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 /**
022 * Computes a statistic related to the Fourth Central Moment. Specifically,
023 * what is computed is the sum of
024 * <p>
025 * (x_i - xbar) ^ 4, </p>
026 * <p>
027 * where the x_i are the
028 * sample observations and xbar is the sample mean. </p>
029 * <p>
030 * The following recursive updating formula is used: </p>
031 * <p>
032 * Let <ul>
033 * <li> dev = (current obs - previous mean) </li>
034 * <li> m2 = previous value of {@link SecondMoment} </li>
035 * <li> m2 = previous value of {@link ThirdMoment} </li>
036 * <li> n = number of observations (including current obs) </li>
037 * </ul>
038 * Then </p>
039 * <p>
040 * new value = old value - 4 * (dev/n) * m3 + 6 * (dev/n)^2 * m2 + <br>
041 * [n^2 - 3 * (n-1)] * dev^4 * (n-1) / n^3 </p>
042 * <p>
043 * Returns <code>Double.NaN</code> if no data values have been added and
044 * returns <code>0</code> if there is just one value in the data set. </p>
045 * <p>
046 * <strong>Note that this implementation is not synchronized.</strong> If
047 * multiple threads access an instance of this class concurrently, and at least
048 * one of the threads invokes the <code>increment()</code> or
049 * <code>clear()</code> method, it must be synchronized externally. </p>
050 *
051 * @version $Revision: 811685 $ $Date: 2009-09-05 13:36:48 -0400 (Sat, 05 Sep 2009) $
052 */
053 public class FourthMoment extends ThirdMoment implements Serializable{
054
055 /** Serializable version identifier */
056 private static final long serialVersionUID = 4763990447117157611L;
057
058 /** fourth moment of values that have been added */
059 protected double m4;
060
061 /**
062 * Create a FourthMoment instance
063 */
064 public FourthMoment() {
065 super();
066 m4 = Double.NaN;
067 }
068
069 /**
070 * Copy constructor, creates a new {@code FourthMoment} identical
071 * to the {@code original}
072 *
073 * @param original the {@code FourthMoment} instance to copy
074 */
075 public FourthMoment(FourthMoment original) {
076 super();
077 copy(original, this);
078 }
079
080 /**
081 * {@inheritDoc}
082 */
083 @Override
084 public void increment(final double d) {
085 if (n < 1) {
086 m4 = 0.0;
087 m3 = 0.0;
088 m2 = 0.0;
089 m1 = 0.0;
090 }
091
092 double prevM3 = m3;
093 double prevM2 = m2;
094
095 super.increment(d);
096
097 double n0 = n;
098
099 m4 = m4 - 4.0 * nDev * prevM3 + 6.0 * nDevSq * prevM2 +
100 ((n0 * n0) - 3 * (n0 -1)) * (nDevSq * nDevSq * (n0 - 1) * n0);
101 }
102
103 /**
104 * {@inheritDoc}
105 */
106 @Override
107 public double getResult() {
108 return m4;
109 }
110
111 /**
112 * {@inheritDoc}
113 */
114 @Override
115 public void clear() {
116 super.clear();
117 m4 = Double.NaN;
118 }
119
120 /**
121 * {@inheritDoc}
122 */
123 @Override
124 public FourthMoment copy() {
125 FourthMoment result = new FourthMoment();
126 copy(this, result);
127 return result;
128 }
129
130 /**
131 * Copies source to dest.
132 * <p>Neither source nor dest can be null.</p>
133 *
134 * @param source FourthMoment to copy
135 * @param dest FourthMoment to copy to
136 * @throws NullPointerException if either source or dest is null
137 */
138 public static void copy(FourthMoment source, FourthMoment dest) {
139 ThirdMoment.copy(source, dest);
140 dest.m4 = source.m4;
141 }
142 }