/*
 * 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.
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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 Kurtosis of the available values.

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

 kurtosis = { [n(n+1) / (n -1)(n - 2)(n-3)] sum[(x_i - mean)^4] / std^4 } - [3(n-1)^2 / (n-2)(n-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 < 4.  Double.Nan
 is returned when there is not sufficient data to compute the statistic.
 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 the Kurtosis of the available values.
 * <p>
 * We use the following (unbiased) formula to define kurtosis:</p>
 *  <p>
 *  kurtosis = { [n(n+1) / (n -1)(n - 2)(n-3)] sum[(x_i - mean)^4] / std^4 } - [3(n-1)^2 / (n-2)(n-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 < 4.  <code>Double.Nan</code>
 *  is returned when there is not sufficient data to compute the statistic.
 *  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>
 *
 */
public class Kurtosis extends AbstractStorelessUnivariateStatistic  implements Serializable {

    
Serializable version identifier /** Serializable version identifier */
    private static final long serialVersionUID = 2784465764798260919L;

    
Fourth Moment on which this statistic is based /**Fourth Moment on which this statistic is based */
    protected FourthMoment moment;

    
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;

    
Construct a Kurtosis
/**
     * Construct a Kurtosis
     */
    public Kurtosis() {
        incMoment = true;
        moment = new FourthMoment();
    }

    
Construct a Kurtosis from an external moment
Params:
m4 – external Moment/**
     * Construct a Kurtosis from an external moment
     *
     * @param m4 external Moment
     */
    public Kurtosis(final FourthMoment m4) {
        incMoment = false;
        this.moment = m4;
    }

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

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

    
{@inheritDoc}
/**
     * {@inheritDoc}
     */
    @Override
    public double getResult() {
        double kurtosis = Double.NaN;
        if (moment.getN() > 3) {
            double variance = moment.m2 / (moment.n - 1);
                if (moment.n <= 3 || variance < 10E-20) {
                    kurtosis = 0.0;
                } else {
                    double n = moment.n;
                    kurtosis =
                        (n * (n + 1) * moment.getResult() -
                                3 * moment.m2 * moment.m2 * (n - 1)) /
                                ((n - 1) * (n -2) * (n -3) * variance * variance);
                }
        }
        return kurtosis;
    }

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

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

    /* UnvariateStatistic Approach  */

    
Returns the kurtosis of the entries in the specified portion of the
input array.
 See Kurtosis for details on the computing algorithm.

Throws IllegalArgumentException if the array is null.
Params:
values – the input array
begin – index of the first array element to include
length – the number of elements to include
Throws:
MathIllegalArgumentException – if the input array is null or the array
index parameters are not valid
Returns:
the kurtosis of the values or Double.NaN if length is less than 4/**
     * Returns the kurtosis of the entries in the specified portion of the
     * input array.
     * <p>
     * See {@link Kurtosis} for details on the computing algorithm.</p>
     * <p>
     * Throws <code>IllegalArgumentException</code> if the array is null.</p>
     *
     * @param values the input array
     * @param begin index of the first array element to include
     * @param length the number of elements to include
     * @return the kurtosis of the values or Double.NaN if length is less than 4
     * @throws MathIllegalArgumentException if the input 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 kurtosis
        double kurt = Double.NaN;

        if (test(values, begin, length) && length > 3) {

            // Compute the mean and standard deviation
            Variance variance = new Variance();
            variance.incrementAll(values, begin, length);
            double mean = variance.moment.m1;
            double stdDev = FastMath.sqrt(variance.getResult());

            // Sum the ^4 of the distance from the mean divided by the
            // standard deviation
            double accum3 = 0.0;
            for (int i = begin; i < begin + length; i++) {
                accum3 += FastMath.pow(values[i] - mean, 4.0);
            }
            accum3 /= FastMath.pow(stdDev, 4.0d);

            // Get N
            double n0 = length;

            double coefficientOne =
                (n0 * (n0 + 1)) / ((n0 - 1) * (n0 - 2) * (n0 - 3));
            double termTwo =
                (3 * FastMath.pow(n0 - 1, 2.0)) / ((n0 - 2) * (n0 - 3));

            // Calculate kurtosis
            kurt = (coefficientOne * accum3) - termTwo;
        }
        return kurt;
    }

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

    
Copies source to dest.
Neither source nor dest can be null.
Params:
source – Kurtosis to copy
dest – Kurtosis 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 Kurtosis to copy
     * @param dest Kurtosis to copy to
     * @throws NullArgumentException if either source or dest is null
     */
    public static void copy(Kurtosis source, Kurtosis dest)
        throws NullArgumentException {
        MathUtils.checkNotNull(source);
        MathUtils.checkNotNull(dest);
        dest.setData(source.getDataRef());
        dest.moment = source.moment.copy();
        dest.incMoment = source.incMoment;
    }

}