/* * 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.math.stat.descriptive.moment; import java.io.Serializable; import org.apache.commons.math.stat.descriptive.AbstractStorelessUnivariateStatistic; import org.apache.commons.math.util.FastMath; /** * Computes the skewness of the available values. *
* We use the following (unbiased) formula to define skewness:
** skewness = [n / (n -1) (n - 2)] sum[(x_i - mean)^3] / std^3
** where n is the number of values, mean is the {@link Mean} and std is the * {@link StandardDeviation}
*
* 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 increment()
or
* clear()
method, it must be synchronized externally.
* Statistics based on (constructed from) external moments cannot * be incremented or cleared.
*/ 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 */ public Skewness(Skewness original) { copy(original, this); } /** * {@inheritDoc} */ @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. ** See {@link Skewness} for the definition used in the computation.
* * @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. ** See {@link Skewness} for the definition used in the computation.
*
* Throws IllegalArgumentException
if the array is null.
Neither source nor dest can be null.
* * @param source Skewness to copy * @param dest Skewness to copy to * @throws NullPointerException if either source or dest is null */ public static void copy(Skewness source, Skewness dest) { dest.setData(source.getDataRef()); dest.moment = new ThirdMoment(source.moment.copy()); dest.incMoment = source.incMoment; } }