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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
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 * distributed under the License is distributed on an "AS IS" BASIS,
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package org.apache.commons.math3.stat.descriptive.moment;

import java.io.Serializable;

import org.apache.commons.math3.exception.MathIllegalArgumentException;
import org.apache.commons.math3.exception.NullArgumentException;
import org.apache.commons.math3.stat.descriptive.AbstractStorelessUnivariateStatistic;
import org.apache.commons.math3.util.FastMath;
import org.apache.commons.math3.util.MathUtils;

Computes the skewness of the available values.

We use the following (unbiased) formula to define skewness:

skewness = [n / (n -1) (n - 2)] sum[(x_i - mean)^3] / std^3 
 where n is the number of values, mean is the Mean and std is the StandardDeviation 

Note that this statistic is undefined for n < 3.  Double.Nan
is returned when there is not sufficient data to compute the statistic.
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 the skewness of the available values.
 * <p>
 * We use the following (unbiased) formula to define skewness:</p>
 * <p>
 * skewness = [n / (n -1) (n - 2)] sum[(x_i - mean)^3] / std^3 </p>
 * <p>
 * where n is the number of values, mean is the {@link Mean} and std is the
 * {@link StandardDeviation} </p>
 * <p>
 * Note that this statistic is undefined for n < 3.  <code>Double.Nan</code>
 * is returned when there is not sufficient data to compute the statistic.
 * 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>
 *
 */
public class Skewness extends AbstractStorelessUnivariateStatistic implements Serializable {

    
Serializable version identifier /** Serializable version identifier */
    private static final long serialVersionUID = 7101857578996691352L;

    
Third moment on which this statistic is based /** Third moment on which this statistic is based */
    protected ThirdMoment moment = null;

     
Determines whether or not this statistic can be incremented or cleared.

Statistics based on (constructed from) external moments cannot
be incremented or cleared.
/**
     * Determines whether or not this statistic can be incremented or cleared.
     * <p>
     * Statistics based on (constructed from) external moments cannot
     * be incremented or cleared.</p>
    */
    protected boolean incMoment;

    
Constructs a Skewness
/**
     * Constructs a Skewness
     */
    public Skewness() {
        incMoment = true;
        moment = new ThirdMoment();
    }

    
Constructs a Skewness with an external moment
Params:
m3 – external moment/**
     * Constructs a Skewness with an external moment
     * @param m3 external moment
     */
    public Skewness(final ThirdMoment m3) {
        incMoment = false;
        this.moment = m3;
    }

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

    
{@inheritDoc}
Note that when Skewness(ThirdMoment) is used to create a Skewness, this method does nothing. In that case, the ThirdMoment should be incremented directly.
/**
     * {@inheritDoc}
     * <p>Note that when {@link #Skewness(ThirdMoment)} is used to
     * create a Skewness, this method does nothing. In that case, the
     * ThirdMoment should be incremented directly.</p>
     */
    @Override
    public void increment(final double d) {
        if (incMoment) {
            moment.increment(d);
        }
    }

    
Returns the value of the statistic based on the values that have been added.
 See Skewness for the definition used in the computation.
Returns:
the skewness of the available values./**
     * Returns the value of the statistic based on the values that have been added.
     * <p>
     * See {@link Skewness} for the definition used in the computation.</p>
     *
     * @return the skewness of the available values.
     */
    @Override
    public double getResult() {

        if (moment.n < 3) {
            return Double.NaN;
        }
        double variance = moment.m2 / (moment.n - 1);
        if (variance < 10E-20) {
            return 0.0d;
        } else {
            double n0 = moment.getN();
            return  (n0 * moment.m3) /
            ((n0 - 1) * (n0 -2) * FastMath.sqrt(variance) * variance);
        }
    }

    
{@inheritDoc}
/**
     * {@inheritDoc}
     */
    public long getN() {
        return moment.getN();
    }

    
{@inheritDoc}
/**
     * {@inheritDoc}
     */
    @Override
    public void clear() {
        if (incMoment) {
            moment.clear();
        }
    }

    
Returns the Skewness of the entries in the specifed portion of the
input array.
 See Skewness for the definition used in the computation.

Throws IllegalArgumentException if the array is null.
Params:
values – the input array
begin – the index of the first array element to include
length – the number of elements to include
Throws:
MathIllegalArgumentException – if the array is null or the array index
 parameters are not valid
Returns:
the skewness of the values or Double.NaN if length is less than
3/**
     * Returns the Skewness of the entries in the specifed portion of the
     * input array.
     * <p>
     * See {@link Skewness} for the definition used in the computation.</p>
     * <p>
     * Throws <code>IllegalArgumentException</code> if the array is null.</p>
     *
     * @param values the input array
     * @param begin the index of the first array element to include
     * @param length the number of elements to include
     * @return the skewness of the values or Double.NaN if length is less than
     * 3
     * @throws MathIllegalArgumentException if the array is null or the array index
     *  parameters are not valid
     */
    @Override
    public double evaluate(final double[] values,final int begin,
            final int length) throws MathIllegalArgumentException {

        // Initialize the skewness
        double skew = Double.NaN;

        if (test(values, begin, length) && length > 2 ){
            Mean mean = new Mean();
            // Get the mean and the standard deviation
            double m = mean.evaluate(values, begin, length);

            // Calc the std, this is implemented here instead
            // of using the standardDeviation method eliminate
            // a duplicate pass to get the mean
            double accum = 0.0;
            double accum2 = 0.0;
            for (int i = begin; i < begin + length; i++) {
                final double d = values[i] - m;
                accum  += d * d;
                accum2 += d;
            }
            final double variance = (accum - (accum2 * accum2 / length)) / (length - 1);

            double accum3 = 0.0;
            for (int i = begin; i < begin + length; i++) {
                final double d = values[i] - m;
                accum3 += d * d * d;
            }
            accum3 /= variance * FastMath.sqrt(variance);

            // Get N
            double n0 = length;

            // Calculate skewness
            skew = (n0 / ((n0 - 1) * (n0 - 2))) * accum3;
        }
        return skew;
    }

    
{@inheritDoc}
/**
     * {@inheritDoc}
     */
    @Override
    public Skewness copy() {
        Skewness result = new Skewness();
        // 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 – Skewness to copy
dest – Skewness 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 Skewness to copy
     * @param dest Skewness to copy to
     * @throws NullArgumentException if either source or dest is null
     */
    public static void copy(Skewness source, Skewness dest)
        throws NullArgumentException {
        MathUtils.checkNotNull(source);
        MathUtils.checkNotNull(dest);
        dest.setData(source.getDataRef());
        dest.moment = new ThirdMoment(source.moment.copy());
        dest.incMoment = source.incMoment;
    }
}