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/*
* Licensed to the Apache Software Foundation (ASF) under one or more
* contributor license agreements. See the NOTICE file distributed with
* this work for additional information regarding copyright ownership.
* The ASF licenses this file to You under the Apache License, Version 2.0
* (the "License"); you may not use this file except in compliance with
* the License. You may obtain a copy of the License at
*
* http://www.apache.org/licenses/LICENSE-2.0
*
* Unless required by applicable law or agreed to in writing, software
* distributed under the License is distributed on an "AS IS" BASIS,
* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
* See the License for the specific language governing permissions and
* limitations under the License.
*/
package org.apache.commons.math.stat.descriptive.moment;
import java.io.Serializable;
/**
* Computes a statistic related to the Fourth Central Moment. Specifically,
* what is computed is the sum of
* <p>
* (x_i - xbar) ^ 4, </p>
* <p>
* where the x_i are the
* sample observations and xbar is the sample mean. </p>
* <p>
* The following recursive updating formula is used: </p>
* <p>
* Let <ul>
* <li> dev = (current obs - previous mean) </li>
* <li> m2 = previous value of {@link SecondMoment} </li>
* <li> m2 = previous value of {@link ThirdMoment} </li>
* <li> n = number of observations (including current obs) </li>
* </ul>
* Then </p>
* <p>
* new value = old value - 4 * (dev/n) * m3 + 6 * (dev/n)^2 * m2 + <br>
* [n^2 - 3 * (n-1)] * dev^4 * (n-1) / n^3 </p>
* <p>
* Returns <code>Double.NaN</code> if no data values have been added and
* returns <code>0</code> if there is just one value in the data set. </p>
* <p>
* <strong>Note that this implementation is not synchronized.</strong> If
* multiple threads access an instance of this class concurrently, and at least
* one of the threads invokes the <code>increment()</code> or
* <code>clear()</code> method, it must be synchronized externally. </p>
*
* @version $Revision: 811685 $ $Date: 2009-09-05 19:36:48 +0200 (sam. 05 sept. 2009) $
*/
public class FourthMoment extends ThirdMoment implements Serializable{
/** Serializable version identifier */
private static final long serialVersionUID = 4763990447117157611L;
/** fourth moment of values that have been added */
protected double m4;
/**
* Create a FourthMoment instance
*/
public FourthMoment() {
super();
m4 = Double.NaN;
}
/**
* Copy constructor, creates a new {@code FourthMoment} identical
* to the {@code original}
*
* @param original the {@code FourthMoment} instance to copy
*/
public FourthMoment(FourthMoment original) {
super();
copy(original, this);
}
/**
* {@inheritDoc}
*/
@Override
public void increment(final double d) {
if (n < 1) {
m4 = 0.0;
m3 = 0.0;
m2 = 0.0;
m1 = 0.0;
}
double prevM3 = m3;
double prevM2 = m2;
super.increment(d);
double n0 = n;
m4 = m4 - 4.0 * nDev * prevM3 + 6.0 * nDevSq * prevM2 +
((n0 * n0) - 3 * (n0 -1)) * (nDevSq * nDevSq * (n0 - 1) * n0);
}
/**
* {@inheritDoc}
*/
@Override
public double getResult() {
return m4;
}
/**
* {@inheritDoc}
*/
@Override
public void clear() {
super.clear();
m4 = Double.NaN;
}
/**
* {@inheritDoc}
*/
@Override
public FourthMoment copy() {
FourthMoment result = new FourthMoment();
copy(this, result);
return result;
}
/**
* Copies source to dest.
* <p>Neither source nor dest can be null.</p>
*
* @param source FourthMoment to copy
* @param dest FourthMoment to copy to
* @throws NullPointerException if either source or dest is null
*/
public static void copy(FourthMoment source, FourthMoment dest) {
ThirdMoment.copy(source, dest);
dest.m4 = source.m4;
}
}
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