Raymond | dee0849 | 2015-04-02 10:43:13 -0700 | [diff] [blame] | 1 | /* |
| 2 | * Licensed to the Apache Software Foundation (ASF) under one or more |
| 3 | * contributor license agreements. See the NOTICE file distributed with |
| 4 | * this work for additional information regarding copyright ownership. |
| 5 | * The ASF licenses this file to You under the Apache License, Version 2.0 |
| 6 | * (the "License"); you may not use this file except in compliance with |
| 7 | * the License. You may obtain a copy of the License at |
| 8 | * |
| 9 | * http://www.apache.org/licenses/LICENSE-2.0 |
| 10 | * |
| 11 | * Unless required by applicable law or agreed to in writing, software |
| 12 | * distributed under the License is distributed on an "AS IS" BASIS, |
| 13 | * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. |
| 14 | * See the License for the specific language governing permissions and |
| 15 | * limitations under the License. |
| 16 | */ |
| 17 | package org.apache.commons.math.stat.descriptive.moment; |
| 18 | |
| 19 | import java.io.Serializable; |
| 20 | |
| 21 | import org.apache.commons.math.MathRuntimeException; |
| 22 | import org.apache.commons.math.exception.util.LocalizedFormats; |
| 23 | import org.apache.commons.math.stat.descriptive.AbstractStorelessUnivariateStatistic; |
| 24 | import org.apache.commons.math.util.FastMath; |
| 25 | |
| 26 | |
| 27 | /** |
| 28 | * Computes the Kurtosis of the available values. |
| 29 | * <p> |
| 30 | * We use the following (unbiased) formula to define kurtosis:</p> |
| 31 | * <p> |
| 32 | * 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)] |
| 33 | * </p><p> |
| 34 | * where n is the number of values, mean is the {@link Mean} and std is the |
| 35 | * {@link StandardDeviation}</p> |
| 36 | * <p> |
| 37 | * Note that this statistic is undefined for n < 4. <code>Double.Nan</code> |
| 38 | * is returned when there is not sufficient data to compute the statistic.</p> |
| 39 | * <p> |
| 40 | * <strong>Note that this implementation is not synchronized.</strong> If |
| 41 | * multiple threads access an instance of this class concurrently, and at least |
| 42 | * one of the threads invokes the <code>increment()</code> or |
| 43 | * <code>clear()</code> method, it must be synchronized externally.</p> |
| 44 | * |
| 45 | * @version $Revision: 1006299 $ $Date: 2010-10-10 16:47:17 +0200 (dim. 10 oct. 2010) $ |
| 46 | */ |
| 47 | public class Kurtosis extends AbstractStorelessUnivariateStatistic implements Serializable { |
| 48 | |
| 49 | /** Serializable version identifier */ |
| 50 | private static final long serialVersionUID = 2784465764798260919L; |
| 51 | |
| 52 | /**Fourth Moment on which this statistic is based */ |
| 53 | protected FourthMoment moment; |
| 54 | |
| 55 | /** |
| 56 | * Determines whether or not this statistic can be incremented or cleared. |
| 57 | * <p> |
| 58 | * Statistics based on (constructed from) external moments cannot |
| 59 | * be incremented or cleared.</p> |
| 60 | */ |
| 61 | protected boolean incMoment; |
| 62 | |
| 63 | /** |
| 64 | * Construct a Kurtosis |
| 65 | */ |
| 66 | public Kurtosis() { |
| 67 | incMoment = true; |
| 68 | moment = new FourthMoment(); |
| 69 | } |
| 70 | |
| 71 | /** |
| 72 | * Construct a Kurtosis from an external moment |
| 73 | * |
| 74 | * @param m4 external Moment |
| 75 | */ |
| 76 | public Kurtosis(final FourthMoment m4) { |
| 77 | incMoment = false; |
| 78 | this.moment = m4; |
| 79 | } |
| 80 | |
| 81 | /** |
| 82 | * Copy constructor, creates a new {@code Kurtosis} identical |
| 83 | * to the {@code original} |
| 84 | * |
| 85 | * @param original the {@code Kurtosis} instance to copy |
| 86 | */ |
| 87 | public Kurtosis(Kurtosis original) { |
| 88 | copy(original, this); |
| 89 | } |
| 90 | |
| 91 | /** |
| 92 | * {@inheritDoc} |
| 93 | */ |
| 94 | @Override |
| 95 | public void increment(final double d) { |
| 96 | if (incMoment) { |
| 97 | moment.increment(d); |
| 98 | } else { |
| 99 | throw MathRuntimeException.createIllegalStateException( |
