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.stat.descriptive.AbstractStorelessUnivariateStatistic; 22 23 /** 24 * Computes the skewness of the available values. 25 * <p> 26 * We use the following (unbiased) formula to define skewness:</p> 27 * <p> 28 * skewness = [n / (n -1) (n - 2)] sum[(x_i - mean)^3] / std^3 </p> 29 * <p> 30 * where n is the number of values, mean is the {@link Mean} and std is the 31 * {@link StandardDeviation} </p> 32 * <p> 33 * <strong>Note that this implementation is not synchronized.</strong> If 34 * multiple threads access an instance of this class concurrently, and at least 35 * one of the threads invokes the <code>increment()</code> or 36 * <code>clear()</code> method, it must be synchronized externally. </p> 37 * 38 * @version $Revision: 617953 $ $Date: 2008-02-02 22:54:00 -0700 (Sat, 02 Feb 2008) $ 39 */ 40 public class Skewness extends AbstractStorelessUnivariateStatistic implements Serializable { 41 42 /** Serializable version identifier */ 43 private static final long serialVersionUID = 7101857578996691352L; 44 45 /** Third moment on which this statistic is based */ 46 protected ThirdMoment moment = null; 47 48 /** 49 * Determines whether or not this statistic can be incremented or cleared. 50 * <p> 51 * Statistics based on (constructed from) external moments cannot 52 * be incremented or cleared.</p> 53 */ 54 protected boolean incMoment; 55 56 /** 57 * Constructs a Skewness 58 */ 59 public Skewness() { 60 incMoment = true; 61 moment = new ThirdMoment(); 62 } 63 64 /** 65 * Constructs a Skewness with an external moment 66 * @param m3 external moment 67 */ 68 public Skewness(final ThirdMoment m3) { 69 incMoment = false; 70 this.moment = m3; 71 } 72 73 /** 74 * @see org.apache.commons.math.stat.descriptive.StorelessUnivariateStatistic#increment(double) 75 */ 76 public void increment(final double d) { 77 if (incMoment) { 78 moment.increment(d); 79 } 80 } 81 82 /** 83 * Returns the value of the statistic based on the values that have been added. 84 * <p> 85 * See {@link Skewness} for the definition used in the computation.</p> 86 * 87 * @return the skewness of the available values. 88 */ 89 public double getResult() { 90 91 if (moment.n < 3) { 92 return Double.NaN; 93 } 94 double variance = moment.m2 / (double) (moment.n - 1); 95 if (variance < 10E-20) { 96 return 0.0d; 97 } else { 98 double n0 = (double) moment.getN(); 99 return (n0 * moment.m3) / 100 ((n0 - 1) * (n0 -2) * Math.sqrt(variance) * variance); 101 } 102 } 103 104 /** 105 * @see org.apache.commons.math.stat.descriptive.StorelessUnivariateStatistic#getN() 106 */ 107 public long getN() { 108 return moment.getN(); 109 } 110 111 /** 112 * @see org.apache.commons.math.stat.descriptive.StorelessUnivariateStatistic#clear() 113 */ 114 public void clear() { 115 if (incMoment) { 116 moment.clear(); 117 } 118 } 119 120 /** 121 * Returns the Skewness of the entries in the specifed portion of the 122 * input array. 123 * <p> 124 * See {@link Skewness} for the definition used in the computation.</p> 125 * <p> 126 * Throws <code>IllegalArgumentException</code> if the array is null.</p> 127 * 128 * @param values the input array 129 * @param begin the index of the first array element to include 130 * @param length the number of elements to include 131 * @return the skewness of the values or Double.NaN if length is less than 132 * 3 133 * @throws IllegalArgumentException if the array is null or the array index 134 * parameters are not valid 135 */ 136 public double evaluate(final double[] values,final int begin, 137 final int length) { 138 139 // Initialize the skewness 140 double skew = Double.NaN; 141 142 if (test(values, begin, length) && length > 2 ){ 143 Mean mean = new Mean(); 144 // Get the mean and the standard deviation 145 double m = mean.evaluate(values, begin, length); 146 147 // Calc the std, this is implemented here instead 148 // of using the standardDeviation method eliminate 149 // a duplicate pass to get the mean 150 double accum = 0.0; 151 double accum2 = 0.0; 152 for (int i = begin; i < begin + length; i++) { 153 accum += Math.pow((values[i] - m), 2.0); 154 accum2 += (values[i] - m); 155 } 156 double stdDev = Math.sqrt((accum - (Math.pow(accum2, 2) / ((double) length))) / 157 (double) (length - 1)); 158 159 double accum3 = 0.0; 160 for (int i = begin; i < begin + length; i++) { 161 accum3 += Math.pow(values[i] - m, 3.0d); 162 } 163 accum3 /= Math.pow(stdDev, 3.0d); 164 165 // Get N 166 double n0 = length; 167 168 // Calculate skewness 169 skew = (n0 / ((n0 - 1) * (n0 - 2))) * accum3; 170 } 171 return skew; 172 } 173 }