| /* |
| * 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.math4.legacy.stat.descriptive.moment; |
| |
| import java.io.Serializable; |
| |
| import org.apache.commons.math4.legacy.exception.MathIllegalArgumentException; |
| import org.apache.commons.math4.legacy.exception.NullArgumentException; |
| import org.apache.commons.math4.legacy.stat.descriptive.AbstractStorelessUnivariateStatistic; |
| import org.apache.commons.math4.legacy.core.jdkmath.AccurateMath; |
| import org.apache.commons.math4.legacy.core.MathArrays; |
| |
| /** |
| * 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> |
| * Note that this statistic is undefined for {@code n < 3}. <code>Double.Nan</code> |
| * is returned when there is not sufficient data to compute the statistic. |
| * 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 Skewness extends AbstractStorelessUnivariateStatistic implements Serializable { |
| |
| /** Serializable version identifier. */ |
| private static final long serialVersionUID = 20150412L; |
| |
| /** The value below which the variance is considered zero and thus skewness is zero. */ |
| private static final double ZERO_VARIANCE_THRESHOLD = 10E-20; |
| |
| /** Third moment on which this statistic is based. */ |
| protected ThirdMoment 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; |
| |
| /** |
| * 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 < ZERO_VARIANCE_THRESHOLD) { |
| return 0.0d; |
| } else { |
| double n0 = moment.getN(); |
| return (n0 * moment.m3) / |
| ((n0 - 1) * (n0 -2) * AccurateMath.sqrt(variance) * variance); |
| } |
| } |
| |
| /** |
| * {@inheritDoc} |
| */ |
| @Override |
| public long getN() { |
| return moment.getN(); |
| } |
| |
| /** |
| * {@inheritDoc} |
| */ |
| @Override |
| public void clear() { |
| if (incMoment) { |
| moment.clear(); |
| } |
| } |
| |
| /** |
| * Returns the Skewness of the entries in the specified 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 (MathArrays.verifyValues(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); |
| if (variance < ZERO_VARIANCE_THRESHOLD) { |
| skew = 0.0d; |
| } else { |
| double accum3 = 0.0; |
| for (int i = begin; i < begin + length; i++) { |
| final double d = values[i] - m; |
| accum3 += d * d * d; |
| } |
| accum3 /= variance * AccurateMath.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 { |
| NullArgumentException.check(source); |
| NullArgumentException.check(dest); |
| dest.moment = new ThirdMoment(source.moment.copy()); |
| dest.incMoment = source.incMoment; |
| } |
| } |
