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.exception.NullArgumentException;
022 import org.apache.commons.math.stat.descriptive.AbstractStorelessUnivariateStatistic;
023 import org.apache.commons.math.util.FastMath;
024 import org.apache.commons.math.util.MathUtils;
025
026 /**
027 * Computes the skewness of the available values.
028 * <p>
029 * We use the following (unbiased) formula to define skewness:</p>
030 * <p>
031 * skewness = [n / (n -1) (n - 2)] sum[(x_i - mean)^3] / std^3 </p>
032 * <p>
033 * where n is the number of values, mean is the {@link Mean} and std is the
034 * {@link StandardDeviation} </p>
035 * <p>
036 * <strong>Note that this implementation is not synchronized.</strong> If
037 * multiple threads access an instance of this class concurrently, and at least
038 * one of the threads invokes the <code>increment()</code> or
039 * <code>clear()</code> method, it must be synchronized externally. </p>
040 *
041 * @version $Id: Skewness.java 1132432 2011-06-05 14:59:29Z luc $
042 */
043 public class Skewness extends AbstractStorelessUnivariateStatistic implements Serializable {
044
045 /** Serializable version identifier */
046 private static final long serialVersionUID = 7101857578996691352L;
047
048 /** Third moment on which this statistic is based */
049 protected ThirdMoment moment = null;
050
051 /**
052 * Determines whether or not this statistic can be incremented or cleared.
053 * <p>
054 * Statistics based on (constructed from) external moments cannot
055 * be incremented or cleared.</p>
056 */
057 protected boolean incMoment;
058
059 /**
060 * Constructs a Skewness
061 */
062 public Skewness() {
063 incMoment = true;
064 moment = new ThirdMoment();
065 }
066
067 /**
068 * Constructs a Skewness with an external moment
069 * @param m3 external moment
070 */
071 public Skewness(final ThirdMoment m3) {
072 incMoment = false;
073 this.moment = m3;
074 }
075
076 /**
077 * Copy constructor, creates a new {@code Skewness} identical
078 * to the {@code original}
079 *
080 * @param original the {@code Skewness} instance to copy
081 */
082 public Skewness(Skewness original) {
083 copy(original, this);
084 }
085
086 /**
087 * {@inheritDoc}
088 */
089 @Override
090 public void increment(final double d) {
091 if (incMoment) {
092 moment.increment(d);
093 }
094 }
095
096 /**
097 * Returns the value of the statistic based on the values that have been added.
098 * <p>
099 * See {@link Skewness} for the definition used in the computation.</p>
100 *
101 * @return the skewness of the available values.
102 */
103 @Override
104 public double getResult() {
105
106 if (moment.n < 3) {
107 return Double.NaN;
108 }
109 double variance = moment.m2 / (moment.n - 1);
110 if (variance < 10E-20) {
111 return 0.0d;
112 } else {
113 double n0 = moment.getN();
114 return (n0 * moment.m3) /
115 ((n0 - 1) * (n0 -2) * FastMath.sqrt(variance) * variance);
116 }
117 }
118
119 /**
120 * {@inheritDoc}
121 */
122 public long getN() {
123 return moment.getN();
124 }
125
126 /**
127 * {@inheritDoc}
128 */
129 @Override
130 public void clear() {
131 if (incMoment) {
132 moment.clear();
133 }
134 }
135
136 /**
137 * Returns the Skewness of the entries in the specifed portion of the
138 * input array.
139 * <p>
140 * See {@link Skewness} for the definition used in the computation.</p>
141 * <p>
142 * Throws <code>IllegalArgumentException</code> if the array is null.</p>
143 *
144 * @param values the input array
145 * @param begin the index of the first array element to include
146 * @param length the number of elements to include
147 * @return the skewness of the values or Double.NaN if length is less than
148 * 3
149 * @throws IllegalArgumentException if the array is null or the array index
150 * parameters are not valid
151 */
152 @Override
153 public double evaluate(final double[] values,final int begin,
154 final int length) {
155
156 // Initialize the skewness
157 double skew = Double.NaN;
158
159 if (test(values, begin, length) && length > 2 ){
160 Mean mean = new Mean();
161 // Get the mean and the standard deviation
162 double m = mean.evaluate(values, begin, length);
163
164 // Calc the std, this is implemented here instead
165 // of using the standardDeviation method eliminate
166 // a duplicate pass to get the mean
167 double accum = 0.0;
168 double accum2 = 0.0;
169 for (int i = begin; i < begin + length; i++) {
170 final double d = values[i] - m;
171 accum += d * d;
172 accum2 += d;
173 }
174 final double variance = (accum - (accum2 * accum2 / length)) / (length - 1);
175
176 double accum3 = 0.0;
177 for (int i = begin; i < begin + length; i++) {
178 final double d = values[i] - m;
179 accum3 += d * d * d;
180 }
181 accum3 /= variance * FastMath.sqrt(variance);
182
183 // Get N
184 double n0 = length;
185
186 // Calculate skewness
187 skew = (n0 / ((n0 - 1) * (n0 - 2))) * accum3;
188 }
189 return skew;
190 }
191
192 /**
193 * {@inheritDoc}
194 */
195 @Override
196 public Skewness copy() {
197 Skewness result = new Skewness();
198 copy(this, result);
199 return result;
200 }
201
202 /**
203 * Copies source to dest.
204 * <p>Neither source nor dest can be null.</p>
205 *
206 * @param source Skewness to copy
207 * @param dest Skewness to copy to
208 * @throws NullArgumentException if either source or dest is null
209 */
210 public static void copy(Skewness source, Skewness dest)
211 throws NullArgumentException {
212 MathUtils.checkNotNull(source);
213 MathUtils.checkNotNull(dest);
214 dest.setData(source.getDataRef());
215 dest.moment = new ThirdMoment(source.moment.copy());
216 dest.incMoment = source.incMoment;
217 }
218 }