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# Commons Math example source code file (Kurtosis.java)

This example Commons Math source code file (Kurtosis.java) is included in the DevDaily.com "Java Source Code Warehouse" project. The intent of this project is to help you "Learn Java by Example" TM.

## Java - Commons Math tags/keywords

abstractstorelessunivariatestatistic, fourthmoment, fourthmoment, io, kurtosis, kurtosis, override, override, serializable, variance, variance

## The Commons Math Kurtosis.java source code

/*
* Licensed to the Apache Software Foundation (ASF) under one or more
* contributor license agreements.  See the NOTICE file distributed with
* 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
*
*
* Unless required by applicable law or agreed to in writing, software
* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
* See the License for the specific language governing permissions and
*/
package org.apache.commons.math.stat.descriptive.moment;

import java.io.Serializable;

import org.apache.commons.math.MathRuntimeException;
import org.apache.commons.math.stat.descriptive.AbstractStorelessUnivariateStatistic;

/**
* 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>

* 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 n < 4. * is returned when there is not sufficient data to compute the statistic.</p> * <p> * <strong>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 <code>increment() or * <code>clear() method, it must be synchronized externally.

* * @version \$Revision: 811833 \$ \$Date: 2009-09-06 12:27:50 -0400 (Sun, 06 Sep 2009) \$ */ public class Kurtosis extends AbstractStorelessUnivariateStatistic implements Serializable { /** Serializable version identifier */ private static final long serialVersionUID = 2784465764798260919L; /**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(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) { double variance = moment.m2 / (moment.n - 1); if (moment.n <= 3 || variance < 10E-20) { kurtosis = 0.0; } else { 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 if the array is null.

* * @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 Variance variance = new Variance(); variance.incrementAll(values, begin, length); double mean = variance.moment.m1; 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 double n0 = length; double coefficientOne = (n0 * (n0 + 1)) / ((n0 - 1) * (n0 - 2) * (n0 - 3)); 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() { Kurtosis result = new Kurtosis(); copy(this, result); return result; } /** * Copies source to dest. * <p>Neither source nor dest can be null.

* * @param source Kurtosis to copy * @param dest Kurtosis to copy to * @throws NullPointerException if either source or dest is null */ public static void copy(Kurtosis source, Kurtosis dest) { dest.moment = source.moment.copy(); dest.incMoment = source.incMoment; } }

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