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With inspiration from other libraries
/*
* 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.
*
* 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 statistic is undefined for n < 3. Double.Nan
* 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.
*
* 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.
*
*/
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.
*
* 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
* @throws NullArgumentException if original is null
*/
public Skewness(Skewness original) throws NullArgumentException {
copy(original, this);
}
/**
* {@inheritDoc}
* 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.
*/
@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.
*
* @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.
* Neither source nor dest can be null.
*
* @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;
}
}