1 /* 2 * Copyright 2003-2004 The Apache Software Foundation. 3 * 4 * Licensed under the Apache License, Version 2.0 (the "License"); 5 * you may not use this file except in compliance with the License. 6 * You may obtain a copy of the License at 7 * 8 * http://www.apache.org/licenses/LICENSE-2.0 9 * 10 * Unless required by applicable law or agreed to in writing, software 11 * distributed under the License is distributed on an "AS IS" BASIS, 12 * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. 13 * See the License for the specific language governing permissions and 14 * limitations under the License. 15 */ 16 package org.apache.commons.math.stat.descriptive.moment; 17 18 import org.apache.commons.math.stat.descriptive.AbstractStorelessUnivariateStatistic; 19 20 /** 21 * Computes the Kurtosis of the available values. 22 * <p> 23 * We use the following (unbiased) formula to define kurtosis: 24 * <p> 25 * 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)] 26 * <p> 27 * where n is the number of values, mean is the {@link Mean} and std is the 28 * {@link StandardDeviation} 29 * <p> 30 * Note that this statistic is undefined for n < 4. <code>Double.Nan</code> 31 * is returned when there is not sufficient data to compute the statistic. 32 * <p> 33 * <strong>Note that this implementation is not synchronized.</strong> If 34 * multiple threads access an instance of this class concurrently, and at least 35 * one of the threads invokes the <code>increment()</code> or 36 * <code>clear()</code> method, it must be synchronized externally. 37 * 38 * @version $Revision: 348519 $ $Date: 2005-11-23 12:12:18 -0700 (Wed, 23 Nov 2005) $ 39 */ 40 public class Kurtosis extends AbstractStorelessUnivariateStatistic { 41 42 /** Serializable version identifier */ 43 private static final long serialVersionUID = 2784465764798260919L; 44 45 /**Fourth Moment on which this statistic is based */ 46 protected FourthMoment moment; 47 48 /** 49 * Determines whether or not this statistic can be incremented or cleared. 50 * <p> 51 * Statistics based on (constructed from) external moments cannot 52 * be incremented or cleared. 53 */ 54 protected boolean incMoment; 55 56 /** 57 * Construct a Kurtosis 58 */ 59 public Kurtosis() { 60 incMoment = true; 61 moment = new FourthMoment(); 62 } 63 64 /** 65 * Construct a Kurtosis from an external moment 66 * 67 * @param m4 external Moment 68 */ 69 public Kurtosis(final FourthMoment m4) { 70 incMoment = false; 71 this.moment = m4; 72 } 73 74 /** 75 * @see org.apache.commons.math.stat.descriptive.StorelessUnivariateStatistic#increment(double) 76 */ 77 public void increment(final double d) { 78 if (incMoment) { 79 moment.increment(d); 80 } else { 81 throw new IllegalStateException 82 ("Statistics constructed from external moments cannot be incremented"); 83 } 84 } 85 86 /** 87 * @see org.apache.commons.math.stat.descriptive.StorelessUnivariateStatistic#getResult() 88 */ 89 public double getResult() { 90 double kurtosis = Double.NaN; 91 if (moment.getN() > 3) { 92 double variance = moment.m2 / (double) (moment.n - 1); 93 if (moment.n <= 3 || variance < 10E-20) { 94 kurtosis = 0.0; 95 } else { 96 double n = (double) moment.n; 97 kurtosis = 98 (n * (n + 1) * moment.m4 - 99 3 * moment.m2 * moment.m2 * (n - 1)) / 100 ((n - 1) * (n -2) * (n -3) * variance * variance); 101 } 102 } 103 return kurtosis; 104 } 105 106 /** 107 * @see org.apache.commons.math.stat.descriptive.StorelessUnivariateStatistic#clear() 108 */ 109 public void clear() { 110 if (incMoment) { 111 moment.clear(); 112 } else { 113 throw new IllegalStateException 114 ("Statistics constructed from external moments cannot be cleared"); 115 } 116 } 117 118 /** 119 * @see org.apache.commons.math.stat.descriptive.StorelessUnivariateStatistic#getN() 120 */ 121 public long getN() { 122 return moment.getN(); 123 } 124 125 /* UnvariateStatistic Approach */ 126 127 /** 128 * Returns the kurtosis of the entries in the specified portion of the 129 * input array. 130 * <p> 131 * See {@link Kurtosis} for details on the computing algorithm. 132 * <p> 133 * Throws <code>IllegalArgumentException</code> if the array is null. 134 * 135 * @param values the input array 136 * @param begin index of the first array element to include 137 * @param length the number of elements to include 138 * @return the kurtosis of the values or Double.NaN if length is less than 139 * 4 140 * @throws IllegalArgumentException if the input array is null or the array 141 * index parameters are not valid 142 */ 143 public double evaluate(final double[] values,final int begin, final int length) { 144 // Initialize the kurtosis 145 double kurt = Double.NaN; 146 147 if (test(values, begin, length) && length > 3) { 148 149 // Compute the mean and standard deviation 150 Variance variance = new Variance(); 151 variance.incrementAll(values, begin, length); 152 double mean = variance.moment.m1; 153 double stdDev = Math.sqrt(variance.getResult()); 154 155 // Sum the ^4 of the distance from the mean divided by the 156 // standard deviation 157 double accum3 = 0.0; 158 for (int i = begin; i < begin + length; i++) { 159 accum3 += Math.pow((values[i] - mean), 4.0); 160 } 161 accum3 /= Math.pow(stdDev, 4.0d); 162 163 // Get N 164 double n0 = length; 165 166 double coefficientOne = 167 (n0 * (n0 + 1)) / ((n0 - 1) * (n0 - 2) * (n0 - 3)); 168 double termTwo = 169 ((3 * Math.pow(n0 - 1, 2.0)) / ((n0 - 2) * (n0 - 3))); 170 171 // Calculate kurtosis 172 kurt = (coefficientOne * accum3) - termTwo; 173 } 174 return kurt; 175 } 176 177 }