 }