src/main/java/org/apache/commons/math/stat/descriptive/moment/FourthMoment.java

/*
 * 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;
    }
}