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Java example source code file (Kurtosis.java)

This example Java source code file (Kurtosis.java) is included in the alvinalexander.com "Java Source Code Warehouse" project. The intent of this project is to help you "Learn Java by Example" TM.

Learn more about this Java project at its project page.

Java - Java tags/keywords

abstractstorelessunivariatestatistic, fourthmoment, kurtosis, mathillegalargumentexception, nullargumentexception, override, serializable, variance

The Kurtosis.java Java example source code

/*
 * 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.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.
 * <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>

* 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. * 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. If * multiple threads access an instance of this class concurrently, and at least * one of the threads invokes the <code>increment() or * <code>clear() method, it must be synchronized externally.

* */ public class Kurtosis extends AbstractStorelessUnivariateStatistic implements Serializable { /** Serializable version identifier */ private static final long serialVersionUID = 2784465764798260919L; /**Fourth Moment on which this statistic is based */ protected 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.</p> */ protected boolean incMoment; /** * Construct a Kurtosis */ public Kurtosis() { incMoment = true; moment = new FourthMoment(); } /** * 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 {@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} * <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} */ 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 if the array is null.

* * @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} */ @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. * <p>Neither source nor dest can be null.

* * @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; } }

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