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.math.stat.descriptive.moment; 018 019 import java.io.Serializable; 020 021 import org.apache.commons.math.stat.descriptive.AbstractStorelessUnivariateStatistic; 022 023 /** 024 * Computes the skewness of the available values. 025 * <p> 026 * We use the following (unbiased) formula to define skewness:</p> 027 * <p> 028 * skewness = [n / (n -1) (n - 2)] sum[(x_i - mean)^3] / std^3 </p> 029 * <p> 030 * where n is the number of values, mean is the {@link Mean} and std is the 031 * {@link StandardDeviation} </p> 032 * <p> 033 * <strong>Note that this implementation is not synchronized.</strong> If 034 * multiple threads access an instance of this class concurrently, and at least 035 * one of the threads invokes the <code>increment()</code> or 036 * <code>clear()</code> method, it must be synchronized externally. </p> 037 * 038 * @version $Revision: 764209 $ $Date: 2009-04-11 11:32:18 -0400 (Sat, 11 Apr 2009) $ 039 */ 040 public class Skewness extends AbstractStorelessUnivariateStatistic implements Serializable { 041 042 /** Serializable version identifier */ 043 private static final long serialVersionUID = 7101857578996691352L; 044 045 /** Third moment on which this statistic is based */ 046 protected ThirdMoment moment = null; 047 048 /** 049 * Determines whether or not this statistic can be incremented or cleared. 050 * <p> 051 * Statistics based on (constructed from) external moments cannot 052 * be incremented or cleared.</p> 053 */ 054 protected boolean incMoment; 055 056 /** 057 * Constructs a Skewness 058 */ 059 public Skewness() { 060 incMoment = true; 061 moment = new ThirdMoment(); 062 } 063 064 /** 065 * Constructs a Skewness with an external moment 066 * @param m3 external moment 067 */ 068 public Skewness(final ThirdMoment m3) { 069 incMoment = false; 070 this.moment = m3; 071 } 072 073 /** 074 * Copy constructor, creates a new {@code Skewness} identical 075 * to the {@code original} 076 * 077 * @param original the {@code Skewness} instance to copy 078 */ 079 public Skewness(Skewness original) { 080 copy(original, this); 081 } 082 083 /** 084 * {@inheritDoc} 085 */ 086 @Override 087 public void increment(final double d) { 088 if (incMoment) { 089 moment.increment(d); 090 } 091 } 092 093 /** 094 * Returns the value of the statistic based on the values that have been added. 095 * <p> 096 * See {@link Skewness} for the definition used in the computation.</p> 097 * 098 * @return the skewness of the available values. 099 */ 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 }