/*
* 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.openejb.math.stat.descriptive.moment;
import org.apache.openejb.math.MathRuntimeException;
import org.apache.openejb.math.stat.descriptive.AbstractStorelessUnivariateStatistic;
import java.io.Serializable;
/**
* Computes the Kurtosis of the available values.
* <p>
* We use the following (unbiased) formula to define kurtosis:</p>
* <p>
* kurtosis = { [n(n+1) / (n -1)(n - 2)(n-3)] sum[(x_i - mean)^4] / std^4 } - [3(n-1)^2 / (n-2)(n-3)]
* </p><p>
* where n is the number of values, mean is the {@link Mean} and std is the
* {@link org.apache.commons.math.stat.descriptive.moment.StandardDeviation}</p>
* <p>
* Note that this statistic is undefined for n < 4. <code>Double.Nan</code>
* is returned when there is not sufficient data to compute the statistic.</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 $Revision: 811833 $ $Date: 2009-09-06 09:27:50 -0700 (Sun, 06 Sep 2009) $
*/
public class Kurtosis extends AbstractStorelessUnivariateStatistic implements Serializable {
/**
* Serializable version identifier
*/
private static final long serialVersionUID = 1234465764798260919L;
/**
* Fourth Moment on which this statistic is based
*/
protected FourthMoment 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;
/**
* Construct a Kurtosis
*/
public Kurtosis() {
incMoment = true;
moment = new FourthMoment();
}
/**
* Construct a Kurtosis from an external moment
*
* @param m4 external Moment
*/
public Kurtosis(final FourthMoment m4) {
incMoment = false;
this.moment = m4;
}
/**
* Copy constructor, creates a new {@code Kurtosis} identical
* to the {@code original}
*
* @param original the {@code Kurtosis} instance to copy
*/
public Kurtosis(final Kurtosis original) {
copy(original, this);
}
/**
* {@inheritDoc}
*/
@Override
public void increment(final double d) {
if (incMoment) {
moment.increment(d);
} else {
throw MathRuntimeException.createIllegalStateException(
"statistics constructed from external moments cannot be incremented");
}
}
/**
* {@inheritDoc}
*/
@Override
public double getResult() {
double kurtosis = Double.NaN;
if (moment.getN() > 3) {
final double variance = moment.m2 / (moment.n - 1);
if (moment.n <= 3 || variance < 10E-20) {
kurtosis = 0.0;
} else {
final double n = moment.n;
kurtosis =
(n * (n + 1) * moment.m4 -
3 * moment.m2 * moment.m2 * (n - 1)) /
((n - 1) * (n - 2) * (n - 3) * variance * variance);
}
}
return kurtosis;
}
/**
* {@inheritDoc}
*/
@Override
public void clear() {
if (incMoment) {
moment.clear();
} else {
throw MathRuntimeException.createIllegalStateException(
"statistics constructed from external moments cannot be cleared");
}
}
/**
* {@inheritDoc}
*/
public long getN() {
return moment.getN();
}
/* UnvariateStatistic Approach */
/**
* Returns the kurtosis of the entries in the specified portion of the
* input array.
* <p>
* See {@link Kurtosis} for details on the computing algorithm.</p>
* <p>
* Throws <code>IllegalArgumentException</code> if the array is null.</p>
*
* @param values the input array
* @param begin index of the first array element to include
* @param length the number of elements to include
* @return the kurtosis of the values or Double.NaN if length is less than
* 4
* @throws IllegalArgumentException if the input array is null or the array
* index parameters are not valid
*/
@Override
public double evaluate(final double[] values, final int begin, final int length) {
// Initialize the kurtosis
double kurt = Double.NaN;
if (test(values, begin, length) && length > 3) {
// Compute the mean and standard deviation
final Variance variance = new Variance();
variance.incrementAll(values, begin, length);
final double mean = variance.moment.m1;
final double stdDev = Math.sqrt(variance.getResult());
// Sum the ^4 of the distance from the mean divided by the
// standard deviation
double accum3 = 0.0;
for (int i = begin; i < begin + length; i++) {
accum3 += Math.pow(values[i] - mean, 4.0);
}
accum3 /= Math.pow(stdDev, 4.0d);
// Get N
final double n0 = length;
final double coefficientOne =
n0 * (n0 + 1) / ((n0 - 1) * (n0 - 2) * (n0 - 3));
final double termTwo =
3 * Math.pow(n0 - 1, 2.0) / ((n0 - 2) * (n0 - 3));
// Calculate kurtosis
kurt = coefficientOne * accum3 - termTwo;
}
return kurt;
}
/**
* {@inheritDoc}
*/
@Override
public Kurtosis copy() {
final Kurtosis result = new Kurtosis();
copy(this, result);
return result;
}
/**
* Copies source to dest.
* <p>Neither source nor dest can be null.</p>
*
* @param source Kurtosis to copy
* @param dest Kurtosis to copy to
* @throws NullPointerException if either source or dest is null
*/
public static void copy(final Kurtosis source, final Kurtosis dest) {
dest.moment = source.moment.copy();
dest.incMoment = source.incMoment;
}
}