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.math4.legacy.stat.descriptive.moment; 018 019import org.apache.commons.math4.legacy.exception.MathIllegalArgumentException; 020import org.apache.commons.math4.legacy.exception.NullArgumentException; 021import org.apache.commons.math4.legacy.stat.descriptive.AbstractStorelessUnivariateStatistic; 022import org.apache.commons.math4.core.jdkmath.JdkMath; 023import org.apache.commons.math4.legacy.core.MathArrays; 024 025/** 026 * Computes the skewness of the available values. 027 * <p> 028 * We use the following (unbiased) formula to define skewness:</p> 029 * <p> 030 * skewness = [n / (n -1) (n - 2)] sum[(x_i - mean)^3] / std^3 </p> 031 * <p> 032 * where n is the number of values, mean is the {@link Mean} and std is the 033 * {@link StandardDeviation} </p> 034 * <p> 035 * Note that this statistic is undefined for {@code n < 3}. <code>Double.Nan</code> 036 * is returned when there is not sufficient data to compute the statistic. 037 * Double.NaN may also be returned if the input includes NaN and / or 038 * infinite values.</p> 039 * <p> 040 * <strong>Note that this implementation is not synchronized.</strong> If 041 * multiple threads access an instance of this class concurrently, and at least 042 * one of the threads invokes the <code>increment()</code> or 043 * <code>clear()</code> method, it must be synchronized externally. </p> 044 */ 045public class Skewness extends AbstractStorelessUnivariateStatistic { 046 /** The value below which the variance is considered zero and thus skewness is zero. */ 047 private static final double ZERO_VARIANCE_THRESHOLD = 10E-20; 048 049 /** Third moment on which this statistic is based. */ 050 protected ThirdMoment moment; 051 052 /** 053 * Determines whether or not this statistic can be incremented or cleared. 054 * <p> 055 * Statistics based on (constructed from) external moments cannot 056 * be incremented or cleared.</p> 057 */ 058 protected boolean incMoment; 059 060 /** 061 * Constructs a Skewness. 062 */ 063 public Skewness() { 064 incMoment = true; 065 moment = new ThirdMoment(); 066 } 067 068 /** 069 * Constructs a Skewness with an external moment. 070 * @param m3 external moment 071 */ 072 public Skewness(final ThirdMoment m3) { 073 incMoment = false; 074 this.moment = m3; 075 } 076 077 /** 078 * Copy constructor, creates a new {@code Skewness} identical 079 * to the {@code original}. 080 * 081 * @param original the {@code Skewness} instance to copy 082 * @throws NullArgumentException if original is null 083 */ 084 public Skewness(Skewness original) throws NullArgumentException { 085 copy(original, this); 086 } 087 088 /** 089 * {@inheritDoc} 090 * <p>Note that when {@link #Skewness(ThirdMoment)} is used to 091 * create a Skewness, this method does nothing. In that case, the 092 * ThirdMoment should be incremented directly.</p> 093 */ 094 @Override 095 public void increment(final double d) { 096 if (incMoment) { 097 moment.increment(d); 098 } 099 } 100 101 /** 102 * Returns the value of the statistic based on the values that have been added. 103 * <p> 104 * See {@link Skewness} for the definition used in the computation.</p> 105 * 106 * @return the skewness of the available values. 107 */ 108 @Override 109 public double getResult() { 110 111 if (moment.n < 3) { 112 return Double.NaN; 113 } 114 double variance = moment.m2 / (moment.n - 1); 115 if (variance < ZERO_VARIANCE_THRESHOLD) { 116 return 0.0d; 117 } else { 118 double n0 = moment.getN(); 119 return (n0 * moment.m3) / 120 ((n0 - 1) * (n0 -2) * JdkMath.sqrt(variance) * variance); 121 } 122 } 123 124 /** 125 * {@inheritDoc} 126 */ 127 @Override 128 public long getN() { 129 return moment.getN(); 130 } 131 132 /** 133 * {@inheritDoc} 134 */ 135 @Override 136 public void clear() { 137 if (incMoment) { 138 moment.clear(); 139 } 140 } 141 142 /** 143 * Returns the Skewness of the entries in the specified portion of the 144 * input array. 145 * <p> 146 * See {@link Skewness} for the definition used in the computation.</p> 147 * <p> 148 * Throws <code>IllegalArgumentException</code> if the array is null.</p> 149 * 150 * @param values the input array 151 * @param begin the index of the first array element to include 152 * @param length the number of elements to include 153 * @return the skewness of the values or Double.NaN if length is less than 3 154 * @throws MathIllegalArgumentException if the array is null or the array index 155 * parameters are not valid 156 */ 157 @Override 158 public double evaluate(final double[] values,final int begin, final int length) 159 throws MathIllegalArgumentException { 160 161 // Initialize the skewness 162 double skew = Double.NaN; 163 164 if (MathArrays.verifyValues(values, begin, length) && length > 2 ) { 165 Mean mean = new Mean(); 166 // Get the mean and the standard deviation 167 double m = mean.evaluate(values, begin, length); 168 169 // Calc the std, this is implemented here instead 170 // of using the standardDeviation method eliminate 171 // a duplicate pass to get the mean 172 double accum = 0.0; 173 double accum2 = 0.0; 174 for (int i = begin; i < begin + length; i++) { 175 final double d = values[i] - m; 176 accum += d * d; 177 accum2 += d; 178 } 179 final double variance = (accum - (accum2 * accum2 / length)) / (length - 1); 180 if (variance < ZERO_VARIANCE_THRESHOLD) { 181 skew = 0.0d; 182 } else { 183 double accum3 = 0.0; 184 for (int i = begin; i < begin + length; i++) { 185 final double d = values[i] - m; 186 accum3 += d * d * d; 187 } 188 accum3 /= variance * JdkMath.sqrt(variance); 189 190 // Get N 191 double n0 = length; 192 193 // Calculate skewness 194 skew = (n0 / ((n0 - 1) * (n0 - 2))) * accum3; 195 } 196 } 197 return skew; 198 } 199 200 /** 201 * {@inheritDoc} 202 */ 203 @Override 204 public Skewness copy() { 205 Skewness result = new Skewness(); 206 // No try-catch or advertised exception because args are guaranteed non-null 207 copy(this, result); 208 return result; 209 } 210 211 /** 212 * Copies source to dest. 213 * <p>Neither source nor dest can be null.</p> 214 * 215 * @param source Skewness to copy 216 * @param dest Skewness to copy to 217 * @throws NullArgumentException if either source or dest is null 218 */ 219 public static void copy(Skewness source, Skewness dest) 220 throws NullArgumentException { 221 NullArgumentException.check(source); 222 NullArgumentException.check(dest); 223 dest.moment = new ThirdMoment(source.moment.copy()); 224 dest.incMoment = source.incMoment; 225 } 226}