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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 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> * <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: Skewness.java 1416643 2012-12-03 19:37:14Z tn $ */ public class Skewness extends AbstractStorelessUnivariateStatistic implements Serializable { /** Serializable version identifier */ private static final long serialVersionUID = 7101857578996691352L; /** Third moment on which this statistic is based */ protected ThirdMoment moment = null; /** * 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 */ public Skewness() { incMoment = true; moment = new ThirdMoment(); } /** * 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 {@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} * <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. * <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} */ public long getN() { return moment.getN(); } /** * {@inheritDoc} */ @Override public void clear() { if (incMoment) { moment.clear(); } } /** * 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} */ @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. * <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; } }