/*
 * 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.math3.stat.descriptive.moment;

import java.io.Serializable;

import org.apache.commons.math3.exception.NullArgumentException;
import org.apache.commons.math3.util.MathUtils;

Computes a statistic related to the Fourth Central Moment.  Specifically,
what is computed is the sum of

(x_i - xbar) ^ 4, 

where the x_i are the
sample observations and xbar is the sample mean. 

The following recursive updating formula is used: 

Let 

 dev = (current obs - previous mean) 
 m2 = previous value of SecondMoment 
 m2 = previous value of ThirdMoment 
 n = number of observations (including current obs) 

Then 


new value = old value - 4 * (dev/n) * m3 + 6 * (dev/n)^2 * m2 + 

[n^2 - 3 * (n-1)] * dev^4 * (n-1) / n^3 

Returns Double.NaN if no data values have been added and
returns 0 if there is just one value in the data set. Note that
Double.NaN may also be returned if the input includes NaN and / or infinite
values. 

Note that this implementation is not synchronized. If
multiple threads access an instance of this class concurrently, and at least
one of the threads invokes the increment() or
clear() method, it must be synchronized externally. 
/**
 * 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. Note that
 * Double.NaN may also be returned if the input includes NaN and / or infinite
 * values. </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>
 *
 */
class FourthMoment extends ThirdMoment implements Serializable{

    
Serializable version identifier /** Serializable version identifier */
    private static final long serialVersionUID = 4763990447117157611L;

    
fourth moment of values that have been added /** fourth moment of values that have been added */
    private double m4;

    
Create a FourthMoment instance
/**
     * Create a FourthMoment instance
     */
    FourthMoment() {
        super();
        m4 = Double.NaN;
    }

    
Copy constructor, creates a new FourthMoment identical to the original 
Params:
original – the FourthMoment instance to copy
Throws:
NullArgumentException – if original is null/**
     * Copy constructor, creates a new {@code FourthMoment} identical
     * to the {@code original}
     *
     * @param original the {@code FourthMoment} instance to copy
     * @throws NullArgumentException if original is null
     */
     FourthMoment(FourthMoment original) throws NullArgumentException {
         super();
         copy(original, this);
     }

    
{@inheritDoc}
/**
     * {@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}
/**
     * {@inheritDoc}
     */
    @Override
    public double getResult() {
        return m4;
    }

    
{@inheritDoc}
/**
     * {@inheritDoc}
     */
    @Override
    public void clear() {
        super.clear();
        m4 = Double.NaN;
    }

    
{@inheritDoc}
/**
     * {@inheritDoc}
     */
    @Override
    public FourthMoment copy() {
        FourthMoment result = new FourthMoment();
        // No try-catch or advertised exception because args are guaranteed non-null
        copy(this, result);
        return result;
    }

    
Copies source to dest.
Neither source nor dest can be null.
Params:
source – FourthMoment to copy
dest – FourthMoment to copy to
Throws:
NullArgumentException – if either source or dest is null/**
     * 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 NullArgumentException if either source or dest is null
     */
    public static void copy(FourthMoment source, FourthMoment dest)
        throws NullArgumentException {
        MathUtils.checkNotNull(source);
        MathUtils.checkNotNull(dest);
        ThirdMoment.copy(source, dest);
        dest.m4 = source.m4;
    }
}