| 100 | LocalizedFormats.CANNOT_INCREMENT_STATISTIC_CONSTRUCTED_FROM_EXTERNAL_MOMENTS); |
| 101 | } |
| 102 | } |
| 103 | |
| 104 | /** |
| 105 | * {@inheritDoc} |
| 106 | */ |
| 107 | @Override |
| 108 | public double getResult() { |
| 109 | double kurtosis = Double.NaN; |
| 110 | if (moment.getN() > 3) { |
| 111 | double variance = moment.m2 / (moment.n - 1); |
| 112 | if (moment.n <= 3 || variance < 10E-20) { |
| 113 | kurtosis = 0.0; |
| 114 | } else { |
| 115 | double n = moment.n; |
| 116 | kurtosis = |
| 117 | (n * (n + 1) * moment.m4 - |
| 118 | 3 * moment.m2 * moment.m2 * (n - 1)) / |
| 119 | ((n - 1) * (n -2) * (n -3) * variance * variance); |
| 120 | } |
| 121 | } |
| 122 | return kurtosis; |
| 123 | } |
| 124 | |
| 125 | /** |
| 126 | * {@inheritDoc} |
| 127 | */ |
| 128 | @Override |
| 129 | public void clear() { |
| 130 | if (incMoment) { |
| 131 | moment.clear(); |
| 132 | } else { |
| 133 | throw MathRuntimeException.createIllegalStateException( |
| 134 | LocalizedFormats.CANNOT_CLEAR_STATISTIC_CONSTRUCTED_FROM_EXTERNAL_MOMENTS); |
| 135 | } |
| 136 | } |
| 137 | |
| 138 | /** |
| 139 | * {@inheritDoc} |
| 140 | */ |
| 141 | public long getN() { |
| 142 | return moment.getN(); |
| 143 | } |
| 144 | |
| 145 | /* UnvariateStatistic Approach */ |
| 146 | |
| 147 | /** |
| 148 | * Returns the kurtosis of the entries in the specified portion of the |
| 149 | * input array. |
| 150 | * <p> |
| 151 | * See {@link Kurtosis} for details on the computing algorithm.</p> |
| 152 | * <p> |
| 153 | * Throws <code>IllegalArgumentException</code> if the array is null.</p> |
| 154 | * |
| 155 | * @param values the input array |
| 156 | * @param begin index of the first array element to include |
| 157 | * @param length the number of elements to include |
| 158 | * @return the kurtosis of the values or Double.NaN if length is less than |
| 159 | * 4 |
| 160 | * @throws IllegalArgumentException if the input array is null or the array |
| 161 | * index parameters are not valid |
| 162 | */ |
| 163 | @Override |
| 164 | public double evaluate(final double[] values,final int begin, final int length) { |
| 165 | // Initialize the kurtosis |
| 166 | double kurt = Double.NaN; |
| 167 | |
| 168 | if (test(values, begin, length) && length > 3) { |
| 169 | |
| 170 | // Compute the mean and standard deviation |
| 171 | Variance variance = new Variance(); |
| 172 | variance.incrementAll(values, begin, length); |
| 173 | double mean = variance.moment.m1; |
| 174 | double stdDev = FastMath.sqrt(variance.getResult()); |
| 175 | |
| 176 | // Sum the ^4 of the distance from the mean divided by the |
| 177 | // standard deviation |
| 178 | double accum3 = 0.0; |
| 179 | for (int i = begin; i < begin + length; i++) { |
| 180 | accum3 += FastMath.pow(values[i] - mean, 4.0); |
| 181 | } |
| 182 | accum3 /= FastMath.pow(stdDev, 4.0d); |
| 183 | |
| 184 | // Get N |
| 185 | double n0 = length; |
| 186 | |
| 187 | double coefficientOne = |
| 188 | (n0 * (n0 + 1)) / ((n0 - 1) * (n0 - 2) * (n0 - 3)); |
| 189 | double termTwo = |
| 190 | (3 * FastMath.pow(n0 - 1, 2.0)) / ((n0 - 2) * (n0 - 3)); |
| 191 | |
| 192 | // Calculate kurtosis |
| 193 | kurt = (coefficientOne * accum3) - termTwo; |
| 194 | } |
| 195 | return kurt; |
| 196 | } |
| 197 | |
| 198 | /** |
| 199 | * {@inheritDoc} |
| 200 | */ |
| 201 | @Override |
| 202 | public Kurtosis copy() { |
| 203 | Kurtosis result = new Kurtosis(); |
| 204 | copy(this, result); |
| 205 | return result; |
| 206 | } |
| 207 | |
| 208 | /** |
| 209 | * Copies source to dest. |
| 210 | * <p>Neither source nor dest can be null.</p> |
| 211 | * |
| 212 | * @param source Kurtosis to copy |
| 213 | * @param dest Kurtosis to copy to |
| 214 | * @throws NullPointerException if either source or dest is null |
| 215 | */ |
| 216 | public static void copy(Kurtosis source, Kurtosis dest) { |
| 217 | dest.setData(source.getDataRef()); |
| 218 | dest.moment = source.moment.copy(); |
| 219 | dest.incMoment = source.incMoment; |
| 220 | } |
| 221 | |
| 222 | } |