Kurtosis.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
*
* https://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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/*
* This is not the original file distributed by the Apache Software Foundation
* It has been modified by the Hipparchus project
*/
package org.hipparchus.stat.descriptive.moment;
import java.io.Serializable;
import org.hipparchus.exception.MathIllegalArgumentException;
import org.hipparchus.exception.NullArgumentException;
import org.hipparchus.stat.descriptive.AbstractStorelessUnivariateStatistic;
import org.hipparchus.util.FastMath;
import org.hipparchus.util.MathArrays;
import org.hipparchus.util.MathUtils;
/**
* Computes the Kurtosis of the available values.
* <p>
* We use the following (unbiased) formula to define kurtosis:
* <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>
* where n is the number of values, mean is the {@link Mean} and std is the
* {@link StandardDeviation}.
* <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>
* <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.
*/
public class Kurtosis extends AbstractStorelessUnivariateStatistic implements Serializable {
/** Serializable version identifier */
private static final long serialVersionUID = 20150412L;
/**Fourth Moment on which this statistic is based */
protected final FourthMoment moment;
/**
* Determines whether or not this statistic can be incremented or cleared.
* <p>
* Statistics based on (constructed from) external moments cannot
* be incremented or cleared.
*/
protected final boolean incMoment;
/**
* Construct a Kurtosis.
*/
public Kurtosis() {
moment = new FourthMoment();
incMoment = true;
}
/**
* Construct a Kurtosis from an external moment.
*
* @param m4 external Moment
*/
public Kurtosis(final FourthMoment m4) {
this.moment = m4;
incMoment = false;
}
/**
* 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 {
MathUtils.checkNotNull(original);
this.moment = original.moment.copy();
this.incMoment = original.incMoment;
}
/**
* {@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} */
@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} */
@Override
public void clear() {
if (incMoment) {
moment.clear();
}
}
/** {@inheritDoc} */
@Override
public long getN() {
return moment.getN();
}
/* UnvariateStatistic Approach */
/**
* 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 (MathArrays.verifyValues(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} */
@Override
public Kurtosis copy() {
return new Kurtosis(this);
}
}