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 }