Skewness.java
/*
* 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 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.core.jdkmath.JdkMath;
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 {
/** 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) * JdkMath.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 * JdkMath.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;
}
}