fourthmoment.java

Apache的common math数学软件包

/*
 * 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: 617953 $ $Date: 2008-02-02 22:54:00 -0700 (Sat, 02 Feb 2008) $
 */
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;
    }
    
    /**
     * @see org.apache.commons.math.stat.descriptive.StorelessUnivariateStatistic#increment(double)
     */
    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 = (double) n;

        m4 = m4 - 4.0 * nDev * prevM3 + 6.0 * nDevSq * prevM2 +
            ((n0 * n0) - 3 * (n0 -1)) * (nDevSq * nDevSq * (n0 - 1) * n0);
    }

    /**
     * @see org.apache.commons.math.stat.descriptive.StorelessUnivariateStatistic#getResult()
     */
    public double getResult() {
        return m4;
    }

    /**
     * @see org.apache.commons.math.stat.descriptive.StorelessUnivariateStatistic#clear()
     */
    public void clear() {
        super.clear();
        m4 = Double.NaN;
    }

}