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: 617953 $ $Date: 2008-02-02 22:54:00 -0700 (Sat, 02 Feb 2008) $
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 * @see org.apache.commons.math.stat.descriptive.StorelessUnivariateStatistic#increment(double)
75 */
76 public void increment(final double d) {
77 if (incMoment) {
78 moment.increment(d);
79 }
80 }
81
82 /**
83 * Returns the value of the statistic based on the values that have been added.
84 * <p>
85 * See {@link Skewness} for the definition used in the computation.</p>
86 *
87 * @return the skewness of the available values.
88 */
89 public double getResult() {
90
91 if (moment.n < 3) {
92 return Double.NaN;
93 }
94 double variance = moment.m2 / (double) (moment.n - 1);
95 if (variance < 10E-20) {
96 return 0.0d;
97 } else {
98 double n0 = (double) moment.getN();
99 return (n0 * moment.m3) /
100 ((n0 - 1) * (n0 -2) * Math.sqrt(variance) * variance);
101 }
102 }
103
104 /**
105 * @see org.apache.commons.math.stat.descriptive.StorelessUnivariateStatistic#getN()
106 */
107 public long getN() {
108 return moment.getN();
109 }
110
111 /**
112 * @see org.apache.commons.math.stat.descriptive.StorelessUnivariateStatistic#clear()
113 */
114 public void clear() {
115 if (incMoment) {
116 moment.clear();
117 }
118 }
119
120 /**
121 * Returns the Skewness of the entries in the specifed portion of the
122 * input array.
123 * <p>
124 * See {@link Skewness} for the definition used in the computation.</p>
125 * <p>
126 * Throws <code>IllegalArgumentException</code> if the array is null.</p>
127 *
128 * @param values the input array
129 * @param begin the index of the first array element to include
130 * @param length the number of elements to include
131 * @return the skewness of the values or Double.NaN if length is less than
132 * 3
133 * @throws IllegalArgumentException if the array is null or the array index
134 * parameters are not valid
135 */
136 public double evaluate(final double[] values,final int begin,
137 final int length) {
138
139 // Initialize the skewness
140 double skew = Double.NaN;
141
142 if (test(values, begin, length) && length > 2 ){
143 Mean mean = new Mean();
144 // Get the mean and the standard deviation
145 double m = mean.evaluate(values, begin, length);
146
147 // Calc the std, this is implemented here instead
148 // of using the standardDeviation method eliminate
149 // a duplicate pass to get the mean
150 double accum = 0.0;
151 double accum2 = 0.0;
152 for (int i = begin; i < begin + length; i++) {
153 accum += Math.pow((values[i] - m), 2.0);
154 accum2 += (values[i] - m);
155 }
156 double stdDev = Math.sqrt((accum - (Math.pow(accum2, 2) / ((double) length))) /
157 (double) (length - 1));
158
159 double accum3 = 0.0;
160 for (int i = begin; i < begin + length; i++) {
161 accum3 += Math.pow(values[i] - m, 3.0d);
162 }
163 accum3 /= Math.pow(stdDev, 3.0d);
164
165 // Get N
166 double n0 = length;
167
168 // Calculate skewness
169 skew = (n0 / ((n0 - 1) * (n0 - 2))) * accum3;
170 }
171 return skew;
172 }
173 }