1dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond/* 2dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond * Licensed to the Apache Software Foundation (ASF) under one or more 3dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond * contributor license agreements. See the NOTICE file distributed with 4dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond * this work for additional information regarding copyright ownership. 5dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond * The ASF licenses this file to You under the Apache License, Version 2.0 6dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond * (the "License"); you may not use this file except in compliance with 7dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond * the License. You may obtain a copy of the License at 8dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond * 9dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond * http://www.apache.org/licenses/LICENSE-2.0 10dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond * 11dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond * Unless required by applicable law or agreed to in writing, software 12dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond * distributed under the License is distributed on an "AS IS" BASIS, 13dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. 14dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond * See the License for the specific language governing permissions and 15dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond * limitations under the License. 16dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond */ 17dee0849a9704d532af0b550146cbafbaa6ee1d19Raymondpackage org.apache.commons.math.stat.descriptive.moment; 18dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond 19dee0849a9704d532af0b550146cbafbaa6ee1d19Raymondimport java.io.Serializable; 20dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond 21dee0849a9704d532af0b550146cbafbaa6ee1d19Raymondimport org.apache.commons.math.MathRuntimeException; 22dee0849a9704d532af0b550146cbafbaa6ee1d19Raymondimport org.apache.commons.math.exception.util.LocalizedFormats; 23dee0849a9704d532af0b550146cbafbaa6ee1d19Raymondimport org.apache.commons.math.stat.descriptive.AbstractStorelessUnivariateStatistic; 24dee0849a9704d532af0b550146cbafbaa6ee1d19Raymondimport org.apache.commons.math.util.FastMath; 25dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond 26dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond 27dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond/** 28dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond * Computes the Kurtosis of the available values. 29dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond * <p> 30dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond * We use the following (unbiased) formula to define kurtosis:</p> 31dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond * <p> 32dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond * 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)] 33dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond * </p><p> 34dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond * where n is the number of values, mean is the {@link Mean} and std is the 35dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond * {@link StandardDeviation}</p> 36dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond * <p> 37dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond * Note that this statistic is undefined for n < 4. <code>Double.Nan</code> 38dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond * is returned when there is not sufficient data to compute the statistic.</p> 39dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond * <p> 40dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond * <strong>Note that this implementation is not synchronized.</strong> If 41dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond * multiple threads access an instance of this class concurrently, and at least 42dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond * one of the threads invokes the <code>increment()</code> or 43dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond * <code>clear()</code> method, it must be synchronized externally.</p> 44dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond * 45dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond * @version $Revision: 1006299 $ $Date: 2010-10-10 16:47:17 +0200 (dim. 10 oct. 2010) $ 46dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond */ 47dee0849a9704d532af0b550146cbafbaa6ee1d19Raymondpublic class Kurtosis extends AbstractStorelessUnivariateStatistic implements Serializable { 48dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond 49dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond /** Serializable version identifier */ 50dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond private static final long serialVersionUID = 2784465764798260919L; 51dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond 52dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond /**Fourth Moment on which this statistic is based */ 53dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond protected FourthMoment moment; 54dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond 55dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond /** 56dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond * Determines whether or not this statistic can be incremented or cleared. 57dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond * <p> 58dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond * Statistics based on (constructed from) external moments cannot 59dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond * be incremented or cleared.</p> 60dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond */ 61dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond protected boolean incMoment; 62dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond 63dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond /** 64dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond * Construct a Kurtosis 65dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond */ 66dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond public Kurtosis() { 67dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond incMoment = true; 68dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond moment = new FourthMoment(); 69dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond } 70dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond 71dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond /** 72dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond * Construct a Kurtosis from an external moment 73dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond * 74dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond * @param m4 external Moment 75dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond */ 76dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond public Kurtosis(final FourthMoment m4) { 77dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond incMoment = false; 78dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond this.moment = m4; 79dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond } 80dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond 81dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond /** 82dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond * Copy constructor, creates a new {@code Kurtosis} identical 83dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond * to the {@code original} 84dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond * 85dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond * @param original the {@code Kurtosis} instance to copy 86dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond */ 87dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond public Kurtosis(Kurtosis original) { 88dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond copy(original, this); 89dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond } 90dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond 91dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond /** 92dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond * {@inheritDoc} 93dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond */ 94dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond @Override 95dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond public void increment(final double d) { 96dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond if (incMoment) { 97dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond moment.increment(d); 98dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond } else { 99dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond throw MathRuntimeException.createIllegalStateException( 100dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond LocalizedFormats.CANNOT_INCREMENT_STATISTIC_CONSTRUCTED_FROM_EXTERNAL_MOMENTS); 101dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond } 102dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond } 103dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond 104dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond /** 105dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond * {@inheritDoc} 106dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond */ 107dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond @Override 108dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond public double getResult() { 109dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond double kurtosis = Double.NaN; 110dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond if (moment.getN() > 3) { 111dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond double variance = moment.m2 / (moment.n - 1); 112dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond if (moment.n <= 3 || variance < 10E-20) { 113dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond kurtosis = 0.0; 114dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond } else { 115dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond double n = moment.n; 116dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond kurtosis = 117dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond (n * (n + 1) * moment.m4 - 118dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond 3 * moment.m2 * moment.m2 * (n - 1)) / 119dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond ((n - 1) * (n -2) * (n -3) * variance * variance); 120dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond } 121dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond } 122dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond return kurtosis; 123dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond } 124dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond 125dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond /** 126dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond * {@inheritDoc} 127dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond */ 128dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond @Override 129dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond public void clear() { 130dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond if (incMoment) { 131dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond moment.clear(); 132dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond } else { 133dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond throw MathRuntimeException.createIllegalStateException( 134dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond LocalizedFormats.CANNOT_CLEAR_STATISTIC_CONSTRUCTED_FROM_EXTERNAL_MOMENTS); 135dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond } 136dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond } 137dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond 138dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond /** 139dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond * {@inheritDoc} 140dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond */ 141dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond public long getN() { 142dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond return moment.getN(); 143dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond } 144dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond 145dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond /* UnvariateStatistic Approach */ 146dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond 147dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond /** 148dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond * Returns the kurtosis of the entries in the specified portion of the 149dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond * input array. 150dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond * <p> 151dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond * See {@link Kurtosis} for details on the computing algorithm.</p> 152dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond * <p> 153dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond * Throws <code>IllegalArgumentException</code> if the array is null.</p> 154dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond * 155dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond * @param values the input array 156dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond * @param begin index of the first array element to include 157dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond * @param length the number of elements to include 158dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond * @return the kurtosis of the values or Double.NaN if length is less than 159dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond * 4 160dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond * @throws IllegalArgumentException if the input array is null or the array 161dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond * index parameters are not valid 162dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond */ 163dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond @Override 164dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond public double evaluate(final double[] values,final int begin, final int length) { 165dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond // Initialize the kurtosis 166dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond double kurt = Double.NaN; 167dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond 168dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond if (test(values, begin, length) && length > 3) { 169dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond 170dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond // Compute the mean and standard deviation 171dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond Variance variance = new Variance(); 172dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond variance.incrementAll(values, begin, length); 173dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond double mean = variance.moment.m1; 174dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond double stdDev = FastMath.sqrt(variance.getResult()); 175dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond 176dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond // Sum the ^4 of the distance from the mean divided by the 177dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond // standard deviation 178dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond double accum3 = 0.0; 179dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond for (int i = begin; i < begin + length; i++) { 180dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond accum3 += FastMath.pow(values[i] - mean, 4.0); 181dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond } 182dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond accum3 /= FastMath.pow(stdDev, 4.0d); 183dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond 184dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond // Get N 185dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond double n0 = length; 186dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond 187dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond double coefficientOne = 188dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond (n0 * (n0 + 1)) / ((n0 - 1) * (n0 - 2) * (n0 - 3)); 189dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond double termTwo = 190dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond (3 * FastMath.pow(n0 - 1, 2.0)) / ((n0 - 2) * (n0 - 3)); 191dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond 192dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond // Calculate kurtosis 193dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond kurt = (coefficientOne * accum3) - termTwo; 194dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond } 195dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond return kurt; 196dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond } 197dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond 198dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond /** 199dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond * {@inheritDoc} 200dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond */ 201dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond @Override 202dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond public Kurtosis copy() { 203dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond Kurtosis result = new Kurtosis(); 204dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond copy(this, result); 205dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond return result; 206dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond } 207dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond 208dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond /** 209dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond * Copies source to dest. 210dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond * <p>Neither source nor dest can be null.</p> 211dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond * 212dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond * @param source Kurtosis to copy 213dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond * @param dest Kurtosis to copy to 214dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond * @throws NullPointerException if either source or dest is null 215dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond */ 216dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond public static void copy(Kurtosis source, Kurtosis dest) { 217dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond dest.setData(source.getDataRef()); 218dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond dest.moment = source.moment.copy(); 219dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond dest.incMoment = source.incMoment; 220dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond } 221dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond 222dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond} 223