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 java.io.Serializable; 20 21 import org.apache.commons.math.stat.descriptive.AbstractStorelessUnivariateStatistic; 22 23 /** 24 * Computes the skewness of the available values. 25 * <p> 26 * We use the following (unbiased) formula to define skewness:</p> 27 * <p> 28 * skewness = [n / (n -1) (n - 2)] sum[(x_i - mean)^3] / std^3 </p> 29 * <p> 30 * where n is the number of values, mean is the {@link Mean} and std is the 31 * {@link StandardDeviation} </p> 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. </p> 37 * 38 * @version $Revision: 764209 $ $Date: 2009-04-11 11:32:18 -0400 (Sat, 11 Apr 2009) $ 39 */ 40 public class Skewness extends AbstractStorelessUnivariateStatistic implements Serializable { 41 42 /** Serializable version identifier */ 43 private static final long serialVersionUID = 7101857578996691352L; 44 45 /** Third moment on which this statistic is based */ 46 protected ThirdMoment moment = null; 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.</p> 53 */ 54 protected boolean incMoment; 55 56 /** 57 * Constructs a Skewness 58 */ 59 public Skewness() { 60 incMoment = true; 61 moment = new ThirdMoment(); 62 } 63 64 /** 65 * Constructs a Skewness with an external moment 66 * @param m3 external moment 67 */ 68 public Skewness(final ThirdMoment m3) { 69 incMoment = false; 70 this.moment = m3; 71 } 72 73 /** 74 * Copy constructor, creates a new {@code Skewness} identical 75 * to the {@code original} 76 * 77 * @param original the {@code Skewness} instance to copy 78 */ 79 public Skewness(Skewness original) { 80 copy(original, this); 81 } 82 83 /** 84 * {@inheritDoc} 85 */ 86 @Override 87 public void increment(final double d) { 88 if (incMoment) { 89 moment.increment(d); 90 } 91 } 92 93 /** 94 * Returns the value of the statistic based on the values that have been added. 95 * <p> 96 * See {@link Skewness} for the definition used in the computation.</p> 97 * 98 * @return the skewness of the available values. 99 */ 100 @Override 101 public double getResult() { 102 103 if (moment.n < 3) { 104 return Double.NaN; 105 } 106 double variance = moment.m2 / (moment.n - 1); 107 if (variance < 10E-20) { 108 return 0.0d; 109 } else { 110 double n0 = moment.getN(); 111 return (n0 * moment.m3) / 112 ((n0 - 1) * (n0 -2) * Math.sqrt(variance) * variance); 113 } 114 } 115 116 /** 117 * {@inheritDoc} 118 */ 119 public long getN() { 120 return moment.getN(); 121 } 122 123 /** 124 * {@inheritDoc} 125 */ 126 @Override 127 public void clear() { 128 if (incMoment) { 129 moment.clear(); 130 } 131 } 132 133 /** 134 * Returns the Skewness of the entries in the specifed portion of the 135 * input array. 136 * <p> 137 * See {@link Skewness} for the definition used in the computation.</p> 138 * <p> 139 * Throws <code>IllegalArgumentException</code> if the array is null.</p> 140 * 141 * @param values the input array 142 * @param begin the index of the first array element to include 143 * @param length the number of elements to include 144 * @return the skewness of the values or Double.NaN if length is less than 145 * 3 146 * @throws IllegalArgumentException if the array is null or the array index 147 * parameters are not valid 148 */ 149 @Override 150 public double evaluate(final double[] values,final int begin, 151 final int length) { 152 153 // Initialize the skewness 154 double skew = Double.NaN; 155 156 if (test(values, begin, length) && length > 2 ){ 157 Mean mean = new Mean(); 158 // Get the mean and the standard deviation 159 double m = mean.evaluate(values, begin, length); 160 161 // Calc the std, this is implemented here instead 162 // of using the standardDeviation method eliminate 163 // a duplicate pass to get the mean 164 double accum = 0.0; 165 double accum2 = 0.0; 166 for (int i = begin; i < begin + length; i++) { 167 accum += Math.pow((values[i] - m), 2.0); 168 accum2 += (values[i] - m); 169 } 170 double stdDev = Math.sqrt((accum - (Math.pow(accum2, 2) / length)) / 171 (length - 1)); 172 173 double accum3 = 0.0; 174 for (int i = begin; i < begin + length; i++) { 175 accum3 += Math.pow(values[i] - m, 3.0d); 176 } 177 accum3 /= Math.pow(stdDev, 3.0d); 178 179 // Get N 180 double n0 = length; 181 182 // Calculate skewness 183 skew = (n0 / ((n0 - 1) * (n0 - 2))) * accum3; 184 } 185 return skew; 186 } 187 188 /** 189 * {@inheritDoc} 190 */ 191 @Override 192 public Skewness copy() { 193 Skewness result = new Skewness(); 194 copy(this, result); 195 return result; 196 } 197 198 /** 199 * Copies source to dest. 200 * <p>Neither source nor dest can be null.</p> 201 * 202 * @param source Skewness to copy 203 * @param dest Skewness to copy to 204 * @throws NullPointerException if either source or dest is null 205 */ 206 public static void copy(Skewness source, Skewness dest) { 207 dest.moment = new ThirdMoment(source.moment.copy()); 208 dest.incMoment = source.incMoment; 209 } 210 }