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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 * * 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><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.</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> * * @version $Id: Kurtosis.java 1416643 2012-12-03 19:37:14Z tn $ */ 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</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} */ @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.</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; } }