| /* |
| * 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.MathRuntimeException; |
| import org.apache.commons.math.exception.util.LocalizedFormats; |
| import org.apache.commons.math.stat.descriptive.AbstractStorelessUnivariateStatistic; |
| import org.apache.commons.math.util.FastMath; |
| |
| |
| /** |
| * 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 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: 1006299 $ $Date: 2010-10-10 16:47:17 +0200 (dim. 10 oct. 2010) $ |
| */ |
| 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( |
| LocalizedFormats.CANNOT_INCREMENT_STATISTIC_CONSTRUCTED_FROM_EXTERNAL_MOMENTS); |
| } |
| } |
| |
| /** |
| * {@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( |
| LocalizedFormats.CANNOT_CLEAR_STATISTIC_CONSTRUCTED_FROM_EXTERNAL_MOMENTS); |
| } |
| } |
| |
| /** |
| * {@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 |
| Variance variance = new Variance(); |
| variance.incrementAll(values, begin, length); |
| double mean = variance.moment.m1; |
| double stdDev = FastMath.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 += FastMath.pow(values[i] - mean, 4.0); |
| } |
| accum3 /= FastMath.pow(stdDev, 4.0d); |
| |
| // Get N |
| double n0 = length; |
| |
| double coefficientOne = |
| (n0 * (n0 + 1)) / ((n0 - 1) * (n0 - 2) * (n0 - 3)); |
| double termTwo = |
| (3 * FastMath.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.</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(Kurtosis source, Kurtosis dest) { |
| dest.setData(source.getDataRef()); |
| dest.moment = source.moment.copy(); |
| dest.incMoment = source.incMoment; |
| } |
| |
| } |